MAGNETIC FIELD ASSISTED FLUIDIZATION A

MAGNETIC FIELD ASSISTED FLUIDIZATION A UNIFIED APPROACH

Part 1. Fundamentals and relevant hydrodynamics of gas-fluidized beds (batch solids mode) Jordan Hristov Department of Chemical Engineering University of Chemical Technology and Metallurgy Sofia 1756, 8 "Kliment Ohridsky", blvd, Bulgaria, e-mail: [email protected]

CONTENTS SUMMARY I. INTRODUCTION I.I.What is the magnetic field assisted fluidization I.l.Historical development- a short description 1.3. Paper idea and major goals of the review II. FUNDAMENTALS OF MFAF II. 1. Ferromagnetic materials II. 1.1. Basic properties II. 1.2. Classification of the magnetic materials II. 1.2 Temperature limitations of the magnetic properties II.2. Magnetic field generation 11.2.1. Magnetic fields generated by electric current loops 11.2.1.1. Axial fields H.2.1.2. Systems for transverse fields 11.2.2. Magnetic field effects on ferromagnetic particle suspended in a fluid 11.2.2.1. Ponderomotive forces acting on real particles with magnetic moments 11.2.2.2. Magnetic flocculation 11.2.2.3. Magnetic permeability - effects of the suspension properties

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11.2.2.4. Magnetic field effect on large non-magnetic voids in the suspension 11.3. Operating conditions of MFAF II.3.1 Magnetization modes H.3.1.1 Magnetization FIRST mode H.3.1.2. Magnetization LAST mode H.3.1.3. Magnetization On-Off 11.3.2. Solids flow through the reactor - operating modes 11.3.3. Classification - an attempt to unify the process descriptions 11.4. Basic phenomena under fluidization of magnetizable particles in a magnetic field 11.4.1. Three main scenarios 11.4.2. Homogeneous or non-homogeneous magnetic field should be applied? 111. RELEVANT HYDRODYNAM1C PROBLEMS OF GAS-SOLID MFA BEDS (BATCH SOLIDS MODE) III.l Fluidization of pure magnetic particles or magnetizable composite particles HI. 1.1. Experimental conditions - two main problems III. .2. Homogeneous magnetic fields employed (1960-1989) III. .2.1. Axial fields III. .2.2. Transverse fields III. .3. Magnetic systems employed since 1990 HI. .3.1. Axial fields HI. .3.2. Transverse fields III. .3.3. Magnetic systems for transverse rotating magnetic fields III. 1.3.4. Magnetic systems generating homogenous fields with neither axial nor transverse orientations III. 1.4. Non-homogeneous magnetic fields with axial symmetries IH.1.4.1. Short solenoids (1960- 1980) HI.4.1.1. Short solenoids employed since 1980 HI. 1.4.2. A comparison between the solenoids employed III.2. Magnetization FIRST (solids batch) of pure magnetic particles - Results HI. 2.1. Experimental findings III.2.1.1. Phenomena description by phase diagrams HI.2.1.2. Fluidization curves

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IH.2.1.3. Symbols used by Rosensweig's groups and the present review I1I.2. .4. Pressure drop at the transition points III.2. .5. Pressure drop across the bed (stabilized bed regime) III.2. .6. Short comments on the pressure drop across the bed and the energy dissipation 111.2. .7. Bed expansion III.2. .S.Hysteresis phenomena III.2. .9. Minimum fluidization (minimum bubbling) velocity III.2. .10. Velocity ranges of MFAF I1I.2. .11. Field intensity required for MFAF III.2. .12 A generalized expression for Umf III.2. .13. Time -Varying magnetic fields applications III.2. .14. Space varying (rotating) fields. 111.2.2. Results obtained in non-homogeneous fields or undefined conditions IH.2.2.1 Pressure drop curves 111.2.3. Minimum fluidization velocity IH.2.3.1. Minimum fluidization velocity-experimental findings 111.2.3.2. Minimum fluidization velocity-data correlations 111.2.4. Bed expansion 111.2.5 Short comments on the results obtained by short solenoids 111.2.6 Doctrines (and dilemmas) -comments on some conflicting interpretations IH.2.7. Delayed fluidization - a point of view 111.3. Magnetization LAST mode of pure magnetic particles or composites HI. 3.1. Observations and results till 1998 III. 3.2. Recent results HI.3.2.1. Experimental conditions required and major experimental data III. 3.2.2. Phase diagrams, pressure drop and bed collapse curves III. 3.2.3. Frozen bed -properties IH.3.2.4. Frozen bed - Minimum field intensity required III.3.2.S.Experiments in non-homogeneous fields 111.4. Generalized (Common) descriptions of magnetization FIRST and LAST Modes

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111.4.1. A brief comparison of the phenomena with the modes FIRST and LAST 111.4.2. Two macroscopic approaches in phenomena description IH.4.2.2. Pseudo-thermodynamic diagrams III.4.2.1. Order-Disorder transitions III.4.2.3. Hysteresis of the phase diagrams III. 5 "ON-OFF' magnetization mode (intermittent field) 111.5.1. Experimental findings 111.5.2. Remarks on On-Off magnetization mode III.6. Pressure drop pulsations (pure magnetic particles) and bubbles 111.6.1 Pressure drop pulsations - first results and macroscopic observations 111.6.2 Pressure drop pulsations - more deep studies III.6.2.1. Pressure noise analysis and a phase diagram reconstruction IH.6.2.2. Specific frequency III. 6.2.3. Bed stability analysis III6.3. Bubbles IH.6.3.1. Does the field affect the phenomenon? ΠΙ.6.3.2. Bubble size- different techniques give different results IV. GAS-SOLIDS FLUIDIZATION (SOLIDS BATCH MODE) OF ADMIXTURES (MAGNETIC AND NON-MAGNETIC PARTICLES) IV. 1. Way admixture beds? IV.2. Basic idea IV.3. Magnetization FIRST mode IV.3.1 .Results - axial field I V.3.1.1 .Compositions employed IV.3.1.2.MSB onset and minimum fluidization velocity I V.3.1.3 .Pressure drop IV.3.1.4. Bed stability lV.3.2.Results - Transverse field I V.3.3. Data correlations I V.3.3.1. Data correlations -Axial fields IV.3.3.2. Data correlations - a more deep analysis IV.3.3.3.Data correlations -treatments of Saxena's group the data IV.4 Magnetization LAST IV.5. Comments on gas-fluidized admixture beds

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V. MAGNETIC FIELD ASSISTED FLUIDIZATION OF COHESIVE POWDERS V.l. Vibrating beds V.2. Fluidization of admixtures in an axial field. V.3. Fluidization of admixtures in a transverse rotating field VI. FINAL COMMENTS SYMBOLS REFERENCES

SUMMARY This review discusses the fundamentals of magnetic field assisted fluidization and relevant hydrodynamics problems of gas fluidized beds with a batch solids mode. The data treatment and the analysis of the phenomena published in various sources over 40 years since 1960 till the beginning of 2000 have been discussed from a unified point of view. The analysis done and the data collection allows a balance to be struck of that attractive fluidization technique at the beginning of the third millennium

I. INTRODUCTION I.l.What is the magnetic field assisted fluidization The wide application of fluidized beds (mainly gas-solids systems) in the industry is accompanied with an undesirable gas bypass in the form of large voids known as "bubbles" (Kunii and Levenspiel, 1989). An attractive method to eliminate the bubbles is to create a homogenous fluidization due to induced interparticle forces by means of external fields acting on the solids. Taking into account the well-known properties of the magnetic field action of ferromagnetic materials and the electric field on dielectrics (Katz and Sears, 1969; Johnson and Melcher, 1975; Colver and Bosshart, 1980;Moissis and Zahn, 1988) two principal branches have been developed: • Fluidization of ferromagnetic particles in an external magnetic field Magnetic Field Assisted Fluidization (MFAF) • Fluidization of dielectrics in an electric field - Electric Field Assisted Fluidization (EFAF)

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Both approaches consider a fluidization due to the fluid passing up the particle bed, while the external field acts on the solids only (mainly by the induction of attractive forces of cohesion). The field itself does not cause particle fluidization. Because of that the term "field assisted" is used here. However, when the field produces strong body forces and causes particle motions inside the fluidization volume without the help of the liquid (low fluid velocities or a stagnant fluid) the process is termed "Magnetic Driven Fluidization" (MDF). Neither term has been used in the literature and in many cases these types of fluidization have not been separated. The introduction of the terms in the present review has as its goal the better understanding of the phenomena in fluidized beds under the action of external fields.

1.2. Historical development- a short description

Forty years ago (1960-1962) Kirko and Filippov (1960) and Filippov (1961a, 1961b, 1962) applied a magnetic field generated by a solenoid (the field lines are parallel to the fluid flow) on a liquid fluidized iron cylinders and gas-fluidized magnetite. At the same time Nekrassov and Chekin (1961,1962) performed the first investigations in an alternating field oriented normally to the fluidizing flow. Both groups in Russia created a new branch of the fluidization technique that has been under intensive investigations over 40 years. The schematic presentations of these historical experimental setups are shown in Fig. 1. Katz and Sears (1969) studied the stabilization effect of an axial magnetic field on iron particle bed and of a transverse electric field on dielectric particles (glass and silica gel). Sonolikar et al. (1972) reported that the minimum fluidization velocity of an iron powder bed increases parallel to the increase of the field intensity applied. Further, the possibility of the external field to hold up the ferromagnetic phase in the vessel volume at fluid velocities significantly greater than the minimum fluidization velocity has been applied by Ivanov and Grozev (1970a, 1970b)) for conversion of CO and ammonia synthesis. At the same time Ivanov and Zrunchev (1969), Zrunchev (1970, 1975a, 1975b) and Zrunchev and Popova (1975) started laboratory experiments on enhanced ammonia synthesis with iron based catalyst under the action of a steady field. Shumkov and Ivanov (1970, 1974) and Shumkov et al. (1975) developed the hydrodynamics of magnetically controlled fluidized bed of ferromagnetic

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(c) Fig. 1:

The experimental set-ups of the creators of magnetic field assisted fiuidization a) Gas fluidized beds in an axial field (Filippov, 1961b): E - a periscope. b) Liquid fluidized bed in an axial field (Filippov, 196la; Kirko and Filippov, 1960); S- a periscope; K- column; NI and N2 pressure drop tubes. c) Nekrassov and Chekin (1961) - magnetic field distribution between the poles of the electromagnet employed. d) Nekrassov and Chekin (1961,1962) - a schematic presentation of the experimental set up (present author illustration in accordance with the description in Nekrassov and Chekin (1961).

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ammonia catalysts. The main idea of all these investigations performed in Bulgaria was oriented toward the creation of a large reactor for ammonia synthesis. In 1975 Ivanov (1975) and Ivanov et al (1975) reported plant investigations of such a reactor. A patent was invented earlier (Ivanov et al. 1969). Bologa and Syutkin (1977) published the first review on the MFAF. The paper collected all the data available and focussed on the problems challenging further investigations. Parallel to the hydrodynamic studies the heat transfer in magnetically controlled fluidized beds was investigated by various research groups. Zabrodsky and Tambovtsev (1976) and Bologa and Syutkin (1976) published the first investigations on heat transfer with immersed surfaces. Neff and Rubinsky (1983), Arnaldos (1985), and Amaldos et al. (1986,1987) further developed the problem. Recently the group of Saxena (1994) has published a number of studies on heat transfer in MFA beds. Reviews of all these studies are developed in Part 3 of the present series. Since 1979 a significant breakthrough in magnetic field assisted fluidization has been made by Rosensweig's group in Exxon (Lucchessi et al, 1979, Rosensweig, 1979). A series of systematic studies have been carried out by Rosensweig et al. (1981a,1981b), Siegell (1982,1987,1988), Lee (1984), Siegell and Coulaloglou (1984a, 1984b) toward many technological applications (Rosensweig, 1980,1983; Siegell, 1984; Siegell and Coulaloglou, 1985; Siegell et al. 1985,1986) Jaraiz (1983), Jaraiz et al (1983;1984a,1984b), Zhang et α/.(1984), Davis and Levenspiel (1985), Jaraiz and Estevez (1987) have originated countercurrent gas-solids contactors magnetic valves for solids as a separate branch of MFAF (a special part of the series is arranged). The features of the fluidized beds with MFAF have been applied successfully for biotechnological applications (Burns and Graves, 1985, 1987; Terranova and Burns, Bramble et al, 1990) and aerosol filtration (Albert and Tien, 1985;Warrior and Tien, 1986; Geuzens and Thoenes, 1988). Since 1990-1991 a series of studies have appeared on hydrodynamics in axial fields (Penchev and Hristov, 1990a), transverse fields (Penchev and Hristov, 1990b; Cental et al. 1992; Cental, 1994; Hristov, 1998b), aerosol filtration (Cohen and Tien, 1991; Hristov et al., 1992), high velocity magnetically semifluidized beds (Hristov, 1998a) fluidization of admixtures (Navada and Saxena, 1997; Wu et al, 1997a, 1997b; Saxena and Wu, 1999; Hristov et al, 2000). Bioreactors with immobilized cells and enzymes have

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been developed successfully (Moffat et al., 1994,1995; Ivanova et al, 1996; Webb et al. 1996, Hristov and Ivanova, 1999). A new branch that is under intensive investigations is the three-phase (gas-liquid-solid) fluidization (Wang et al., Kwauk, et al., 1992; Sajc et al 1996a; Hristov and Hadzissavas, 1997; Thomson and Worden, 1997; Pesic, 1992 ). This paper tries to arrange the data on gas-solid fluidization (batch solids mode) obtained during almost the entire development of the MFAF technique since the pioneering work of Filippov (196la, 1961b, and 1962) up to the beginning of 2000. The unified approach applied here allows a great deal of data and results dispersed in various sources and written in different languages to be collated. The data obtained and the interpretation of different research groups in various periods of time (over 40 years) are discussed.. Recently a series on some particular problems of gas- fluidization has appeared (Hristov, 1998c; Hristov (1999a,b). These papers initiated the unified approach developed here. Part 1 covers almost all the fundamental problems of the MFAF with batch solids mode. The magnetization modes, flow of solids through the reactor volume, type of solids subjected to fluidization and the field configuration effects on the fluidized bed performance are discussed. The paper starts with a section "Fundamentrals of MFAF' including different data on magnetism and magnetic field generations. The magnetic materials and the magnetic system employed are the major tool of that fluidization technique. The possibilities of creating a field with a desired topology are discussed in contrast to all the previous reviews. The unified approach in the paper separates the results obtained by various authors on the basis of the field applied and the magnetization modes. The line drawn in the Fundamentals allows easy interpretations of results obtained by various research groups over 40 years (1960-2000).

II. FUNDAMENTALS OF MFAF ILL Ferromagnetic materials II.1.1. Basic properties The magnetic permeability of the ferromagnetic materials depends on the intensity of the external magnetic field. Moreover, they exhibit a remanent magnetization when the field is turned-off. The magnetic susceptibility of the materials is a function of the field intensity applied, while the relationship M 303

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= f (H)- Fig.2a. The magnetization M reaches its limit at the value of magnetization at saturation Ms under sufficiently higher field intensities H. The relationship between B and H (Fig.2b) is

(1) The cyclic changes of the field direction result in a hysteresis curve shown in Fig. 2c. The field induction Br (inside the material) at zero external fields is termed a remanent induction, Br. The ratio

B

=

(2)

is termed a relative magnetic permeability μΓ demonstrating a maximum with variations of the field intensity. (Fig.2d). For ferromagnetic materials μΓ = ΙΟ3

Β

Μ Ms

0

0

H (b)

(a)

ο (c) Fig.2.:

304

H

(d)

Basic characteristics of ferromagnetic materials. a) Magnetization at saturation b) Magnetization curve c) Hysteresis cycle d) Variations of the magnetic permeability with the field intensity.

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11.1.2. Classification of the magnetic materials The ferromagnetic materials may be divided into two major groups. • Magnetically soft materials. They are ferromagnetic materials with high magnetic permeabilities. It is easy to magnetize them by steady and alternating magnetic fields. Moreover, the coercivity He (see Fig. 2c) is low. Most of the materials discussed here belongs to that group. • Magnetically hard materials. They have relatively low magnetic permeabilities. It is very hard to magnetize them, but they exhibit significant values of the remanent induction Br and the coercivity He. The magnetic hard materials are the bases of the permanent magnets. Several investigations (see for example Coulaloglou, 1979) have been performed with fluidized permanently magnetic particles. II. 1.2 Temperature limitation of the magnetic properties. The spontaneous magnetization of the ferromagnetic materials reduces with the increasing temperature. They lose their magnetic properties at the so-called Curie point (Tk). At higher temperature the materials exhibit paramagnetic properties. Some data relevant to the problems discussed in the present paper are summarized in Table 1 and Fig. 3.

Table 1 Magnetic properties of some materials employed in MFAF Material

Ms,A/m Th-C

Fe Co Ni

1.72. 10* 770 1.51.10* 1121 4.84. 105 358 4.74. 105 563-590

FejO« Monel 400 Fe-Ni(46%Ni) Maghemite ( γΡβζΟ3) Fc-Co (50% Co)

316-333 733 858 998

Reference Heck (1973);Tikadzumi (1983) Heck (1973);Tikadzumi (1983L Heck (1973);Tikadzumi (1983) Heck (1973);Tikadzumi (1983) Rosensweig(1980) Arnaldos et al.(1983) Arnaldos et al.(1983) Arnaldos et al.(1983) Arnaldos et al.(1983)

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I

6

123 4

fL 4 x

CO

ι -200

0 200 400

T,°C Fig. 3:

Temperature relationships of Ms for some ferromagnetic materials and compositions Adapted from Smith and Wein (1962): 1- FeO. Fe2O3; 2 - Mn. Fe2O3;3 -Ni 0.35 Zn 0.65. Fe2O3; 4- Mn O.s Zn „.5. Fe203.

II.2. Magnetic field generation The magnetic field employed in MFAF is an important tool for the process. The field is applied independently of the gas flow on the magnetic materials under fluidization. It is important to know the characteristics of the magnetic systems employed. In the earlier investigations (mainly performed by the group of Ivanov) the characteristics of the magnetic systems employed and their effects on the fluidization have been neglected. In 1990 Penchev and Hristov (1990a) pointed out that the results obtained by different research groups cannot be compared directly due to strong inequalities of the conditions imposed by the magnetic systems. This opinion was discussed by Liu et al. (1991) as an important fact focussing on the problem concerning the field topology and homogeneity. The recent studies of Contal et al, (1998) and Wu and Saxena (1997b) have reported details concerning the magnetic system employed that allow easy comparison of the results. The next sub-section will describe briefly the technical facilities allowing generations of various magnetic fields. II.2.1. Magnetic fields generated by electric current loops 11.2.1.1. Axial fields The induction of a magnetic field generated by an electric current I passing though an electric wire is

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The magnetic flux lines are circular lines lying in a plane perpendicular to the current. The superposition of the magnetic fields of many currents may be employed for a magnetic field generation over a desired volume. Such magnetic systems will be discussed below in order to elucidate the technical facilities available for creation of a magnetic field with desired topology and orientation. System generating homogeneous magnetic fields only will be discussed. The effect of the field non-homogeneity on MFAF will be discussed further in the paper. The generations of homogeneous magnetic field by a system of electric currents employ the principle of superposition. Several currents distributed in the space generate independent fields, but their vector summation over a desired volume gives a homogeneous field. The principle may be realized in practice by several technical devices: a) Long solenoids (Fig. 4a). Theoretically, the field non-homogeneity less than 1% along the solenoid axis may be obtained if Ls/Ds > 3. However, in practice this ratio should be > 6 in order to assure such nonhomogeneity over the entire solenoid volume. This hinders the applications of long solenoids in large-scale applications (for example MFAF). b) Solenoid with compensating coils (Fig.4b,c). There are several constructions of such short solenoids with compensating coils (Montgomery, 1969). The design allows generation of a homogenous field with easy control of the working volume (inside the solenoid) thus overcoming the problems hindering the application of long solenoids. For example Filippov has employed such a solenoid (See Fig.l a, b) in his pioneering investigations. c) Systems of short coils (Fig. Sa) These magnetic systems generate strong axial magnetic fields. • The Helmholtz pair (Garret, 1967) shown in Fig.Sa has been employed in many investigations with MFAF (see for example Rosensweig, 1979, 1980; Penchev and Hristov, 1990a; Wu et al, 1997a, 1997b; Saxena and Shrivastava, 1990, 1991). Two square coils may create the Helmholtz pair too. Such a system has been employed by Hristov (1996) (see further )

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.. .4- - — . .

I I (a)

Fig. 4:

•

(b)

Solenoids generating homogeneous axial magnetic fields a) Long solenoid; b) Solenoid with compensating coils (Girard and Sauzade, 1964) c) Solenoid with compensating coils (Montgomery, 1969).

The Maxwell system (Fig. 5b) (Garret, 1967) consists of coils located on a surface of a sphere. The system allows the generation of threedimensional homogenous fields. • Barcker's systems (Garret, 1967) consist of coils with equal radii placed on a common cylindrical surface. The system is an alternative to the Helmholtz pair and the solenoids with compensating coils in the cases of large working volumes desired. Such systems have been employed by some investigators in China (see for example Kwauk et al. (1992)) and recently Hausmann et al. (2000).

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(a) I

a2

(d) Fig. 5:

t[

(c)

Magnetic system generating homogeneous axial magnetic fields (Hristov, 1994) a) Heimholte pair; b) Maxwell system; c) Garretsystem d) Barcker system;

•

Garret's systems (Garret, 1967) employ short coils separated in two sections. Each section consists of coils located in one plane. The employment of the system has not been detected in the literature concerning MFAF. However, it is an alternative to Helmholtz pairs and solenoids with compensations in the case of small laboratory units. All the systems generating axial fields by means of solenoids or short coils have a common disadvantage: the diameter of the central zone (with a homogenous field distribution) does not exceed 30 % of the internal solenoid

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volume. The field intensity increases toward the windings that causes strong lateral field non-homogeneity. The working volume for MFAF should not exceed this zone in order to assure a homogeneous magnetic field. The effects of the field non-homogeneity of short solenoids employed by several authors (Ivanov's group, for example) will be discussed in a separate section. 11.2.1.2. Systems for transverse fields A system based on flat poles of electromagnet with an iron yoke (Fig.6a) - it is easy to build-up in a laboratory scale only. The non-homogeneity of PERMANENT MAGNETS ELECTROMAGNETS WITH IRON YOKES

COIL

YOKE

COIlT

YOKE

(a) z

k

\ \

χ

-f (b) Fig. 6:

310

(c)

Magnetic system for a transverse field generation. a) Magnetic systems based on iron yoke electromagnets and permanent magnets. b) Saddle coils design- Basic idea. Adapted from Laverick, (1967) c) Saddle coils system conceived for MFAF by Penchev and Hristov(1990b).

.Ionian Uristov


the field in a lateral direction (clearly seen on the picture of Nekrassov and Chekin- Fig Ic) imposes limits similar to those discussed for axial magnetic systems. Moreover, the amount of iron needed for such an electromagnet increases significantly with the enlargement of the air gap between the poles. These facts hinder the application of transverse field systems for large-scale applications. Some laboratory studies will be discussed further. Does an alternative to the electromagnets with iron details exist? Yes, the solenoids and the short coils generating axial fields have their counterparts systems generating a field transverse to the symmetry line of the working volume based on saddle coils. The basic idea of saddle shaped coils is shown in Fig.9b. The saddle coils use the same idea, already illustrated on Fig.oa. The saddle coils are widely applied in magnetohydrodynamic power generation (Laverick, 1967). Penchev and Hristov (1990b) have conceived saddle coils for MFAF purposes (Fig. 6b) based on the optimal design proposed by Ginsberg and Melchner (1970). The principle advantage of the saddle shaped coils is the fact that the field non-homogeneity at r/R = 0.9 (i.e. close to the windings) does not exceed 5 %, thus offering large possibilities for applications in MFAF devices (see further). 11.2.2. Magnetic field effects on ferromagnetic particle suspended in a fluid The fluidized beds controlled by an external magnetic field are two or three-phase systems with particles suspended in a fluid. Because of this, a brief description of the basic phenomena would help further discussion. 11.2.2.1. Ponderomotive forces acting on real particles with magnetic moments The body forces acting on a magnetizable particle placed in an external magnetic field are (Tamm, 1970)

or its component along the co-ordinate x, for example

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However, the above relationships do not take into account the effect of the medium density on its magnetic susceptibility. The problem is of great importance for the disperse systems fluidized in external field (MFAF) because the variation of the particle concentration affects their magnetic susceptibilities. According to Tamm (1970) the real reason for the occurrence of the ponderomotive forces may be explained by the Heimholte stress tensor (Tc) (expressed along the axis χ for example: T

cxx =TCYy =TC = — Η ρ— 2 dp

(6)

where ρ is the density of the magnetic medium. The Heimholte tensor affects the distribution of the ponderomotive forces over the volume of the ferromagnetic body, because their vector sum is zero or is compensated by the hydrostatic pressure of the surrounding fluid

P-^H'pfi 2

(7)

dp

The system of stresses acting on the ferromagnetic body may be divided into Forces of strain along the direction of the field lines

and

Pressure (tension) in a direction transverse to the field lines. (8b)

This component is the reason for the magnetic particle flocculation phenomenon (see below). For example, if two magnetic particles are in contact the surface forces of attraction between them are

B2

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(9)

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-mH Fig. 7:

^Λ

A mechanical moment of rotation (a) and a force of tension (b) acting on an elongated particle in a magnetic field. Adapted from Tikadzumi(1983).

A field applied on real particles (Tikadzumi, 1983) acts on them by a moment of rotation (Fig. 7a) Mmcch=-[m.H]

(lOa)

and a ponderomotive force (Fig. 7b) F M =-V[m.H]

(lOb)

where m denotes the particle magnetic moment. 11.2.2.2. Magneticflocculation In systems consisting of magnetic particles suspended in a fluid the above defined forces result in particle aggregation known as "magnetic flocculation" (Laurila, 1959). The flocculation is a physical phenomenon that follows from the tendency of a magnetic mass to minimize its volume (a potential energy) in the presence of an external magnetic field (Earnshaw's theorem) (see for example Weinstock ,1976). The density of the magnetic aggregates ("flocks", "strings") depends on the particle packing and affects their magnetic permeabilities. The aggregate density changes with increasing field intensity due to increasing forces of tension and pressure - Eqs (8). The resulting form of the particle aggregates is an ellipsoid of revolution extended along the field lines. The mechanical strength of the aggregates depends on the intensity of the field applied and the process of aggregate formation. According to Karmazin and Karmazin (1984) the force of tension applied to aggregates of magnetite particle may reach 3.104 Pa (per unit cross-section of the aggregate) for H< 128 kA/m, while in a transverse direction the flocks are very fragile. 313

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11.2.2.3. Magnetic permeability - effects of the suspension properties The concentration of the ferromagnetic particles is important from several points of view: • The fluidization behaviour under fluidization • The particle-particle interaction and the field effect on the gross bed behaviour under MFAF • The bed of suspended particles is a magnetic medium with an effective susceptibility depending both on the concentration and the properties of the particles. The effective magnetic permeability of a fluidized bed in a magnetic field μι, has been studied by Filippov (1961s). His results with 230 μηι magnetite and ferrite particles (Fig. 8a) in alternative axial field (50Hz) demonstrated that in the range of relative bed expansion ratio hb/hbo= l-s-1.5 the effective bed permeability μεί{ -(25+3)μ0. The upper values belong to the fixed bed state (~2.9)and H - 8 k A / m . Filippov (1961c) pointed out that the magnetic permeability of the particle material does not significantly affect the effective permeability of the suspension. The increase of pb with increased gas velocity is attributed to the formation of elongated aggregates along the field lines (fluid flow) despite the reduction of the effective particle . dp = 714 Microns

13

5δ 10" 9 α: UJ

α. 100 H[oe]

0£6

0.70

0.74

0.78

0.82

POROSITY, ε (a) Fig. 8:

314

(b)

Magnetic permeability of M FA fluidized beds a) Air-magnetite Filippov (1961c) (redrawn and adapted without data labels) b) Variations of the bed permeability with the porosity (i.e. the concentration of the magnetic phase - mild steel powder) Adapted from Sonolikar(1989).

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concentration. The earlier results of Grigoriev and Kirko (1956) have demonstrated the magnetic permeability of admixture of magnetic and non-magnetic particles varies in the range of με{Γ - (ΐ+12)μ0 in the case of iron cylinders (μ= 167 Mo)andX v ? =50% vol. Sonolikar (1974) measured μι, for a gas-fluidized bed of several magnetic particulates: mild steel (164-714 μηι), nickel powder (164 - 504 μηι) and magnetic steel powder (164-504 μηι) in the range of Η up to 8 kA/m (like that of Filippov). Sonolikar's results shown in Fig.Sb indicate that the value of μι, increases with the particle diameter, while the porosity effect is just the opposite - contradicting the results of Filippov (1961c). Rosensweig et al (1981 b) have decided that the value of μι is independent of the particle size in the range of 74-h2000 μηι. Rosensweig's results confirm those of Sonolikar with respect to the μ\, variations with the bed porosity. Rosensweig suggested the following correlations for bed permeability: Parallel model

(1 la)

J U L _ e + -£-(L

μο

μο

Series model

μο

μ

(lib)

μ(ΐ-ε) Cavity model 1-ε

μο

(lie)

μ-ι The model of Rosensweig has been developed for spherical particles. The particle shape (or aggregate shape) and orientation in the bed structure affect the magnetic susceptibility of the suspension. Figure 9 illustrates these effects together with the concentration influence on the susceptibility χ.

315


Vol. 18, Nos. 4-5, 2002

0

Fig. 9:

0.2 0.4 0.6 0.8 VM λ ν

Effect of the volumetric concentration of the ferromagnetic particles and their shapes and orientations on the bed volumetric susceptibility. Adapted (redrawn and arranged with the present nomenclature by the present author) from Karmazin and Karmazin (1984). 1- axially oriented elongated particles; 2- spherical particles; 3- transversally oriented elongated particles.

11.2.2.4. Magnetic field effect on large non-magnetic voids in the suspension The problem considered in this subsection is directly related to the fluidization of coarse particles. Large voids usually emerge in fluidized beds of normally fluidizable particles (Geldart's Β group). The idea persisting for more than 20 years (since the studies of Rosensweig) is that the external field applied suppresses bubbling. The problem will be considered in a special section later, but for now the physical base will be commented upon briefly. According to Jones et al. (1987) in the case of cubical particle packing the cohesion forces induced by the external field acting on a surface area a2 of the cavity (fracture plane - Fig. 10) are:

PM 4πμ0

316

H-transversel H-axial

(12a)

Jordan Hristov


where if

-Μ--μ0(μ-ΐ)Η

n C - — u ιι I 4π °^

(12b)

|H-transveise| -0.96H-axiaI

(12c)

Here Η-axial and Η-transverse correspond to the orientation of the field intensity vector with respect to fracture plane.

POWDER

FRACTURE

SURFACE STRESS

Fig. 10: Cohesive stresses acting on a void in a magnetizable medium. A scheme used by Jones et al. (1987) for development of Eqs. (12)

11.3. Operating conditions of MFAF The definition of the operating conditions follows the unified approach of the paper. Some of these definitions have been employed earlier (magnetization modes) while the other ones (the solid flow modes) have not been discussed previously. The systematization of the operating modes has the unique goal of the better understanding and comparisons of the results obtained by various authors. As reported earlier by Hristov (1999) the people working with biotechnological applications did not define the operating conditions in a sense already established in the hydrodynamic studies. Moreover, in the cases of heat transfer studies (Part 3) most of the hydrodynamic conditions are also not clear. The classifications of the operating modes done here do permit to recover and reconstruct the conditions in almost all the cases of MFAF.

317

Vol. 18, Nos. 4-5, 2002


11.3.1 Magnetization modes The classical fluidized bed is a two-phase system with an intensive movement of dispersed solids. The balance of the forces acting upon particles determines the behaviour of fluidized bed systems: gravitational forces, fluid/particle drag forces and friction forces between the particles (Yates, 1983; Kunii and Levenspiel, 1991). The fluid flow and the magnetic field may be applied independently, so two principal magnetization modes are possible. II. 3.1.1 Magnetization FIRST mode The mode involves the application of the field on a fixed bed and fluidization after that. Siegel (1987) has introduced the term. With this mode, the fluidization and the bed structures formed as the flow rate increases, arise under the simultaneous action of gravitational forces, friction forces (fluid/particle and interparticle friction) and the external field. The starting state is ordinary fixed bed. In this case the interparticle forces play a much more important role than the fluid/particle interaction. Most previous works on the fluidization behaviour of ferromagnetic particles in a magnetic field have been performed by the "Magnetization FIRST" mode (Rosensweig, 1979; Kirko and Filippov, 1960; Casal, 1982; Arnaldos, 1986; Penchev and Hristov, 1990a, 1900b; Saxena and Shrivastava, 19090, 1991; Cental, 1994). The main attraction of this operating mode is "the magnetically stabilized bed" (MSB) (see further). 77.3.7.2. Magnetization LAST mode The second mode involves the application of the field on a preliminarily fluidized bed. The structure of an already fluidized bed depends on the type of the fluidizing agent (gas or liquid), its velocity and the particle size. Filippov (196la, 1962 was the first to apply the "Magnetization LAST" mode on a liquid/solid system. He called it "sedimentation" of the bed under the influence of a magnetic field. Later Bologa and Syutkin (1977) and Siegel (1982,1987) have studied this mode. Siegel (1982) reported that the increase of field intensity led to a bed collapse and defined three principal states of the bed: random motion regime, roll-cell regime and stabilized bed. Comprehensive reviews of previous studies and new experimental data were reported recently by Hristov (1998, 1999a).

318

Jordan Hrislov

Revi&vs in Chemical Engineering

11.3.1.3. Magnetization On-Off(or intermittent magnetization) The former magnetization modes consider a continuous action of the field on the solids despite the type of the field - steady state or alternating (time varying). The On-Off magnetization mode has not been defined in such a manner in the literature. Some authors (Kamholtz, 1979; Levenspiel and Kamholtz, 1981) have applied an intermittent magnetization in order to avoid particle aggregation and temperature gradients in magnetically stabilized beds. Recently (Hristov, 2000a) this magnetization mode has been discussed at large in the case of heat transfer in MFA fluidized beds. It will be discussed in detail in Part 3 of the present series. Despite this, it would be better to note that the On-Off mode has not been investigated from a hydrodynamic point of view like the two former modes. Some scarce data are available dispersed in various sources. They will be reviewed and discussed in order to elucidate the effect of this type of magnetization and its potential for further applications.

77.5.2. Solids flow through the reactor - operating modes This problem has not been discussed in the literature like the order of actions in the previous subsection. Thus the following definitions focus on that problem in order to classify the possible situations. The information available in the literature indicates that there are two operating modes with respect to the flow of solids through the reactor volume. 1. Solids Batch - there is an amount of solids charged in the reactor. After the process ends, they may be removed or not for the next step of regeneration. In this case the solids and fluid flow may be arranged as a liquid upflow through a stabilized or a fluidized bed. It has been well investigated at large with ferromagnetic solids from a hydrodynamic point of view. Moreover, this is a classical operating mode in the fluidized bed technology. Solids Batch operations are also applicable to particles beds of admixtures of magnetic particles and non-magnetic biosupports. Under the action of the magnetic field the magnetizable particles form a matrix that entraps the non-magnetic beads immobilizing them. The mixture bed is fixed and suitable for various adsorption/desorption separations. The studies concerning such gas-fluidized beds will be discussed in detail in the present paper. 319

Vol. 18, Nos. 4-5, 2002

Magnetic Field Assisted Fluidi=alionA Unified Approach

•

Solids FIRST mode. The solids start to fill the column before the action of the fluidizing flow and the magnetic field. Magnetization FIRST or Magnetization LAST fluidization modes may follow this operation. In both cases the desired (from a technological point of view - biotechnology applications for example) (Hristov, 1999c) state is the magnetically stabilized bed (MSB) or the frozen bed (see further the comments on the basic phenomena in MFAF). • Solids LAST mode. This approach is opposite. Usually the particles are introduced into the column from the top. The fluid may start to flow through the working volume accompanied (Magnetization FIRST) or not (Magnetization LAST) by the action of the external magnetic field. The solids flow into the reactor is under the action of the fluid flow that causes fluidization (liquid upflow) or fixed bed formation (liquid downflow). The former situation corresponds to particle-liquid cocurrent downflow, while the second to particle-liquid countercurrentflow. 2. Moving Solids (or Moving Beds) - there is a continuous particle flow through the reactor. There are three modes that may be created: •

Particle-fluid cocurrent upflow against the gravity forces (gas or liquid as a fluid phase) or particle-liquid downflow. • Particle-fluid cocurrent downflow toward the action of the net forces (usually by liquid as a fluid). • Particle- fluid countercurrent flow (liquid upflow). The creation of moving beds is possible with the all the magnetization modes - Magnetization FIRST, Magnetization LAST and On-Off mode. II.3.3. Classifications - an attempt to unify the process descriptions The following nomenclature in operating mode description shows the viewpoint of the author, so it is under discussion and further developments. The nomenclature created concerns only the combination of the solids flow modes and the Fluidization (Magnetization Modes) described in Figs. 11 and 12. In accordance with this nomenclature the type of solids flow is general and it predetermines the following actions of the fluid flow and the magnetic field. The author's experience and the data published on bed hydrodynamics (Rosensweig, 1979; Siegel, 1987; Hristov, 1996, 1998b, 1998c; Penchev and Hristov, 1990) indicate that these phenomena are general. The nomenclature does not describe the three-phase (G-L-S) MFA beds. A specific

320

Jordan Hristov


MAGNETIZATION FIRST MODE

MAGNETIZATION LAST MODE

1 SOLIDS 1

n

ION

COLUMN Γ

IT

η

1 FLOW 1

1 FIELD

Η

FROZEN BED (SublUzedbtd)

1

Fig. 11 Operating mode».

FIRST and Magnetization LAST and Solids How mod» Schematized presentations of the Older of actions on the solids and bed formation. Hristov (I999c) Hristov and Ivanova (1999)

MAGNETIZATION FIRST MODE STABILIZED BED

1 FIELD

1 FLOW

1 SOLIDS

K

| COLUMN 1=3!

l

MAGNETIZATION LAST MODE

FLUIDIZATION I—;,

FROZEN BED (Stabilized bed)

1 |

(This mode correspond! to SOLIDS FIRST- MAG NETIZATION LAST)

Fig. 11:

Magnetization modes - Magnetization FIRST and Magnetization LAST. A combined diagram with the SOLIDS flow modes (Hristov, 1999c, Hristov and Ivanova, 1999).

321

Vol. 18, Nos. 4-5, 2002

1 SOLIDS

MAGNETIZATION ON-OFF

FIELD ON |

1

n


•If1 '

1 COLUMN Γ =5J PARTICLE ft 1 FLOW 1

·

FROZEN BED

BED 1

-it

'

FIELD OFF

1

FLUDIZEDBED

\

Fig. 12 On-Off magnetization mode and Solid» flow model Schematized pmenutiom of the older of actions oa the tolids and bed formation.

MAGNETIZATION OlÔFF 1 FLOW 1

COLUMN

I

SOLIDS

\ FIELDON 1 I 1 "* _ Frozen bed (or movugfrozenbed) ^. ^p =5 Solid» BATCH nuldfa»ao» or Moving BED

t FIELD OFF

"~Cr-~| Fhiidizedbed(or ordinary moving bed ) j

Fig. 12: Operating modes. A schematized definition of Magnetization ONOFF and Magnetization LAST mode together with the SOLIDS flow modes.

classification for such beds has been conceived by Hristov and Hadzisavvas, 1997). Figure 13 shows the formation of the abbreviations for some situations (conceived in Hristov (1999c) and developed here). The idea of the present classifications is to allow easy comparisons of the experimental results obtained by different authors. It is not dogmatic and may be developed or changed for better process description.

322

Jordan Hristov

A.-pure magnetics or magnetizable omposiles


of magnetizable particles and active non-magnetic solids

Continuous process

Magnetic \alves far Solids OR

Magneiic OistribuiorDowncomers

Fig. 13 A classification of the operating modes and abbreviation formations.

Fig. 13:

A structured scheme of process performance as a certain combination of the operating modes and abbreviation formations (conceived by Hristov, 1999c and developed here).

Π.4. Basic phenomena under fluidization of magnetizable particles in a magnetic field 11.4.1. Two main scenarios The main effect of an external magnetic field on a granular ferromagnetic medium under the fluidization is based on the following facts:

323

Vol. 18, Nos. 4-5, 2002

Magnetic Field Assisted FluidizalionA Unified Approach

•

First - A magnetically soft (concerned as default particle material hereafter) particle under an external magnetic field is an induced permanent magnet. The effect disappears (low remanent magnetization) when the field is turned off.

•

Second - In the case of great number of particles (Fig. 14) there are two main scenarios concerning the field effects (the Solids BATCH-Solids FIRST mode is described as an example):

1) Scenario 1. The action of the field on particles free suspended in a fluid (i.e. ordinary fluidized bed) (Magnetization LAST). Two consequent phenomena are provoked by the field.: a) First - There is a polarization of each particles followed by particleparticle interactions (magnetic flocculation commented earlier) described by the Coulomb magnetic law (see Eq. (9) (Tamm, 1970; Laurila, 1959). As an effect of this the particles aggregate in elongated "strings" (Fig.l4b). Their anisotropic shapes are results of the forces of strain and the tension (Eqs. Sa-Sb) extending them (forces of strain) along the field lines (Laurila, 1959). b) Second. The ferromagnetic masses (i.e. the particles and strings) will coagulate down to a formation of a large aggregate (in accordance with the Eamshaw theorem (Weinstocks, 1976)) that immobilizes the particles. This state (i.e., the formation of a large particle aggregate under strong fields with Magnetization LAST) is known as "Frozen bed" (Siegell, 1987; Hristov, 1997) or "Condensed bed" (Kwauk et al, 1992) . 2) Scenario 2. In a fixed bed (Magnetization FIRST mode) the magnetic forces superpose the native interparticle forces (cohesion, van der Waals, etc) and may be considered as a magnetic cohesion (Jones et al, 1987). Under fluidization the particle arrangement is unchanged up to the point where the drag forces start to destroy the interparticle contacts. At this moment the particle rearrangement begins - the point of incipient bed expansion. The particles slip and roll and there are no suspending in the fluid flow due to strong magnetic forces of attraction preventing it. The bed structure changes toward anisotropic particle packing defined by the field orientation. However, these changes are not out of control, because at a particular fluid flow the positions of the particles are fixed and there are no "mixing motions" (Rosensweig et al, 198la) The rearrangement stops when the drag forces

324

Jordan Hrislov


Field direction

Forces of attraction

Forces of strain

Moment of rotation

Fig. 14:

r

Field effects on magnetizable particles suspended in a fluid flow (Hristov, 1998c). By courtesy of Thermal Science. a) Magnetization LAST b) Forces acting on particle aggregates ("strings")

overcome the magnetic forces and the particle suspension starts. In accordance with the classical fluidization terminology this is the fluidization onset (Davidson and Harrison, 1963; Yates,1983; Kunii and Levenspiel, 1991) Note 1: At zero field intensity the force balance in a static bed depends on the native cohesion and the gravity. At a particular fluid velocity the drag forces dominate over the interparticle ones and the bed reaches the minimum fluidization point. Note 2: In the case of additional magnetic interparticle attraction the drag forces must be greater than those at zero field corresponding to the minimum fluidization velocity. In this way the state of bed internal rearrangement (i.e. the development of the incipient bed expansion without unrestricted particle motions) may be controlled over a desired velocity range by application of different field intensities.

325

Vol. 18, Nos. 4-5, 2002


The phenomenon described in Scenario 2 is the magnetic stabilization (Rosensweig, 1979). The description given here is general and independent of the field orientation and homogeneity and the type of the fluidizing fluid (gas or liquid or gas-liquid flow). The fields applied by various authors and the technical requirements about magnetic systems and fields generated will be discussed below. 11.4.2. Should a homogeneous or non-homogeneous magnetic field be applied? The magnetic field assisted fluidization (MFAF) is a way to increase the efficiency of various solid-fluid contactors for mass and heat transfer operations. From the description above it is clear that every magnetic field producing significant interparticle forces may cause control on the particle mobility and arranges the bed in magnetically stabilized or magnetically frozen bed in accordance with the scenario applied: •

If the field has a strong non-homogeneity, preferably in a lateral direction Λ// (i.e. the column radius) significant body forces « H occur (see Eqs. dr

(4)-(5)). They pull the suspended particles (Magnetization LAST mode for example) toward the windings (or the poles) of the magnetic system (see Fig. 1 and Figs.4-6) and they adhere on the column wall. • The non- homogeneous fields produce non- homogeneous distributions of the magnetic interparticle forces inside the granular medium (Magnetization FIRST mode), which are in proportion of s(\iH)2 (see Eq.(9)). When the fluid flow starts to flow up, the common effects (after a narrow regime of magnetic stabilization) are the formation of a central channel (the particles are grouped at the vessel wall) and a poor fluidization.

Note: Therefore, the non-homogeneous field leads to nonhomogeneous distribution of the particles over the fluidization vessel and decreases the efficiency of the fluid-particle contacts. This is the reason for large use of homogeneous fields (see also the comments in the next section) despite the fact that from a physical point of view any field may act in accordance to both scenarios described above.

326

Jordan Hristov


III. RELEVANT HYDRODYNAMIC PROBLEMS GAS-SOLID MFA BEDS WITH THE BASIC MAGNETIZATION MODES BATCH SOLIDS MODE

III.l Fluidization of pure magnetic particles or magnetizable composite particles III.l. L Experimental conditions - two main problems Solids used. The investigations of MFAF have been developed mainly on the basis of pure magnetic particles. The use of admixtures of magnetic and non-magnetic particles is a rather new idea (Rosensweig, 1980a), 1980b) and will be reviewed further. The fundamentals of the MFAF hydrodynamics and the basic terms and definitions have been established with gas-fluidized beds consisting totally of magnetizable particles (iron, magnetite, nickel, or magnetic composites). Therefore, the review on the relevant hydrodynamic problems starts with such beds. Table 2 contains the main data concerning the conditions of the principal investigations performed during the last 40 years (1960-2000). Almost all the materials employed in these fundamental studies belong to Geldart's group B (Geldart, 1973); thus they are "normally" fluidizable with a bubbling onset just beyond the minimum fluidization point (Yates, 1983; Kunii and Levenspiel, 1991). The investigations on the fluidization of cohesive (in the absence of a field) magnetic particle have been developed recently and will be discussed in a separate section of the paper. Magnetic fields applied. An important problem not-discussed in all the reviews published since Bologa and Syutkin (19976) is the effect of the magnetic field topology on the results. The problem is discussed here from a position considering the effects of the magnetic system design on the experimental results obtained by various authors. The magnetic systems employed by various groups of researchers will be reviewed shortly in order to define their basic properties and further effects on the fluidization phenomena. Ten years ago Penchev and Hristov (1990a, 1990b) have published comprehensive data about the magnetic systems and the experimental situations applied during a period of 30 years (1960-1990) Figures IS and 16 reproduce that information. According to the analysis done by Penchev and Hristov (1990a) the magnetic systems can be divided into three major groups: • Magnetic system generating homogenous axial fields • Magnetic systems generating non-homogenous axial fields. • Magnetic systems for transverse fields 327

Vol. 18, Nos. 4-5, 2002


Table 2 Pure magnetic particles and magnetizable composite employed in studies of MFAF - major details Reference

Material

Fraction, urn

Fibppov (196U) (1961b)(l961c)

Magnetite

9-12

C

230-300

B

Nckrossov und Chekin(196l) (1962) Doichevetal (1965) Ivoitov Una Grazcv (1970a) (1970b)

Magnetite

53- 1680

Magnetite sand Ni-Cr Catalyst

Sonolikar (1972) (1974) Bologa and Syutkin (1977)

Ivanovand Shoumkov (1976)

Shoumkov (1975) Shoumkov and Ivanov(1974) Ivanovand Znmchev(1969) Zrunchev (1975a) (1975b) Luccheactal. (1979) Rosenswag (1979)(1980a) (1980b) Rosenswag et aL (1981a) Siegel! (1982)

Geuzens(1985)

328

Gddarfs Group

Value

Source· Pcnchevand Hristov(1990a)

A-B

100

No data

400-500

B

40

477.46

400-500 600-750

B

30

No data

Iron Powder

24.4-603

Iron shots

0-40; 40-60; 60-90 90-160. 160-200; 200-250 250-500 13-250 250-750

Cover A andC groups A

1687

78

No data

30 140

No data

80; 150; 300 500

No data

B

800-1000

D

130-250 250-500 630-750

B

Penchevand Hnstov(1990a)

No data

177-180

B

7

Composite beads Sted spheres

300 480 177-180

B B B

76

Steel spheres Magnetite

Penchevand Hristov(l990a)

B

Ammonia catalyst Ammonia catalyst SA-1 (Russia) Sled spheres

Magnetite

Ms,kA/m

477.46

B-D D

Monel

in. nun

31 84

750-1000 1000-2000

Fe-Cr Catalyst And Ammonia catalyst SA-1 (Russia) Ammonia catalyst SA-1 (Russia)

De. mm

No data

177-250 159-177 250-297 100-125 180-250 850-1000 120-210 210-420 420470

No data

B B

76.2

B-D B

152.4

150; 200

477.46

Penchevand Hnstov(1990a)

Jordan Hristov


Table 2 Pure magnetic particles and magnetizable composite employed in studies of MFAF- major details (continued) Reference

Material

Caul (1982)

Nickel

Amaldos (1986X Amaldoseatal (1996. 1987)

Iron

Penchevand Hristov (1990a) (1990b)

Ammonia catalyst

Magnetite Hristov (1996) Hristov (1998)

Iron Invar Metal, dross

Fraction. urn

Geldarfs Group

De. mm

120-177 177-250 297-400 400-500

Β

51

250-120 420-500 Narrow fractions d^lOOum d__=800tim

Β

Narrow fractions dpn^lOOum 100-200 200-315

Saxenaand Shrivastava (1990) Saxenaand Shnvastava (1991) Saxenaet al.(1994) SaxenaandWu (1999) Zimmdsetal (1991 Cental (1994) Cental et al (1992) (1998) Saijcetal (1992) Lin and Leu (1994)(1996) JovanoncetaL (1987)(1989) (1996)

65

Ms. ItAAn Value (Source 485.42 Penchevand Hristov (1990a)

65 100 130

23634

47746 Β

168704 Β

381.97 Β

Narrow fractions d^_=80oZ

Giidler catalyst

Narrow fractions

Sled spheres

α_=400μιη 125-355 d„,=262 μπι

Iron shots

262. 624,

rya \JJLr

Β

N. mm

**pMI

5650 Β

50.133

1 W |U11

1687.04

101.6 D D

101.6

1416

Β B-D D

Fc/polycstcr Composite (2700 kg/m3) Iron

231

Β

89

7

?

700-1000

D

90

88

1687.04

Composite (4050 kg/m3) Iron

320

110

210-250 d_>230um 240(320)

50

90

1687.04

Β

110

160 (100)

7

630

Β

624; 733-.1511;

Faroe (4560 kg/m3) Composite (1710 kg/m3)

Penchevand Hnstov (1990a)

101.6

Penchevand Hristov (1990s)

?

Penchevand Hristov (1990a)

280

329

Vol. 18. Nos. 4-5, 2002


III. 1.2. Homogeneous magnetic fields employed (1960-1989) III. 1.2.1. Axial fields The magnetic systems (Fig. 15) used for more than three decades have been built up on the basis of solenoids (long or short) generating axial magnetic fields (i.e. parallel to the fluid flow). The basic constructions were commented on earlier (II.2). As noted by Penchev and Hristov (1990a) the

335 •i"'.. i"f V:

(Ο Fig. 15:

330

(g)

(h)

Experimental situations in studies performed till 1989. From Penchev and Hristov (1990a) - Adapted and developed a) Kirko and Filippov (I960), Filippov (1961a, 1961b, 1961c) - a solenoid with a compensation; b) Ivanov and Grozev (1970b> a short solenoid; c) Doichev et al. 1965)- a short solenoid; d) Sonolikar et al. (1972) - long solenoid; e) Ivanov and Shumkov (1976)- short solenoids; f) Shumkov (1975) - short solenoids; g) Rosensweig (1979, 1980a,), Rosensweig et al. (1981a)Helmholtz coils h) Casal J (1982) and Arnaldos (1986), Amaldos et al, 1986, 1987) -a moderate length solenoid.

Jordan Hristov


magnetic system creating homogeneous field has been employed by Filippov (1961a, 1961b, 19161c) and Kirko and Filippov (1960), Sonolikar et al. (1972), Rosensweig (1979, 1980a) and Casal (1982), Amaldos (1986) and Arnaldos et al. (1986, 1987), Geuzens (1985), Geuzens and Thoenes (1988) . III. 1.2.2. Transverse fields In contrast to the applications of axial fields, the use of transverse fields (Fig. 16) has not been so popular among the investigators. Probably one of the reasons is the use of magnetic systems based on electromagnets that contain iron details (Nekrassov and Chekin 1961,1962; Katz and Sear, 1969; Zrunchev, 1970). Rosensweig made an attempt to use a magnetic system based on permanent magnets. All of these magnetic systems have significant disadvantages discussed earlier (see the basic designs in 11.2.1.2). This limits the use of such electromagnets for laboratory use only. Moreover, the required amounts of iron and the weights of such electromagnets are terrible. The second and more important disadvantage is the strong non-uniformity

D

ΔΡ

(a) Fig. 16:

(b) Experimental situations concerning the applications of transverse fields till 1989. Adapted and developed from Penchev and Hristov (1990b) a) Nekrassov and Chekin (1961,1962)- electromagnet (see also Fig. Id) b) Zrunchev (1970); Ivanov and Zrunchev (1970)- (electromagnets with flat poles) (see also Fig. 6a) c) Rosensweig (1980a) - permanent magnets

331

Vol. 18, Nos. 4-5, 2002

Magnetic Field Assisted Fluidi:alion.4 Unified Approach

along the lateral symmetry axis, i.e. from the centre of the gap toward the pole as commented earlier. Both disadvantages, the first one caused by the uneconomical use of materials and the small working volume, and the second one due to principal problems of the lateral magnetic gradients, hindered the applications of transverse field for many years. III. 1.3. Magnetic systems employed since 1990 III. 1.3.1. Axial fields The axial homogeneous fields employed since 1990 (Table 3) have been generated by: • Helmholtz coils (Penchev and Hristov, 1990a; Hristov, 1996; Hristov, 1998; Lin and Leu, 1994, 1996; Saxena et al. 1994; Saxena and Wu, 1999) • Solenoids (Ushiki et al. 1991; Sajc et al., 1992, 1996; Jovanovic et al., 1996) Figure 17 presents the systems employed by Saxena's group (Saxena and Shrivastava, 1991; Wu et al., 1997a, 1997b). • Barcker type magnetic systems (see Fig. 5c) employed by Zhu and Li (1994, 1996a, 1996b) are shown in Fig. 18. A similar magnetic system has been used by Zimmels et al. (1991) and Lin and Leu (1996). It is important to note the more professional use of magnetic systems generating homogeneous field in the recent investigations, or in other words the "era of solenoids" disappears. The Helmholtz coils and Barcker systems create axial fields in larger volumes than the solenoids and assure easy control of the working volume due the significant gaps between the coils. ///. /. 3.2. Transverse fields A) "Saddle" - shaped coils Ten years ago (1990) an attempt to overcome the problems of the transverse field magnetic systems commented above has been done by Penchev and Hristov (1990b). The application of saddle shaped coils (See also Fig. 6c) has offered a new trend toward the build-up of large-scale devices due to three principal advantages: • The zone with a homogeneous field may reach about 98% of the volume inside the windings and • The reduced amounts of a copper wire with respect the requirements of the axial magnetic systems). • The field orientation does not allow a channelling in the bed. The saddle coils have been employed successfully for studies on 332

Jordan Hristav


preliminarily gas-fluidized beds (Hristov, 1998) B) Permanent magnets • Permanent magnets have been employed in the further studies of Contal et al (1994, 1996, 1998). Figure 19 illustrates the experimental conditions created by such magnetic system (Contal, 1994).

Table3 Magnetic system employed and principal experiments performed major details Reference

Magncue system

Solenoid dimensions, mm

Filippov (I96la) (I96lb)(l96lc)

Shon solenoid with a compensation

L-250 D-170

DC. mm

D/Dc

Major expenments performed (mode)

84

2.02

• •

Bed expansion Pressure drop (FIRST)

100

No data

• •

Pressure drop (FIRST) Bed effective Viscosity (FIRST)

Axial symmetry non-homogeneous

40

No data

• •

Bed expansion (LAST) Pressure drop (LAST)

Axial symmetry

30

4

•

Minimum fluidization velocity (FIRST) Bed expansion (FIRST)

Field. kA/m Axial homogeneous

9.6- 12 Nckrassovand Chckm(196l) (1962)

Stator

Doichevctal (1965)

Shon solenoid

Ivanovaml Grozcv( 1970s) (I970b)

Shon solenoid

Sonolikar (1972) (1974)

Long solenoid

Ivanovand Shoumkov (1976)

Poles height- 300 mm D-nodata Lundcfined D-90mm D =120 mm L- 130 mm

•

Shon solenoids

Shoumkov (1975) Shoumkov and lvanov(1974) Lucchesi el al. Hclmholtz (1979) coils

D» DC

L-Dc

No data

Rosenswag (1979)(l980a) (1980b) Roscnswcig ct al. (I98la) Roscnsweig (I980a) Siegcll (1982)

HeJmhollz coils

Pemunenl magnets Hehnholtz coils

See Fig. 16c

Casal (1982)

Solenoid

Amaldos(l986), Amaldoscatal (19%. 1987)

Transverse rotating homogenous

See fig. 15g

30 140

Axial Homogeneous 0-6 kA/m Axial Homogeneous

80; 150; 300 500 No data

»1

•

»1.1

• •

• • •

No data

• • •

76

2.0

• • •

ι·1*

See Fig. I5g

Transverse 45 kA/m Axial Homogeneous

L-245 D-120

Axial Homogeneous

51

•

16c 76.2

• • •

2.35

• • • •

Minimum fluidizauon velocity (FIRST) Minimum fluidization velocity (FIRST) Bubble frequency Bubble size Bed parameters effect onUmf Porosity distributions Transition velocity (onset of fluidization) Pressure drop (FIRST) Transition velocity (onset of fluidization) Pressure drop Solids discharge (FIRST) Transition velocity (onset of fluidization) Velocity profiles Axial gas distribution (FIRST A LAST) Transition velocity (onset of fluidizarion) Pressuredrop Bed porosity Bed hysteresis behaviour (FIRST)

333


Vol. 18, Nos. 4-5, 2002

Table 3 Magnetic system employed and principal experiments performed major details (continued) Reference

Magnetic system

Gcuzou(l985)

Solenoid

Penchcvand HnMov (!990aXI998)

Hdmholtz coils

ID - 200

(I990b)(1998)

Saddle coils

ID »200 L = 400

Hristov(1996)

Square Heimholt: coils

Solenoid dimensions, mm L-800 D-450

T=ield, kA/m Axial Homogeneous

Axial

DC. mm 152

D/Dc

Major experiments performed (mode)

2.%

•

65

3.07

Transition velocity (onset of fluidiialion) Pressure drop Axial and radial gas distribution Stabilization onset Bed expansion Fluidization onset Particle materials (magnetic ) properties effects

•

Field orientation effects on the bed stabilization and bed expansion Pressure drop

Transverse

Saxenaand Shnvastava (1990) (1991) Saxenaet al.(1994) SaxenaandWu (1999)

Helmholtz coils

Zimmdsetal (1991)

Barcker system

500x500 mm

See Fig. 17

lD=l80mm

3.07

Various orientations From axial to transverse

50

10 •

Axial

101.6

352

• • *

Pressure drop Porosity variations Field effect on minimum fluidization velocity

Axial

89

2022

•

Pressure drop hysteresis phenomena Bed hysterics behaviour in accordance with Uw magnetization mode Pressure drop Bed expansion Minimum fluidization velocity Pressure drop Bed expansion Minimum fluidization velocity Bubble frequency Bubble size Pressure drop Bed expansion Minimum fluidization velocity Voidage distribution

0-72 kA/m 6 coils

Cental (1994) Cental et al (1992) (1998)

Permanent magnets

Saijc et al (1992)

Solenoid)

•

See Fig. 19

L= 330 mm D-l.l DC

Jovanovic et al. (1987) (1989) (1996) Lin and Leu (19%)

Transverse

90

-

• • •

no

I.I DC

• • •

0-50 kA/m

Axial 0-IOkA/m

Η^/ί2.06

and Barcker system 5 coils

ID- 226 mm

Axial 0-3 kA/m

50

1.17 3.22

• • • • • •

334

Jordan Hrislov


0.076m 0.171m

Support

0.076m

Fig. 17:

Heimholte coils employed by Saxena's group. Basic design (Wu et al., 1997b)

DMnbutor

Fig. 18:

Backer type magnetic system for axial fields a) Magnetic systems employed by Zhu and Li (1994,1996). Adapted from (Zhu and Li, 1994). b) Magnetic system of Zimmels et al. (1991) c) Magnetic system of Lin and Leu (1994, 1996)

335

Vol. 18, Nos. 4-5, 2002

(a)

Magnetic Field Assisted FluidlzationA Unified Approach

(b)

Fig. 19: Magnetic system generating a transverse magnetic field by permanent magnets. Adapted from Cental (1994). a) Space location of the magnets and the column b) Field topology. A determination of the homogeneous field zone. ///. L 3.3. Magnetic systems far transverse rotating magnetic fields The magnetic systems (both for axial and transverse fields) commented above (III.2.1-2.4) generate field that do not change it is orientation in the space. Nekrassov and Chekin (1961, 1962) (see Fig.Id) have employed a rotating transverse field generated by three-pole stator of an electric motor (50Hz AC current supply). The system has not been employed more 40 years. Recently Lu and Li (2000) applied similar inductors for fluidization of cohesive admixtures of magnetic and non -magnetic particles (see the special section further). HI.1.3.4. Magnetic systems generating homogenous fields with neither axial nor transverse orientations A system of square Helmholtz coils (Fig.20) supported by a non-magnetic frame (allowing a rotation around its lateral axis) has been conceived by Hristov (19%). The system permits easy change of the field orientation to a desired angle with respect to the column axis (fluid flow direction). Moreover, the swing allows the inclination of the column axis too.

336

Jordan Hristov


10 Fig 20:

Square Heimholte coils (Hristov, 1996) generating homogeneous fields with various directions: A- support; B- column; C- magnetic system; D-measuring scale; E-a swing for the column support; Inset- the definition of the angle between the column axis (fluid flow) and the Held lines)

III.L4. Non-homogeneous magnetic fields with axial symmetries III. 1.4.1. Short solenoids (1960- 1980) The non-homogeneous fields generated mainly by short solenoids need special attention. In all the previous reviews the results obtained with these devices have been discussed together with those from homogeneous magnetic fields. The group of Ivanov, in contrast to the other investigators (from Western Europe and America), has employed non-homogeneous fields with axial symmetries (Fig. 15, b, e, f,). Hristov (1994) has calculated the field distributions in the solenoids employed by Grozev and Shumkov (Fig. 2la) by a computer code created on the basis of the methodology described by Montgomery (1969). Figure 21a clearly indicates the non-homogeneous field distributions of both the axial (Hz) and radial (Hr) field vector components.

337

Vol. 18, Nos. 4-5, 2002

Magnetic Field Assisted FluidtationA Unified Approach

(a) 14

SONOUKAR (·Κ·3Μ>*

1.2J

i.o ~. 0.8

CASA_L_ ARN ALDOS 2
···ι*ΐ·

Comments Field VI—

-

ΡΌΐΧΗΙΙΠΙΐΜΒ

(am)

No symbol

The bed resembles like that in the axial field

Rosaatmg (19tO>) No comments

Hristov Symbol Unfluulized bed

Comments TheimoalBxedbedat UU. notfluidized.Λ transitional stale before the fluidizabon onset (PoKkamdHristm (199») U_

(U_,-H)

The fluidization starts with bobbles at raedtum field intensities. At higher U the next stale is a slugging Λ

' ^'_^ΛΪ^^

llUHliZ31IO" atl^^ffy

M . .... no investigations U^-lfc NocomnKntl

No investigations U, No comments (Rg.27c)

Us CFig.27c)

(PaKkaautHriam (19901,). The iiiiiuiiioii depends m the magnetic particle properties and the field intensity (PatchniaidHriam UV there is no gas bubbles. The fluidized dements are the particle aggregates (sUingsX but not separate particles (PaidmmdHrilla* (199H>).VcHKm. they are respect the gas flow ffmdiamiHiian (199») The bed is shifted into this regime at IWJ^C-IW (PaKkamd Kristin (199»)

(15b)

359

Vol. 18, Nos. 4-5, 2002


2.0 — A»BH»C.H2 A*BH

1.8

• -IRON SPHERES A-IRON POWDER

1.6

2.2

1.4 CL

2 kA/m 1.0

6.8. ΙΟ'5

R2= 0.003 (61 data points)

1.0 Catalyst ICI35/8, No data LIO" Ms-366kAAn R2= 0.002 (58 data points) 200-315 μm The calculations were performed at a confidential interval of 0.95. The field intensity Η is in A/m.

Eq. (15b) are summarized in Table 8. The data listed indicate the major influence of the magnetic properties of the particles represented by the magnetization at saturation Ms. The experiments performed by Hristov (1994) indicate two main facts supported by the results commented above: 1) The pressure drop required for the initial bed deformation and its transition into the regime of MSB increase parallel to field intensity. The tendency is independent of the field lines orientation. The effect becomes stronger as the field direction changes from axial toward transversal. The ratio —, ^ does not exceed 1.15 for materials exhibiting values of AP(Umfo) Ms in the range of 200- 300 kA/m. For materials such as Fe, Ni, Fe3O4 and ammonia catalyst the ration may reach a value of 2 (see the data ο Hamby and Liu (1991) -Fig. 37a). Under the action of high axial field intensities the ratio —

e

' . has

363

Vol. 18, Nos. 4-5, 2002


lower values than under the action of low fields (Fig. 38a.)- The fact has been confirmed by the behaviour of all the materials investigated by Hristov (1994). It may be attributed to the increased "magnetic cohesion" and the action of the forces of tension and strain (see Eq. (8)) acting on the whole bed: • The increased "magnetic cohesion" needs greater gas pressure (and a consequent pressure drop across the bed) to destroy the interparticle contacts as a first step of the bed body deformation. • Moreover, the Heimholte stress tensor (see Eqs. (7) and (8) ) tends to extend the beds as a whole along the filed lines and to compress it in a lateral direction. With the increase of the angle α from 0° toward 90° (see Fig. 39c) the lateral component (oriented perpendicular to the gas flow) increases, while the vertical (axial) component decreases at a constant field intensity H. As a result, the actions of the compression along the bed vertical axis and the extension along its radius lead to a more compact particle packing. A macroscopic fact confirming these magnetic field actions on the granular bed is the change of the pressure drop at U=Ue shown on Fig. 39c. This mechanism has been mentioned by Penchev and Hristov (1990a, 1990b) and Hristov (1996). 2) The pressure drop at U=Ue is always lower than the ratio G/S . The ratio approaches the value of 1 at higher field intensities and almost

(f) transverse field orientation (see comments below). ii) Fluidization onset: The pressure drop at the fluidization onset (U= Umf, denoted also as Ub and UT) has not been discussed in the literature. As mentioned, the studies till 1990 did not comment on the fluidized state and all the efforts were focussed on the stabilized regime. The results obtained in the last decade of the century make it possible to clarify the problem. The fluidization curves demonstrated earlier (Figs. 31, 32, 33, 34, 35,36) indicate that the pressure drop at U=Umf is always lower than the average pressure drop across the bed (in the regime of MSB) and the value of AP(Ue) as well. Figures 39 (a, b, c) show three examples supporting the above conclusion. As the particle arrangement in the bed becomes more transversally oriented with respect to the fluid flow, the expanded structure of MSB is looser due to repulsive forces between the strings (Hristov, 1996) (see also Fig. 14). A

364

Jordan Hristov

D^ 0_


1.0 .8 .6 .4 .2

H, kA/m 10

15

20

2S

I

*

t

β

Μ)

^»^ 0D

7000 ^ b-

./

T

50

5000

ΐ

/l

40

l

/ l

4000

[FKlidizalion

3000

1 \ MSBonsd

30 •

20 10

Χ" 1

»· L

•^--ί - 70 5739 cm H20 . 6920.9353 (Pa| 6000

Fig. 40

367

Vol. 18, Nos. 4-5, 2002

Fig.40:


Pressure drops across MSB in axial fields. Data from various sources contradicting the Filippov's postulation. a) Rosensweig's data (1908b). Air - steel spheres C 1018 (177250μιη), G= 3.110 kg. Present author graphical presentation (first publication). Original data- Table XVI of Rosensweig (1980b). b) Rosensweig's data (1908b). Pressure drop variations with the field intensity H. From Hristov (1994) (first publication here). DatafromFig. 46a presented as two ratios —--^^ (· ΔΡ0 the left ordinate) and —* „

AV

' (A - the right ordinate).

c) Rosensweig's data (1908b). Air - steel spheres C 1018 (177250 μπι), G = 2.970 kg. H= 48 Oe. Present author graphical presentation (Hristov, 1998c). Original data - Table XIX of Rosensweig (1980b). d) Pressure drop versus the relative bed expansion, E at different field intensities. Velocity range: Uel < U < \Jc2. From Hristov (1998c). Metallurgical dross (200-315 μηι), hbo= 65 mm. H, kA/m: B-0; Ο -8.5; A -20; · -30; · - 42. Note: The same figure has been published by Penchev and Hristov (1990a) without the dashed line and the labels.

Saxena et al. (1994) have reported that (see Fig. 41c) AP(MSB)Av has decreased by about 15 % at U= 0.7 m/s and H= 0- 19.575 kA/m. On the other hand at U> Umf (i.e. U> Ue) the variation of AP(MSB)AV has been a bit involved. According to Saxena et al. (1994) the quantitative variations have been affected by the value of H (see the inset of Fig. 41c). The pressure drop curves on Fig.41d indicate that the value of AP(MSB)AV is greater than the scale defined by G/S. On the other hand Cohen and Tien (1991) have mentioned that AP(MSB)AV ~ 0.8 (G/S) due to channelling in the bed. The pressure drop curves of Cental (1994) presented on Figs. 41a,b demonstrate that in a transverse field AP(MSB)AV > AP0 (or APmf - a symbol used by Cental) and increases with in the increase of H.

368

Jordan Hristov


MOO

Ί

.2

Fig. 41:

·

-t

I

I

Λ

I

Λ

I

I

I

I

ίο

12

U

U

I

U

20 2.2

Pressure drops curves from various sources concerning the field effect on the pressure drop deviations across MSB. Axial and transverse fields. a) Data of Cental (1994). Transverse field. Iron spheres (see Tables 2-3). 1.^= 70 mm. Original Fig. 3-3 of Cental (1994). b) More precise Cental's picture of the data shown on Fig. 4la. Original Fig. 3-4 in Cental (1994). c) Data of Saxena et al. (1994). An axial field. Variations of ΔΡ with U and H for an iron-shot particle bed of 733 μπι. The ratio W/A is equivalent to G/S used here. Original Fig. 15 of Saxena et al. (1994). d) Pressure drop curves for beds of metallurgical dross (315-400 μη·) in a column with Dc= 65 mm: · - hbo= 65 mm; + - hbo= 100 mm; D - hbo= 130 mm; H= 38.454 kA/m. Adapted from Penchev and Hristov (1990a). The dashed lines and the ratios G/S are added here.

Special experiments on the simultaneous effect of the field intensity and the field direction on AP(MSB)Av have been performed by Hristov (1994). The pressure drop curves presented here (especially those on Fig. 35) indicate that the value ΔΡ (Ue) is greater (for o< α 0 and the range of variations is 0 < δΡ (Ue) < 30%. The value of TT

/

sin α ·»

*y- represents the relative contribution of the vertical (axial) /Η component of the field intensity vector. As the value of sin α approaches 1 the contribution of H A diminishes, while the effect of HT increases. According to Eqs. (8) as well as to Eqs (12) the bed compaction ( the decreasing of the gas voids) will increase as sin α -> 1 and the increase of the field intensity. The macroscopic results are the increased pressure drop and a decreasing value of δΡ (Ue). This physical mechanism is confirmed by the

0.2

0.4

0.6

0.8

1.0

sina Fig. 42: Pressure drop across MSB- Variations of 6P(Ue) with the angle of the field lines orientation (see inset of Fig. 20) represented by Sin α. From Hristov (1994).

370

Jordan Hristov


data on Fig.42. Under almost axial fields (0 < sin α < 0.5) and moderate field intensities the range of 5P (Ue) is 0.2 - 0.15. On the other hand, while at 0.7 < sin α < 1 and stronger fields the value of 5P (Ue) sharply decreases toward 0.02- 0.05 (i.e., as the pressure drop approaches the scale G/S). The data have been approximated by a linear relationship Y-An+BnX

(20a)

where Υ = In 5P(Ue) and X = sin a, or in an explicit form

(20b)

Some values of A0and B0 are shown in Table 10.

Table 10 Coefficients A0 and B0 of Eq. (20a) - an example. Material

H,kA/m

AO

Bo

Magnetite (100-200 |im) G= 0.255 kg, G/S= 1277.52 Pa

0 2.4 4.8 7.2 9.6 12

2.87 2.87 2.96 2.95 3.32 3.39 3.06

-0.105 -0.157 -0.202 -0.384 -1.109 -1.056 -0.485

2.51

-0.146

3.12

-1.526

Magnetite (200-315 urn) G= 0.2542 kg, G/S= 1270 Pa 0 0 U,, m/s V U« Loz U vs.Loe E IA-R-Z Eq. 33a U-K-R Eq. 33b dU/Oc =0.0138

2136

4272

6409

854S

10681

3.936

18.240

7.719

8397

7.965

10.9193

3.812

17.668

7,477

7.712

7.712

10.571

3.539

16402

6.941

7.5J1

7.104

9.818

Table 13 Values of n. Metallurgical dross 0 180

12812 2.41

17090 2.63

21363 3.65

0144 0.117 0.129 0.226 2.30 Equation (29b) Note: R-Z (Richardson-Zaki) , K-R (Khan-Richardson)

0282

028

H, A/m n LogUvs.Loee 25 points per a run

RJ

4272 5.13

8545 3.72

n- average 3.51 (n at H=0 excluded)

385

Vol. 18, Nos. 4-5, 2002


The test performed gave answers to several principal questions: 1. Does the Richardson-Zaki equation describe the expansion characteristics of magnetically stabilized beds? The answer is YES, but the data must be interpreted carefully due to the existence of additional physical factors that do not exist in the basic experiments performed by Richardson and Zaki (1954). The values of U,„ must be interpreted very carefully, because Eq. (28) does not take into consideration the interparticle forces (in the original experiments of Richardson and Zaki (1954) with liquid-solid beds they are negligible or do not exist). 2. May the particle terminal velocity be evaluated from bed expansion data by extrapolation U- ε plots at ε=1 ? The increase of Utoo as the field intensity is increased indicates that the interparticle forces hinder the bed expansion toward the limiting situation of ε = 1. Moreover, these values are lower than Utoc determined by methods calculating the terminal velocity for a single particle (or fluidized beds without interparticle forces). The terminal velocities of ferromagnetic particles in a magnetic field have not been reported in the literature. If the external field is homogeneous, no body forces should exist, so the field would not affect the particle free fall (or rise) through the fluid. Thus, the well-known equations developed for a single particle may be employed. On the other hand, any equation developed on the basis of particle bed expansion (or collapse) should be used only formally. The reason is that, especially for ferromagnetic particles in a magnetic field, the ferromagnetic bodies interact and all the ferromagnetic dispersed systems tend to decrease their volume (Earnshaw effect) (see comments in the Fundamentals)). Under these conditions, the limiting situation ε = 1 (U,m respectively), widely used for fluidized beds, must take into consideration the interparticle forces. Unfortunately, such correlations do not exist in the literature. Some comments have been published recently (Hristov, 1998d) for the case of magnetic semifluidized beds. From the data reported, it follows that in bed expansion experiments conducted for Uto determination at ε = 1 the result will be affected by the field intensity. The value should be accepted, as one obtained from the data treatment, but not as a physically adequate quantity.

386

Jordan Hristov


3. Are the values of n correct? The values of n obtained by Hristov (1999d) coincide with those obtained by Richardson-Zaki (1954) .It is clear that under the bed expansion, the particles form aggregates that have no spherical forms. The values of n for MSB are close to those for non-spherical particles reported by RichardsonZaki (1954), i.e. in the range of 2.0-2.5. However, there are some results (Table 13) that reach the values of 3 and 5, reported by Richardson-Zaki (1954) as values of n for spherical particles (see Hristov, 1999d). Similar results have been reported in the original paper of Richardson-Zaki (1954) (original Table VI) demonstrating n = f(Re). The tests of Rosensweig (1979, 1980b) and Foscolo et al. (1985) give values of n = 3 and 3.4 respectively. The data of Hristov (1999d) do not contradict these tests, but give n = 2.39. An important point in the interpretation of the facts is that the gasfluidized bed of Agbim et al. (1971) utilized particles with a remanent magnetism. In this case the particles are not continuously under the orienting action of the external magnetic field like in MSB. In MSB the induced magnetism of the particles is much higher than the remanent magnetism in absence of a field. Moreover, there is a permanent orientation action along the field lines. Agbim's bed resembles the homogeneously fluidized gasparticle beds with A behaviour in accordance with Geldart's map (Geldart, 1973). 4. Does the data treatment with established correlations of Richardson-Zaki give correct results? This question is reasonable, since Eq. (28) has been developed for beds without interparticle forces. However, the formalistic treatment could lead to unrealistic results (Hristov, 1999d). For example, equation (29) predicting n through the particle terminal Reynolds number cannot be used, due to the problems existing in U, evaluation (see Point 2). For example, Eq. 29b (a test performed by Hristov, 1999d) gives a value of n= 2.30. It agrees with the Richardson-Zaki data (1954), but does not agree the slope of experimentally obtained bed expansion curve (n= 1.80). ///.2.1.8. Hysteresis phenomena It is well known that B particles (Geldart, 1973) demonstrate a hysteresis of the pressure drop for increasing and decreasing gas flows (Davidson and Harrison, 1963; Kunii and Levenspiel, 1991). The decrease of particle size (at 387

Vol. 18, Nos. 4-5, 2002


the same particle density) moves the powder materials toward A or C fluidization behaviour due to the increased interparticle forces (increased cohesion). Such material exhibits a significant pressure drop hysteresis for increasing and decreasing gas flow: a fluidization-defluidization cycle. The magnetic materials discussed here are normally fluidizable B particles with a narrow hysteresis loop in absence of a field. The increased particle-to-particle interaction (i.e. the increased bed cohesion) leads to larger hysteresis loops as the field intensity is increased (Fig. 32ab). All the pressure drop-gas velocity curves (despite the field orientation) exhibit hysteresis behaviours. The comments above concern the so-called "one-cycle" of a fluidization-defluidization process. Similar results have been published by Cohen and Tien (1991) for magnetite particle beds. The cyclic fluidization-defluidization operations of magnetically controlled beds (especially in the regime of MSB) (Arnaldos, 1986) and Zimmels et α/., 1991) demonstrate increased final bed porosities (the defluidized bed height respectively) of the final bed (Fig. 52) at the end of the de fluidization branch of the cycle. The pressure drop of the defluidization curve declines almost linearly and does not retrace itself in the velocity range corresponding to MSB. The bed height and the porosity remain constant while the air velocity is reduced. The lower pressure drop under defluidization is due to channelling (axial field) and slits (transverse field) as a result of string-string interaction shown schematically in Fig. 50. The expansion of the final bed (U=0) increase as the intensity of the field applied is increased inspite the field orientation (Fig. 53a,b). The materials exhibiting stronger magnetic properties form loosest beds after the defluidization (Fig. 53a,b). The increase of the number of fluidization-defluidization operations leads to higher final beds (Fig. 52a, b, d ). Figure 54 collects all the data available in the literature concerning the final bed porosity (recalculated on the basis of data available). The maximum number of fluidization-defluidization cycles reported is three (Arnaldos, 1986). 7/7.2.7.9. Minimum fluidization (minimum bubbling) velocity 1) Data correlations The fluidization onset determination is accompanied with many conflicts in the history of MFAF. The transition point (velocity UT) defined by Rosensweig (1979, 1980b) or in other terms the minimum point (velocity Ub)

388

Jordan Hristav


Uo. (ms-1)

Fig. 52:

Uo. (m.8-1)

Hysteresis data obtained in different studies under various conditions (the labels Erina, and the arrows are added by the present author for clarity of explanations. Despite the differences of the symbols used (U, or U|>) in all the case the defluidization starts just after the breakdown of the stabilized bed a) Arnaldos (1986) a bed of iron particles; Axial field. Effect of the cycles on bed porosity, £flfal b) Arnaldos (1986). Nickel particle bed. Effect of the cycles on the bed porosity, Eflnal c) Pressure drop hysteresis obtained after two runs. Transverse filed. Cental (1994) d) Porosity hysteresis. Data corresponding to Fig. 52c. Transverse filed. Contal (1994).

corresponds to the breakdown point of the fixed structure of MSB. Both terms have been established for the phenomena observed in axial fields only. It is a matter of argument how the data may be interpreted (see the discussion on the Doctrines).

389

Vol. 18, Nos. 4-5, 2002


2.0,

(a)

Ms=400kA/m

1.6

ο X

f

1.2

1.6 -(b) 1.2 0.8

0

10000

20000 H, A/m

Fig. 53: Variations of the ratio (hfimi/hb,) for "one-cycle" fluidizationdefluidization in a transverse field. Adapted from Penchev and Hristov (1990b). In all the case h^ 100 mm a) Effect of the particle size: + - 100- 200 μιη; A - 200 - 315 μηι; • -315-400μπι; Χ -400-500 μηι;Δ-500-613 μιη. b) Effect of the magnetic properties represented by the magnetization at saturation, Ms (see Table 3). Keys: Ο Magnetite (200- 315 μιη), X - Catalyst Girdler G3L (400 -500 μηι).

The development of the MFAF technique after 1990 (by applications of fields with directions different from axial) triggered a principal question about the fluidization phenomena interpretations. In accordance with the concept accepted in the present review the fluidization onset corresponds to the breakdown of MSB. However, as reported by Penchev and Hristov (1990b) and Hristov (1996) there is a field orientation effect on the sequence of regimes beyond the breakdown of MSB. For example, in axial fields the 390

Jordan Hristov


0.52

Ni ARNALDOS ------ A */

CONTAL (1994) 0.40 -

0.36

Fig. 54:

2 3 Cycle (run)

Data collection (present author recalculation of the data) demonstrating the effect of the number of fluidizationdefluidization cycles on the final bed porosity. Sources: All the data shown on Figs. 52a,b, d.

fluidization starts with "a homogeneous fluidization of strings" (Penchev and Hristov, 1900a) while in a transverse field the bubbling fluidization precedes the homogeneous regime. The change of field direction gives a more complicated order of fluidization regimes after the onset of unrestricted particle motions in the bed. (Fig. 55). Therefore, the more general term "minimum fluidization velocity, Umf" will be used here despite the question of what regime occurs (bubbling or not) after the destruction of MSB. Table 14 collects all the relationships developed in the cases of homogeneous field applications. The equations are expressed in two versions: in their original forms and in accordance with the unified terminology accepted in the paper. This unification does permit the establishment of the common properties and the differences between the equations reviewed.

391

Vol. 18, Nos. 4-5, 2002


8

5

4

4

2

2

Ο

· HFS

Slugging

6

SFB

, IFB. Β

«

16

»

20

12

It

20

H.kA/m

H.kA/m

8·=

8

6

6 ι

,. „,„

Slugging

J 4 2 Ο

β

12

IS

20

2

SMB

Ο

6

Fig. 55:

12

16

20

Η, kA/m

H.kA/m

Ordinary phase diagrams obtained under homogeneous fields of various orientations. Catalyst ICI 35/8 (200- 315 μηι), hbo= 100 mm; Dc= 50 mm. From Hristov (1994). See the abbreviations in the list of symbols.

The first common feature of the relationships collected in Table 14 is that all of them are expressed in an exponential form

(34a) u

basic

(34b)

or as

Both expressions are very close, because the coefficients in the exponents are of the order of 2.10"2- 2.10"4. It is well known that under such conditions oo

ex may be approximated as e

392

V

ι- -_ TC

|c X

= >— k! = 1 + — J

a»

The relationships of

Jordan Hristov

t»

•ο


i

o

«s

gi

Q

1 i| § l s!«S ._-·» I.JE 1*1 io !if^t His Hl

g

^3

E

Ja

'S 2

0>

ε

its ••i Ϊ1| ll

12

CM ^

to

u 1?

0

i! i

E

i S1 Ja

s °£*Ζ
T

s: R

l„ Ϊ II

•f

II

"""

3 O

«i •g D II £·

D

f

45 ΐ Ξ

*"^

**i

n J|. D £

Cental (1994 Cental et al (1998)

.2 02 υ •α £ ο _o

J "*

«

"ω*

JL ™"

'

'\S' m "% . oq Ο χ T ^ ΐ ·— 'V ^^ AI ^ Οί

'

>
Umn,). The plateaux determine the UmrL close to Umfo (dotted lines and the intersections A and B in Fig.56b-left. Both values are unrealistic: the intersection B corresponds to the state of a unfluidized bed and determines Umf-L < U^,» while the intersection A corresponds to the onset of MSB and UmrL = Uei. The dilemma is that both values of Umf contradict the physical situation in the bed - there are no particle motions (a fixed bed or MSB). On the other hand the point A approach is in agreement with Rosensweig's interpretation (the dotted lines in Fig. 31 a and the straight lines intersection in Fig. 40a).

U

U (a)

U

e2

F-L

b) Fig. 56:

Umth

a, Umfo. The principle question is: how large may the ratio —— (or —— ) U

mfo

U

mfo

be? The results discussed in the previous point show that the increase of Ue may reach values of (1.2- 1.4). Umfo. This fact has not been commented upon until 1990. This "transition zone" (Lin and Leu, 1994) assures a fixed bed state, but at higher pressure drop. The further extension of the velocity range in a fixed bed state (but with oriented particle and lower pressure drop, e.g. MSB) has been declared by Rosensweig (1979, 1980b) as a patent claim in the range (1-20) Umfo . The results of Casal, Amaldos and Geuzens as well as the experimental test performed by Penchev and Hristov (1990a), and the studies of Penchev and Hristov (1990b), and Cental (1994) and Cental et al. (1992) do not confirm Rosensweig's claim. In order to evaluate the effect of the induced interparticle forces on the increase of the ratio — — , Penchev and Hristov (1990a) have introduced a II u

mfo

fluidizability index FIM. The idea of Baems (1966) was developed for the purposes of MFAF. The FIM index was defined as velocity of the fluidization onset at H * 0 Umf FIM ~ =minimum fluidization velocity at H - 0 Umf0 In the case of an axial field it was modified as FIM—

U

.

(37b)

mfo

399

(3 7a)

Vol. 18, Nos. 4-5, 2002

Magnetic Field Assisted FluidbationA Unified Approach

It was estimated that the values of FIM vary in the ranges (1- 0.2) for axial fields and (1- 0.25) for axial fields. These ranges are independent of particle diameter and the particle magnetic properties. At FIM < 0.2 the bed becomes like a "piston" and the fluidization (or the breakdown of MSB) is impossible. The variations of FIM with H strongly indicate the effect of particle size, the field lines orientation and the magnetic particle properties. Figures 57

1.0 tiff 0.8-

'

0.6

•»V A»

0.4 Δ »-

0.2

Δ

(a) 4000

1.0f

8000 12000 H [A/ml

16000

20000

0.8 0.6 0.4 0.2

(b) .

I 10000

H[A/m]

20000

30000

1.0 0.8

α

0.6 0.4 0.2

-(c) 8

H[A/m]

Fig. 57

400

12

16

Jordan Hrislov

Fig. 57:


FIM index variations with the field intensity a) Variations of FIM in an axial field. Effect of the particle size. From Penchev and Hristov (I990a). Magnetite, h^ 65 mm, keys: # -(100-200μπι); · - (200-315 μιη); A -(315-400 μπι); • - (400-500 μπι); Magnetite, hbo= 130 mm keys : + -(100200μπι); D - (200-315 μπι); Δ -(315-400 μπι); ο - (400-500 μπι); b) Variations of FIM in a transverse field. From Penchev and Hristov (1990b) Catalyst ICI 35/8. h^ 65 mm. Keys : + -(100200 μπι); D - (200-315 μπι); Δ -(315-400 μιη); ο - (400-500 μπι); c) Fluidizability index FIM as a function of the field intensity at various orientations. Hristov, 1996. Iron Powder "Manessmann" (100-200 μηι), hbo= 50 mm. Keys (field orientation): D - 0°; +- 15°; Δ-30 °; o-45 °; A -75 °; · -90 °.

shows that in an axial field the values of FIM are practically independent of the particle size (Fig. 57a), while in a transverse field (and in the field with various orientations) they do not coincide- Fig. 57b. This may be attributed to the fact that the general definition of FIM strongly detects the particle orientation (Fig. 57c), particle-to-particle and string-to-string magnetic interactions as well as the solid fluid behaviour in the column. 7/7.2.7.7 7. Field intensity required for MFAF i) Maximum field intensity required The field intensities required for creations of various regimes of MFAF have hardly been discussed in the literature. Since 1979, Rosensweig (1980b) has commented that particles exhibiting low magnetic properties need stronger fields. However, there is no systematization of the results obtained over 40 years. In some papers (Sajc et al. (1992) for example) there are critical comments that in some investigations (Rosensweig, 1979, 1980b; Penchev and Hristov, 1990a, 1900b) the field intensity reaches values which are too high at 50 kA/m. The problem has been partially clarified by Penchev and Hristov (1990a,) by a plot describing the variations of the FIM indexes of particulates materials covering a wide range of magnetic properties (Ms = 40 - 1780

401

Vol. 18, Nos. 4-5, 2002

Magnetic Field Assisted FluidizalionA Unified Approach

kA/m) (see Table 2 in the original work and Table 4 here). Figure 58a reproduces this plot with some additional details supporting the present discussion.

FIM Ms Decreases

10000

20000

30000

40000

H,A/m 15 12

ί

9 6 3 0

(b) 100 200 300 400 500 600 Ms, kA/m

Fig. 58: FIM index properties : a) Variations of FIM index with the field intensities for various magnetic materials. From Penchev and Hristov (1990a). The figure is developed here by the introduction of arrows determining the value of Hm and the inset. b) A variation of the coefficient K of Eq. (38) with the magnetization at saturation Ms.

402

Jordan Hristov


It is clear that the materials like Ni, Fe need low field intensities for creation of all the regimes presented by the phase diagrams, while the decreasing of Ms requires higher field intensities. A correlation has been developed (Penchev and Hristov, 1990a) in the form: = l.exp(K.H)

(38)

with a coefficient K as unique function of Ms (Fig. 58b). Here the coefficient 1 marks that the F1M value is unity for non-magnetic beds. The plot in Fig 58b has been successfully employed by Cental (1994) for calculation of the desired field intensity for a stabilization of a magnetite bed. The graphical procedure (conceived here for the first time) for determination of the maximum field intensity (Hm) required using a simple graphical technique. The procedure detects the intersection between the FIM curve and the line FIM=0.2 (see the previous point). The values of Hm detected by the method and those employed in the literature are summarized in Table 15. Table 15 Maximum field intensities applied - determined by Fig. 69a and data available in the literature Material

Hmax,kA/m Estimated by Fig. 69

Iron

6.4- 7.8 (at FIM=0.2)+ 6.4 -7.8 (at FIM=02) 4 - 4.5 (at FIM= 0 33)* 4 -4 5 (at FIM=0.33)*

Magnetite Nickel

14.2 10.8 (at FIM=0.33)* 14.2 (at FIM=02)+ 12.8 (at FIM=0.2)+ 6.7 (at FIM=0.4)*

H max, kA/m (Literature data) 10

Reference

Saxena and Shrivastava (1990)

6 4 3 3 12 5.6

Lucchesiet «1(1979) Arnaldos (1986)* ; Casal (1982, 1984)* Lin and Leu (1994)+·

4

Arnaldos (1986)··«· ;Casal (1982. 1984)*+ *- the ratio IWUnb is about 2.5-3

Filippov(1961a, 1961b, 1961c) Geuzens(l985)+*

+ not reached in the experiments; * - FIM obtained in the experiments

ii) Minimum stabilization intensity The minimum field intensity, Hmin, required to stabilize the beds, depends on the field line orientation and the properties of the particle materials. The value of Hmin increases with increasing the angle ot-> 90°. For example, Hmin

403

Vol. 18, Nos. 4-5, 2002


in a transverse field is 3-4 times greater than that in an axial field (Fig. 59). The intensity Hmjn can be determined when the stabilized bed starts to expand at velocities, close to Umfo. Thus the value of Hmill corresponds to the field intensity at which the stabilization is first observed. However, the detection of the bed expansion depends on the experience of the investigator and the accuracy of the experiments since, at low fields, it is difficult to detect the occurrence of the stabilized state. Hristov (1996) has developed a simple graphical procedure for Hmin determination. The value of Ho correspond to the intersection of the line U/Umf0 = 1 (an approximation) and the straight lines approximating the curves Urof/Umfo. The straight lines (dotted lines in Fig. 59) extrapolate the curve Umj/Umfo = f(H) or (\3mflJmfo = f(H/Ms ) toward 1 using the data obtained at higher field intensities. The procedure uses the fact that at high field intensities the breakdown of MSB is easy detectable. The abscissa of Fig. 59 is presented as a dimensionless field intensity X = H/Ms (Hristov, 1996) that allows the measurement of the variation in the intensity of the external field by a scale which is specific for each material (Ms) - see the next point.

10

15 20 H/Msx103

25

Fig. 59: Two-dimensional phase diagram showing the effect of the field orientation of the boundaries of a stabilized bed and the minimum field intensity required for the bed stabilization (Hristov, 1994). Material: Magnetite (200-315 μιη); h^ 50mm; ... graphical determination of Xo. Inset: Magnetization curve M= f (H) for magnetite particles - Geuzens (1985)

404

Jordan Hristov


iii) Correlations for Xo. Particle properties effect - an attempt to create a common diagram. The evaluation of the particle material properties (magnetic ones) may be made by the introduction of dimensionless field intensity. As shown at the beginning, the internal field of the material (magnetization M) may varies from 0 to the limiting value of Ms. The value of Ms was chosen (Hristov, 1996) as a specific scale of each material. The maximum field intensity employed (data available in the published papers) has been evaluated about 50 kA/m (see the data collected by Penchev and Hristov (1990a) and those in Table 4). The field intensity (maximum applied) of 50 kA/m is normalized (Table 16) by the specific values of Ms. The range of 0 - 50 kA/m assures almost linear relationship M = f (H) - see for example the inset in Fig. 59. Table 16 Dimensionless field intensity ranges for some material used in the experiments. Hristov (1994) Material

Iron Magnetite Catalyst ICI 35/8 Catalyst Girdler G#L

Hmax, kA/m

Ms, KA/m

Hmax/Ms

Ln (Hmax/Ms). I01

SO SO SO

1750.24 485.42 366.0S6

0 02885 0.10300 0.1365

3.3516 4.6347 4.9169

Ln(X».10J) at o=0" seeEq (39) 00285 0.923 2.2205

50

50.133

0.9997

6.9050

4.307

The arrangements of the dimensionless velocities Um|/Umf0 as a function of In (H/Ms) permit the creation of a common phase diagram (Fig. 60) (Hristov, 1994). The horizontal line at about Umf/Uraf0 = 2.5 (as an example) and the arrows toward the abscissa demonstrate how one and the same Umf/Umf0 ratio may be created under different conditions imposed by the field orientation and intensity. The dimensionless field intensities assuring the minimum stabilization conditions have been correlated (Hristov, 1994) in the form

X

• Bst.exp|Ax (sin a)31

(39)

aO

Some values are summarized in Table 16 (last column)

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Vol. 18, Nos. 4-5, 2002

Magnetic Field Assisted FluidizationA unified Approach

|

ln(H/Msx1000) Fig. 60:

Two-dimensional phase diagram (semi-logarithmic) demonstrating the effect of the particle magnetic properties on the possibility to create MFAF. The value of Ms for each material is different (see Table 3 and Table4). From Hristov (1994).

11.2.1.12. A generalized relationship for Umf The data shown in Fig. 59 make it possible to apply a simple linear relationship (Hristov, 1994): (Umf /Umfo-l) = K a (X - X 0 ) at X > X0

(40)

where X - (H/Ms).103 and X0 - X at U mf /U mfo = 1 The values of K0 for magnetite beds are summarized in Table 17. The best results for data fitting of Κ«, were obtained by a correlation proportional to (since)3.

(41) Equation (41) leads to a new expression of (40)

406

Jordan Hrislav


Table 17 Values of Κα for magnetite beds o,deg

0

15

30

45

60

75

90

Ka(-)

0.356

0.318

0.298

0.233

0.156

0.126

0.117

(Umf/Umfo-l)=Keoexp[-AK(sina)3](X-X0)

(42a)

or in a dimensionless form (Umf /Urafo-l)- K

o -l)exp[-

(42b)

In the particular case of magnetite particles AK = 1.142. The substitution of (39) in (42a) leads to a complete relationship for Umf

(43) where BO-BstKa0Xa0. In the particular case of magnetite (Hristov, 1994) the values of the coefficients are: 1^0=0.356, Bst= 1.16, AK= 1.142, Αχ=1.07, X„o=2.808. ΙΟ3. All the coefficients were established by non-linear regression analysis (based on 164 experimental points) at 0.95 confidential interval and SR=0.259 Thus, BO = 3.25.10"3 and AX-AK= -0.072. These coefficients are consistent with those summarized in Table 14. 11.2.1.13. Time -Varying magnetic fields applications A preponderance of the studies discussed above has employed steadystate magnetic field, usually termed as DC fields. The studies in time varying fields are rare. In fact, the studies of Filippov (19161a, 1961b, 19161c), Kirko and Filippov (1960) and Zabrodsky and Tambovtsev (1976) have been performed in AC fields generated by a solenoid and 50 Hz (European standard) current supply. When the time-varying field is used (AC field) there are some changes of bed behaviour, some favourable (Stevens et al, 1988) and others detrimental (Filippov, 1961b)

407

Vol. 18, Nos. 4-5, 2002


The problem has not been discussed till 1988 when an important study (Stevens et al., 1988) of Rosensweig's group has been published. The paper is a unique report that has discussed various problem of MFAF under an axial AC field. Here only the stabilization phenomena and the transition velocities will be discussed. As mentioned the AC field has an axial orientation. In fact there is no information in Stevens et al. (1988) concerning the magnetic system applied. The present author suggests an employment of an axial filed by Stevens et al. (1988), since the usual device of Rosensweig's group is the Helmholtz pair commented in the paper. Stevens et al. (1988) have found that the DC fields produce wider operating windows (Fig. 6 la) for the stabilized regime at the frequency of the test (60 Hz - American industrial standard). On the other hand the effect of —I

0.36

J

i

1

1

l·

4--

DC Field AC Field

ο

0.28

ο 0.20

Urn § 0.12 0.006 Applied Magnetic Field, T

0.04

0

Applied Magnetic Field =0.0028 Tesl " Steel Spheres -50 +60U.S. Sieve (b)

16

32

48

64

Frequency of AC Magnetic Field, HZ

Fig. 61: Stabilization by time-varying magnetic fields (axially oriented). From Stevens et al. (1988). Note: The authors use the symbol Urn for Umfo. a) Comparison of transition velocities in AC and DC magnetically stabilized beds. Steel particles (300 - 355 μηι) with Umf0 = 0.27 m/s. b) Frequency effect on the transition between MSB and the fluidization. Steel particles (250 - 300 μηι) with \}mfo = 0.19 m/s. Magnetic field induction, B= 2.8. ΙΟ"3 Τ

408

Jordan Hristov


the excitation frequency (Fig. 61b) is important. At lowest frequencies the bed is bubbling cyclically at gas velocities just above the minimum fluidization velocity (U> Ue or U > Vmfo in accordance with the present unified terminology) due to nearly intermittent application of the magnetic field. The velocity of the MSB destruction (U= Uy- Rosensweig, or U= Umf here) increases as an approach the value obtained under DC fields as the frequency of the AC field is increased (Fig. 61b). The above effect (on the boundary between MSB and the fluidized bed) has been investigated theoretically by Stevens et al. (1988). However, the present author intends to explain the results from a physical point of view. The major phenomenon in MFAF is the generation of stable interparticle contacts. The stability of the bed packing against the destructive action of the fluidization flow is the gist of MSB regime. The attractive force between two particles contacting in a magnetic field may be simply explained by Eq. (9). However, the equation has been developed for steady-state magnetic fields. If we have two currents: a DC current with an amplitude IAC equal to a DC current with a strength IDC, the average value (for the period of AC cycle) of IAC is usually average IAC < IDC · Therefore, Eq. (9) indicates that the interaction between ferromagnetic bodies would be stronger if a DC field is applied. The second important fact is that the mechanical resonant frequency of the particle-particle contacts is usually very low (several Hz). The AC fields applied for magnetization have frequencies much higher than the particleparticle resonant frequency. Thus, the interaction is like that in a DC field since the particles have no time to repulse and attract again during one field period. However, the force of attraction is lower than that created by a DC field. The increased frequency (at a fixed IAv) increases the value of FM in Eq. (9) (please see any textbook on electricity) and the stability of interparticle contacts increases. For example, Stevens et al. (1988) have mentioned that at B = 0.003 T (Fig. 60a) the bubbling (i.e. low strengths of the interparticle contacts) in the AC field starts at U = 0.7 m/s, while the DC generated field permits extension of the stabilized bed to U Ξ 1.1 m/s. This mechanistic (physical) model explains the results obtained by Stevens et al. (1988). The effect of the field frequency on the pressure fluctuations has been reported by Jovanovic et a. l (1987) in the study on bubble control (see the section on Bubbles) too.

409

Vol. 18, Nos. 4-5, 2002


IH.2.1.14. Space varying (rotating) fields The space-varying field usually created by stators of electric motors (see at the beginning the comments on the experimental system of Nekrassov and Chekin (1961, 1962)) have only rarely been applied for the purposes of MFAF since 1961. Due to the specific design of the magnetic system these fields are transversally oriented to the gas flow. Recently Lu and Li (2000) have applied a similar field for a fluidization of cohesive admixtures of magnetic and non-magnetic particle (see Fluidization of cohesive magnetic particles). The experiments of Nekrassov and Chekin (1961) have indicated that better solids distributions in the bed have occurred under a transverse field orientation (the experiments have concerned different orientations of the field from 0 to 30°). The bed behaviour resembles that reported for steady-state magnetic fields (see comments of Penchev and Hristov (1990b) and those for transverse field application in the present paper). The main effect of the rotating field (Lu and Li, 2000) is the rotation of the particle aggregates ("chains"). When the field rotates slowly (o>H < oc the chain would rotate in the opposite direction of the field. In the second situation they demonstrated periodic forward and backward rotations. The optimal conditions for fluidization were reported at f = 5 Hz. No pressure drop curves have been reported for beds of pure magnetic particles. On the other hand the pioneering study of Nekrassov and Chekin (1961) clearly demonstrates that the transverse AC field increases the pressure drop across the bed. This result for DC fields appeared 30 years later in Western publications (see comments of Penchev and Hristov, 1990b). Figure 62 shows the pressure drop results of Nekrassov nd Chekin. It has been found that the ratio (G/S). (ΔΡ**1 may reach values of 1.26 that are consistent with the results in DC fields discussed here. Comments on the measuring technique applied by Nekrassov and Chekin (1961) are available elsewhere (Penchev and Hristov, 1990b) The application of rotating fields is an undiscovered and undeveloped area for MFAF. The potential applications for fluidization of fine materials and admixture offer a wide field for investigations.

410


Jordan Hristov

I.D

^

α. w

,2

H

,-i. u N, 3\ S O_u -< -t— 10

)

Fig. 62:

i\ M L

200

h, mm (a)

^

«00

^

U

1«

0»

3

1 )

r

X

^

E

t—K

^ 200

h, mm (b)

10

1 along the bed height at the stabilization onset. Curves : 1- non-magnetized bed; 2- under a rotating field; 3- under a time-varying field (SO Hz) b) Variations of the ratio (G/s). (ΔΡΗ along the bed height at the fluidization onset. Curves : 1- non-magnetized bed; 2- under a rotating field; 3- under a time-varying field (SO Hz) c) Pressure drop as a function of the superficial gas velocity. Lines: 1- a non-magnetized bed; 2- a bed under a rotating field. Label NB - normal bubbling without particle entrainment from bed.

111.2.2. Results obtained in non-homogeneous fields or conditions

undefined

The employment of short solenoids as sources of axially oriented magnetic fields is a distinctive feature of the group of Ivanov in the period of 1969 - 1980. The main idea predetermining all the investigations of Ivanov and coworkers is to create a reactor for ammonia synthesis working with particles of sizes less than 1mm and high velocity of the synthesis gas. This idea is well defined in the thesis of Shumkov (1975). The choice of the magnetic system has been defined as follows: •

The field should pull down the catalyst particle against the drag forces of the fluid flow. • The field should prevent the particle entrainment from the working volume.

411

Vol. IS, Nos. 4-5, 2002

Magnetic Field Assisted Fluidi=ation~ A Unified Approach

The possibilities to design magnetic systems satisfying the above conditions are well known (well before 1970) and some of them were commented upon at the beginning of the paper. However, a magnetic system based on a solenoid design has been chosen. Taking into account all the features ofthat type of magnetic field source, a set of short solenoids has been created and a great deal of experimental work performed. Satisfying both the conditions mentioned above the solenoids employed by the group of Ivanov have been designed with ratios L/D £ 1 (See Fig. 63a,bc). The field distributions in the solenoids of Grozev and Shumkov were shown in Fig. 2la. Despite this, the example shown in Fig.63d notes again that there are strong field gradients along the solenoid radius. This fact should explain most of the data discussed below. The fluidized bed characteristics obtained in short solenoids will be discussed in the same way as those in homogenous magnetic fields. In accordance to the

B.mT

(C)

Fig. 63: Magnetic system for non-homogeneous magnetic fields with an axial symmetry: a) Ivanov and Grozev (1970a, 1970b) b) Shoumkov and Ivanov (1970,1974), Shoumkov at al. (1975) c) Shoumkov (1975) d) An example. A short solenoid and the field distribution in the radial direction. Adapted from Sandulyak and Garashtenko (1982). 412

Jordan Hristov


present classifications all the results noted below have been obtained with the Magnetization FIRST mode. HI.2.3. Pressure drop curves A strange fact among all the results published (Ivanov and Grozev (1970a, 1970b); Shumkov (1975); Shumkov and Ivanov (1974, 1976)) is the absence of pressure drop-gas velocity data neither graphical nor tabulated. No explanation can be found in the published papers about that deficiency. Pressure drop curves obtained by members of that group have appeared since 1980. They are collected in Fig. 64. An unpleasant fact is that these

Μ

(a)

300 (b)

Λ \

/ -»

ΔΡ/ΔΡηηίη

APmmKbO 200

ο-

0

/ )5

1

15

2

U, m/s

(c) 'ο, "·""

260

ι_

220 Cη

Fig. 64:

100 0

Ο

02

ΟΑ

06

03

1JB

U. m/s

• ρ/ ι o-U-

028 036 0« 052 U, m/s

1.2

U, m/s

Pressure drop curves of Zrunchev and Popova. a) Zrunchev and Popova (1981).Fluidization curve of a bed of 900 μηι particles and h^ 150mm. Umfo= 0.42 m/s. No data exist about the material, the column diameter and the magnetic system employed. b) Zrunchev and Popova (1983). No data about the material and the other experimental conditions c) Zrunchev IA and Popova TF (1980). No data about the material and the experimental conditions. d) Zrunchev IA and Popova TF (1987). Fluidization curve obtained in a column with diameter Dc= 150. No data are available about the material and the magnetic system used. Ifixed bed; II- stabilized bed; III- fluidized bed

413

Vol. 18, Nos. 4-5, 2002


curves have different shapes, but no data explaining the differences exist. The figures were collected with a lot of efforts from various sources. An important fact is that since 1980 Zrunchev and Popova have accepted Rosensweig's terminology (see Fig. 64c). 7/7.2.3. Minimum fluidization velocity III.2.3.1. Minimum fluidization velocity-experimentalfindings As mentioned, the achievement of high working velocities for ammonia synthesis has been the main target of these investigators. Therefore, there is a great deal of data concerning the minimum fluidization velocity, Umf. These investigations were performed at a time when the Filippov postulation of the fluidization onset was unknown in Bulgaria. In all the published papers (more than 80) there are no references concerning Filippov's results. The classical results on fluidization from western countries (Leva, 1959, Davidson and Harrison, 1963) and those from Russia (Aerov and Todes, 1968) have influenced the data interpretations. The onset of unrestricted particle motions has been accepted as the fluidization onset. This point corresponds to the minimum bubbling velocity defined by Rosensweig (1979, 1980b) several years later. The results of several studies are summarized in Fig. 65. In both cases the dp=570nm

.90 £0 f10 ".60

0 Fig. 65:

414

12

24 B,mT

.50 80 140

300

500

Minimum fluidization velocities of beds fluidized in magnetic fields generated by short solenoids. a) Shumkov and Ivanov (1976). Simultaneous effect of the particle size and the column diameter. *-Dc = 500 mm;O-Dc= 140 mm. In all the experiments hto/Dc = 1.Ammonia catalyst SA-1 (Russia). CO2 as a fluidizing agent. b) Variations of Umf with the column diameter. Field induction effect on Umf. In all the cases h\JDc = 1 . Ammonia catalyst SA-1 (Russia). CO2 as a fluidizing agent.

Jordan Hristov


values of the minimum fluidization velocity increase as the field intensity is increased. Moreover, it is affected by the column diameter. These are the sole experiments (Fig. 65b) concerning the scale-up effects. No such experiments had been performed over 40 years either in homogenous or in nonhomogenous fields. The reason for the column diameter effect on Umf is the bed non- homogeneity along the solenoid radius (see below). The use of short solenoids has provoked experiments with different positions of the solenoid with respect to the initial static bed. An example is shown in Fig. 66a,b. The solenoid field has a strong gradient along its axis of symmetry. Despite the position of a particular ferromagnetic body in all cases the field tends to pull it towards its centre. Therefore, if the solenoid centre is below the bed it will pull the particles downward and higher fluid velocity is required for bed fluidization. In the opposite situation the field pulls the particles upward and compensates a part of the gravity, so the value of Umf will decrease. Despite the solenoid position in all the experiments the stabilization phenomenon has been observed, but it has not been an object of detailed investigations.

Umf, m/s

220V (a) Fig. 66:

-16/H20-aO-4D 0 40 80 L (b)

Experiments of Ivanov and Grozev (1970a). a) a schematic presentation of the experimental set-up: 1- column; 2- pressure tube; 3- movable support; 4- grid; 5-solenoid. b) Effect of the axial positions L (the zero point corresponds to the situation when the bed bottom coincides with lower face of the solenoid) on the minimum fluidization velocity. Bed of FeCr catalyst particles (750 -1000 μηι), h^ 30 mm. Dc= 30.5 mm. Air as fluidizing agent.

415

Vol. 18, Nos. 4-5, 2002


IU.2.3.2. Minimum fluidization velocity - data correlations The data correlations developed are summarized in Table 18. The general form of all of them may be expressed as

(44a) or Remf = R e m f o e a - c where Re m f o =f (Ar)

(44b) (44c)

Therefore, there are no differences between the formalisms applied on the data correlations in the homogenous and the non-homogeneous fields. However, there are more serious differences in the approaches applied. The relationships developed in homogeneous fields use the value of Umfo determined experimentally. On the other hand the group of Ivanov has applied a differed approach: i) It was assumed that the pressure drop might be expressed as (45,

ii) The pressure drop was assumed equal to the bed weight per unit crosssectional area of the column AP-|--h b (p s -p g )(l- E )

(46)

iii) The combination of (45) and (46) yields in a form

Re = aAr"

(47)

!! All the above steps are well known from the non-magnetic beds. iv) An important step (Ivanov and Grozev (1970a) in the development of the correlations for Umf is the assumption that the field "adds" additional bed weight (!!! First basic assumption) to that generated by the gravity, since the ratio noted as a may be used as a parameter :

a -t — Moreover, it was assumed that the relationship between the additional "magnetic" weight and the gravitational one was linear (!!! Second basic

416


Jordan Hrixtov

H, m|o

'TJ°·

i"

«

Q τ •

"o d Ό

1 Relationship

b

«

v

*o

l 5m S

l* t *

"Λ

II

II

Ϊ 3

·_ £

E

D

v

's

«n °

!'

1

a

i o

00 |0 ·*

> -o"

oo

> -J

OO

CQ

i s« I ^, U

ιβ

1^.

υ 5 5»

1

for a laminar

^< ^

> -o' s'

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429

Vol. 18, Nos. 4-5, 2002

Fig. 73:


Phase diagrams. Air- Catalyst G3L (100-200 μιη), ps = 3000 kg/m3; h,» = 65 mm; Ms= 50.3 kA/m; (Hristov (1999b). By courtesy of Thermal Science. Left -Axial field; Right- Transverse field. Similar diagrams have been published by Hristov (1998c).

The detection of the critical field intensity has been made visually. The phase diagrams demonstrate the effect of the magnetic properties on the critical field intensities. The relevant data concerning the pressure drop (Fig.74) and bed height (Fig.75) variations allow easy detection of these critical points. The further discussion will elucidate the phenomena (Hristov, 1998b, 1999b).

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Fig. 74:

Pressure drop as a function of the magnetic field intensity. Hristov (1998c, 1999b). The arrows and the dashed lines indicate the onsets of the "frozen" beds, a) Axial field- Iron catalyst ICI 35/8 (100-200 μιη).Μ5= 366 kA/m; hbo = 65 mm. b) Transverse field Iron powder ASC (Sweden) (100-200 μπι). Ms= 1750 kA/m; h,» = 100 mm.

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431

Vol. IS. Nos. 4-5, 2002

Magnetic Field Assisted Fluidi:ationA Unified Approach

Under both fields applied and low field intensities only a reduction of particle motions has been observed with a constant pressure drop across the bed. The field applied has no effect on the bubbling in the bed. At higher intensities short particle strings emerged (at the intensity Hstr). The string length grew with the increase of field intensity. At field intensity H=Hah, the "homogeneous fluidization of the strings" started. A continuous decrease of string movement was observed up to the point at which the bed "froze" (at the intensity Hfr) in spite of the field orientation applied. In both fields the pressure drop decreases down to the freezing point. However, the bed depth curves have different behaviours. ///. 3.2.3. Frozen bed-properties The frozen bed has been considered for a long time as a possibility to create a "magnetically stabilized bed" (under the action of axial fields) (Rosensweig, 1979; 1980b; Sonolikar, 1989; Rosensweig et σ/., 1981 a). The main attraction is that the stronger field intensities suppress the bubbling and immobilize the particles. However, the particle-particle and the string-string interactions strongly depend on the field orientation and the particle material properties. The term "frozen bed" used here differs from that used by Siegel (1988). Siegel's "frozen" beds can be created in the "Magnetization FIRST' mode and axial fields at higher field intensities (Rosensweig, 1979, Penchev and Hristov, 1990a, Rosensweig et al. 198la; Saxena and Shrivastava, 1990). Fluidization is than impossible and the bed is like a piston. Table 20 compares the properties of the frozen beds obtained by different approaches and those of the magnetically stabilized beds (MSB). The frozen bed has a fixed structure of particle strings. In an axial field the pressure drop and the bed depth are independent of a further increase of the gas velocity. In a transverse field the behaviour is just the opposite and at the transitional point (H=Hfr) the pressure drop curves reach their minima. The further increase of the field intensity beyond the minimum freezing point (H>Hfr) does not affect the bed depth in an axial field while in a transverse field the bed depth and the pressure drop increase. The mechanism of string-string interaction (see insets of Fig. 75) can explain the differences between bed heights in the regime of a frozen bed. In an axial field the repulsive forces and the drag forces are perpendicular, so the bed height is limited by the maximum string length, and does not depend on the string arrangement in the bed. In a transverse field the repulsive forces and the fluid flow (i.e. the drag forces) are parallel. Hence, both actions tend

432

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Vol. 18. Nos. 4-5, 2002


to increase the distance between the strings and the bed height as a whole. A similar mechanism was discussed with the Magnetization FIRST mode. The pressure drop data and the observations (Hristov, 1998c, 1999b) show that the intensity Hfr corresponds to the point at which the pressure drop-field intensity curves reach their minima (Fig. 74). Despite the field orientation the field intensity, Hfr, required to "freeze" the fluidized particles is in proportion to the gas velocity. However, the field orientation affects the values of Hfr that can be attributed to the different string orientation with respect to the gas flow. A mechanistic model has been proposed by Hristov (1998c). It explains the field orientation effect on Hfr. In an axial field the strings are streamlined along their long axis and the drag forces are minimal. In a transverse field the magnetic moments of rotation tend to orient the aggregates transversally to the fluid flow. It is clear that in a transverse field greater field intensities are required to achieve immobility of the fluidized strings, i.e. the bed freezing. The frozen bed is a fixed bed with an induced stability like the "magnetically stabilized bed" (MSB) . In both cases the particle interactions stabilize the bed against the destructive action of the fluid flow. In some studies (Zhu and Li, 1996) the term "condensed bed" has been introduced Obviously, the field interaction with particles having high magnetic susceptibility needs field intensities lower than in the case of materials with low magnetic properties. This fact has been proved with Magnetization FIRST mode (see III.2.1.11). Figures 76a,b show the particle property effect on the minimum freezing field intensity. Both figures demonstrate similar behaviours despite the different field lines orientations. The plots indicate that in an axial field the intensity needed for bed immobilization is approximately twice lower than that in a transverse field. ///. 3.2.4. Frozen bed-Minimum field intensity required It is clear that the minimum field intensity required to freeze the particles depends simultaneously on the particle properties (Ms), the field orientations and the gas velocity excess above the minimum fluidization point (in the absence of a field). It was proved that the minimum field intensity required for bed stabilization with Magnetization FIRST mode could be determined by graphically (see HI.2.1.11). A similar approach has been conceived by Hristov (1999b) for the case of the Magnetization LAST mode. The main idea is to approximate the points of Hfr obtained at higher field intensity and gas velocities by a smooth line. The detection of these field intensities is

434

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435

Vol. 18, Nos. 4-5, 2002


easier rather than those at lower gas velocities. After that the lines should be used to extrapolate the points toward the lower gas velocities. The intersection with a vertical line

»const (for example U

mfo

= 1) U

mfo

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>1 is chosen at a desired bed expansion. The method is an Umfo

alternative to the graphical determination from the pressure drop curves (Fig. 74). The pressure drop curves may be employed when the column wall is not transparent. III.3.2.5.Experiments in non-homogeneous fields (field non-homogeneity effects on the results) Hristov (1998b) has performed an experimental re-examination of the earlier results. The main reason for the tests was the fact that all the pressure curves demonstrated here did not exhibit minima like that of Filippov (Fig. 71). The pressure drop curves of Hristov (1998c, 1999b) resemble that reported by Bologa and Syutkin (1977) and confirm the data of Zrunchev and Popova (1979, 1980). On the other hand the results of Doichev et al. (1965) obtained in a strongly non-homogeneous axial field gave additional information about the field's non-homogeneity effect on the results. The treatment done by Hristov (1999b) in a way similar to data presentation led to curves with minima (not shown here) like those in Fig. 74b. The results of the experimental re-examination done by Hristov (1998b) are shown in Fig. 77 (the experimental situation is shown in the inset). They confirm the conclusion that Filippov's data (Fig. 71) correspond to the case of a strongly heterogeneous field. More detailed comments on the problem are available elsewhere (Hristov, 1998c, 1999b)

III.4. Generalized (common) descriptions of magnetization FIRST and LAST modes In contrast to Magnetization FIRST mode which has been widely discussed, the data interpretation concerning the Magnetization LAST mode has not been involved in conflicting discussions. This may be explained by the few investigations performed and the fact that the phenomena do not allow interpretations contradicting the classic fluidization theory (Davidson 436

Jordan Hristov


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Fig. 77:

Experimental results obtained from the comparative experiments in an axial field. Adapted from Hristov (1998b). Air Magnetite (315-400 μιη). Dc= 65 mm; h^ = 130 mm. Inset: Test experiments performed in an axial magnetic field (Hristov, 1998b). Dimensions in millimeters, a) Pressure drop. The arrows indicate the onsets of the "frozen" beds, b) Relative bed height E.

and Harrison, 1963; Kunii and Levenspiel, 1991)). The phenomena occurring with both modes of operation (magnetization modes) need a generalization and an estimation of the common properties. III.4.1. A brief comparison of the phenomena with the modes FIRST and LAST In contrast to the "Magnetization LAST" mode, in the "Magnetization FIRST" mode the magnetic field is applied to a fixed bed with an isotropic

437

Vol. 18, Nos. 4-5, 2002


static particle arrangement. As a result of particle magnetization, cohesive forces of a magnetic nature emerge. The increase in the flow rate leads to an incremental deformation of the initial static bed with simultaneous orientation of particles along the field lines. This state has been termed a "magnetically stabilized bed" (Rosensweig, 1979). The stabilized bed is an expanded fixed bed with an anisotropic particle arrangement induced by the field line orientation. The stabilized bed may be assumed to be a transitional state between the initial static one and fluidization (Hristov, 1996; Penchev and Hristov, 1990a, 1990b) or as homogeneous fluidization without bubbling (Casal, 1982). In an axial field only an intermediate state between the breakdown of the stabilized bed and the onset of the fluidization occurs beyond the transition velocity U, (velocity Ue2 here). This state has been termed a "fixed structure of particle strings" (Penchev and Hristov, 1990a, b) and a "metastable state" (Cohen and Tien ,1991) In both modes of operation despite the field orientation an interesting fluidization regime was observed. This is a fluidization of particle aggregates, but not of separate particles, i.e. the magnetic interparticle forces dominate over the fluid drag forces. It was termed "homogeneous fluidization of particle strings". The oriented flow of strings suppresses the formation of gas voids (bubbles). With the Fluidization LAST mode the onset of this regime coincides with the onset of fluidization in an axial field (Penchev and Hristov, 1990a), whereas in a transverse field it is preceded by bubbling fluidization (Penchev and Hristov, 1990b). The macroscopic bed behaviour is independent of the mode of operation, but significantly affected by the field line orientation (Penchev and Hristov, 1990b; Hristov, 1996). Generally, the regime resembles the "roll-cell" regime (Siegelt, 1982) and the "particulate" (Hu and Wu, 1987; Kwauk et al, 1992)16] or "chain" (Kwauk et al., 1992) fluidization in spite of the different fluidizing media. Recently, the term "a heterogeneous bed" has been used by Cental et al. (1996,1998). Following the decrease in the gas flow, the bed passes from a state of intensive motion of the solid phase into a final fixed bed state with an anisotropic structure. Two typical pressure drop-gas velocity curves are shown schematically in Fig. 78. Hristov (1996) and Penchev and Hristov (1990a, 1990b) described the sequence of regimes for both orientations of the field lines in detail. In order to clarify the discussion, the bed regimes and the corresponding terms employed with both modes are summarized in Table 21. 438

Jordan Hristov


MSB FSPSi (EXPANDED FIXED BED)

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Typical pressure drop -gas velocity curves with separate sectors corresponding to different bed regimes with the mode "Magnetization FIRST'. Adapted from Hristov (1999b). Schematic presentation (no data points). Catalyst ICI 35/8 (100200 μηι); Dc=65 mm; hi» = 100 mm; Η = 8 kA/m. Similar curves have been published by Hristov, (1998b)

439

Magnetic Field Assisied FluidizalionA Unified Approach

Vol. 18, Nos. 4-5, 2002

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Vol. 18, Nos. 4-5, 2002


III.4.2. Two macroscopic approaches in phenomena description HI.4.2.2. Pseudo-thermodynamic diagrams The presentation of the bed regimes by phase diagrams is a pseudothermodynamic approach conceived by Rosensweig (1979, 1980b) to explain the phase diagrams in the "Magnetization FIRST" mode. Rosensweig's analogy concerns the velocity as an analogue of pressure. According to Rosensweig (see Fig. 2 of Rosensweig, 1980b and Fig. 23a here) the phase diagrams with the "Magnetization FIRST" mode resemble a thermodynamic phase diagram of a pure substance: • solid state (initial static bed); • liquid phase or molten substance (stabilized bed) and • a vapour phase (fluidized state with bubbling). The same formalism applied to the phenomena in both magnetization modes may be formulated as: • SOLID STATE -(initial static bed) with both modes and MSB (Magnetization FIRST) or frozen bed (Magnetization LAST); • LIQUID PHASE - the stabilized bed with magnetization FIRST. This is a result of the formalism applied since MSB is a fixed bed and it may be assumed as a SOLID STATE. On the other hand an analogue of MSB with the Magnetization LAST mode does not exist • VAPOR PHASE - the fluidized regimes: bubbling with strings or homogeneous fluidization of strings. 111.4.2.1. Order-Disorder Transitions The results obtained in homogeneous magnetic fields (axial and transverse) have been discussed by Hristov (1998c) from the point of view of and order-disorder transitions (ODT) based on a generalized thermodynamic approach of the description of disordered systems (Ziman, 1979; Careri, 1982). The basis of that analysis is the fact that the sequences of states as well as the shape of the pressure drop curves in both magnetization modes give a possibility of drawing a parallel between the bed behaviours. Figure 78 helps to explain the idea.. The fluidized system is affected by the concurrent actions of two physical fields: the first causing a disorder (fluid flow) and the second (magnetic field) causing order. Following this ODT analogy, the final bed regime corresponding to the increasing gas flow (see the label "Disorder" in Fig. 78) corresponds to the point where the disordering action of the gas flow predominates over the ordering action of the field. Figure 79 explains this 442

Jordan Hristov

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INITIAL FIXED BED

10

20

30

H.kA/m

State diagrams showing the similarity between the Magnetization FIRST (decreasing flow) and the Magnetization LAST from the viewpoint of ODT.Adapted from Hristov (1998b). a) Axial field (LAST); b) Axial field (FIRST);c) Transverse field (LAST); d) Transverse field (FIRST). (200-315 μπι). h,» = 100 mm.

approach by ordinary phase diagrams (Hristov, 1998b). With the decrease in gas flow rate ("Magnetization FIRST" mode) or with the increase in the field intensity ("Magnetization LAST" mode) starting from the regime of developed fluidization (a fully disordered system), the gas-particle system aspires to an ordered state due to the predominating action of the magnetic field. With both modes, the particle mobility decreases and the final state is a fixed bed having anisotropic structure. However, in order to support further discussion it should be noted that bed behaviour corresponding to the fluidized regimes (in spite of the details) is similar with both magnetization modes. This allows the rigorous

443

Vol. 18, Nos. 4-5, 2002


assumption that the pressure drop pulsations and the bubble behaviour are similar in the bubbling regimes with the presence of strings. These phenomena will be discussed below. 111.4.2.3. Hysteresis of the phase diagrams The pseudo-symmetry diagrams use the values of the transition velocities between the regimes by treatment of the pressure drop-gas velocity curves. Two examples are shown in Figs. (Fig. 80a,b) and (Fig. 81 a, b). Despite the formal symmetry presented in Figs. 80, 81 some asymmetries with respect to the particular states exist due to the hysteresis behaviour of fluidized system in magnetic fields (Zimmels et al. 1991). Zimmels et al. (1991) have defined a bed stability level ψ

(51)

based on pressure drop pulsations (see comments further). Figure 82 demonstrates the hysteresis in the phase diagrams and the bed expansion (Zimmels et al. 1991) as a result of the bed structural hysteresis.

ΠΙ. 5 "ON-OFF" Magnetization Mode III.5.1. Experimental findings The intermitted magnetization of the particle bed under fluidization has not been investigated separately. There is a small amount of data dispersed in various papers. It may be suggested (as previously mentioned) that the bed should be altered between two distinct states • A free bubbling bed (Field OFF) • Afrozenbed (Field ON) With the two modes discussed in the previous sections the rate of changes of the field intensity is practically zero. For example, with the magnetization LAST mode the field (DC field usually applied) is changed step by step by the investigators. The changes do not affect the time-dependent phenomena such as the magnetic flocculation and the string's orientation along the field lines due to the low viscosity of the fluidizing fluid (usually air). However, the intermittent magnetization led to new results.

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Jordan Hristov


The field effect on the bubble diameter is shown in Figs. 90a. The plots show that the bubble size decreases as the field intensity is increased. The opposite tendency exists when the bubble diameter is plotted (Fig.90b) against the difference (Hms-H) or (Hc-H) termed "a magnetic field deficiency" by Jovanovic et al. (1987;) and Jovanovic and Jovanovic (1993). These data confirm the results of Shumkov.

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(b) Fig. 90:

Field intensity effect on the bubble size. Adapted from Jovanovic et cd. (1989). The conditions are like those in Fig. 89. a) Field intensity effect on the bubble diameter at a fixed gas velocity. b) Bubble diameter v/s the magnetic field deficiency

461

Vol. 18, Nos. 4-5, 2002


The results of Jovanovic mentioned above give very important information about the field effect on the gas void evolution. The works referred to do not interpret the results from the point of view that the fieldinduced anisotropy elongates the bubbles. However, only such phenomenon interpretation may explain the fact that the bubble diameter db (80- 100 mm see Figs. 85, 89,90a) approaches the column diameter of 110 mm. In a conventional gas-fluidized bed of such dimensions these bubble diameters indicate the onset of a slugging regime. However, in magnetizable beds under an axial field this regime does not exist (see Fig. 33 and the corresponding comments). The assumption that the bubbles are pseudo-spherical (the basis of the measuring technique applied) does not give adequate interpretations of the phenomena. On the other hand, the elongated bubble shape noted by Geuzens (1985) and Shumkov (1975) exactly explains the results shown in Fig. 90b. They explain (there are no such comments in the papers of Jovanovic and co-workers) the fact that the bubble diameter (measured by the pressure signal technique) vanishes as the field intensity is increased. It is clear that under strong magnetization the bubble becomes a channel (with large longitudinal dimensions-Fig. 90b and a negligible lateral size - Fig. 90a). Despite the well-documented results these studies have not been developed toward a complete bubble shape description that may be attributed to the restrictions imposed by the measuring techniques used. Recently, similar results have been reported by Hristov (1999b). In contrast to the above experiments induction transducers have detected the bed homogeneity. The transducers are placed at the column wall. The technique is still in progress, but short comments have been reported by Penchev and Hristov, 1990a). The bubble motion disturbs the field lines crossing the short coils of the transducers (see inset of Fig. 91). In a homogeneous field (a fixed bed or a fluidized bed without bubbles) the field lines are parallel to the wall and there are no signals induced in the coils. When a bubble passes though the bed the time and space variations of the magnetic flux through the coils generates electric signals. The phenomenon is basic and detects absolutely the motion of the ferromagnetic solids. Figure 91 presents the decrease of the bubble frequency with the increase of the field intensity and the opposite effect of the gas velocity above the minimum bubbling point. The plots indicate that the bubble frequency varies from 0.3 Hz to 1 Hz that is consistent with the data of Jovanovic et al. (1984, 1987) (f= 2 Hz shown in Fig. 85) and Shumkov and Ivanov (1974). 462

Jordan Hristov


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Bubble frequency as function of the gas velocity. The frequency = 1/T. From Hristov (1999b). By courtesy of Thermal Science. Inset above the plots : The main idea for bubble detection by induction transducers. The frequencies are summarized in Table 24. a) Air - ammonia catalyst Ή. Topsoe" KM-1 (dp =800-1000 μιη); hbo= 100 mm; Dc= 65 mm; Field intensity effect, H, kA/m: · - 13; A -10.5; Ο - 4.3; · - 20 b) Air - metallurgical dross (dp =800-1000 μιη); hbo= 50 mm; Dc= 65 mm; Field: H, kA/m :· - 4; A -16.

IV. GAS-SOLIDS FLUIDIZATION (SOLIDS BATCH MODE) OF ADMIXTURES: (MAGNETIC AND NON-MAGNETIC PARTICLES)

IV.l. Way admixture beds? The behaviour of magnetizable beds discussed in the previous points indicates two main problems hindering the fluidization in the presence of an external magnetic field: • The strong particle aggregation is a native phenomenon as described earlier. However, it decreases the efficiency of the fluid-solid contact that is important for heat and mass transfers operations (see Part 3 of the series). Moreover, the increased field intensity permits higher working velocities, but the price ofthat is the reduced particle mobility. • The applications of pure ferromagnetic particles are limited in the chemical and biochemical industries. Most of the technologies have been created on the basis of suitable non-magnetic solids. A possible solution

•

463

Vol. 18, Nos. 4-5, 2002


is to create composites with a ferromagnetic content sufficient to obtain magnetizable composite particles. This approach was employed at the beginning of the investigations of Exxon (Lucchessi et al., 1979) and widely applied in the biotechnological applications of MSB (Hristov and Ivanova, 1999). Sometimes this approach may be successful, but the better solution is to use the non-magnetic solids directly without any modifications.

IV. 2. Basic idea The idea mentioned above leads directly to the fiuidization of admixtures of magnetic and non-magnetic particles. From a practical point of view such approaches are oriented toward heat and mass transfer operations. The nonactive magnetic component assures the magnetic stabilization of the bed, while the non-magnetic particles take place in the transfer processes. The above comments hardly exist in most of the published literature. The author adds them in order to arrange a unified approach in the results interpretation as well as to explain the experimental situations employed by different authors. It is clear that the widely employed non-magnetic solids have densities lower than those of the ferromagnetic materials (they cover the range of 5100 kg/m3 for Fe3O4 up to 7800 kg/m3 of Fe or 8100 kg/m3 of Ni). Obviously, this will cause particles segregation (Kunii and Levenspiel, 1991). The desired particle bed should assure homogeneous distributions of both components (conditions imposed by the heat and mass transfer applications) for better fluid-solid contacts. Therefore, the suitable magnetization mode is the Magnetization FIRST. However a solitary result of Siegell (1988) on Magnetization LAST mode will be discussed at the end of the section.

IV.3. Magnetization FIRST mode lyj.LResults - axial field IV. 3.1.1 .Compositions employed The studies on gas-fluidized admixtures of magnetic and non-magnetic particles are relatively sparse. The first reports of Lucas et al. (1984), Arnaldos et al. (1983, 1985) and Amaldos (1986) employed silica sandnickel, copper-nickel and steel-silica and steel-copper systems fluidized with air in an axial magnetic field. Lin and Leu (1994) have investigated a similar 464

Jordan Hristov


system (Fe-Sand). The recent works of Saxena's group (Wu et al. 1997a; 1997b, Ganzha and Saxena, 1998; Saxena and Wu, 1999) presented further results in an axial magnetic field. Girenko and Hristov (1999), Hristov et al. (2000) have reported recently new results on fluidization behaviour of such beds in both axial and transverse fields. The entire admixtures investigated contain coarse particles of Geldart's group B, i.e. normally fluidizable in the absence of a field. Tables 25 and 26 summarize details of all the studies carried out. The results obtained between 1985 and 1997 have a common feature. All of them have been performed with axial magnetic fields. Thus, they follow the tradition in magnetic stabilization applying the experimental conditions well known from the earlier work of Filippov (Kirko and Filippov, 1960; Fillippov, 1961a) and Rosensweig (1979). iy.3.1.2.MSB onset and minimum fluidization velocity Amaldos' studies (Arnaldos, 1986, Amaldos et al., 1983) and the report of Lucas et al. (1984) have concerned the effect of the concentration of the non-magnetic solids on the bed stability in the sense discussed by Rosensweig (1979, 1980a, 1980b). They discovered that the minimum fluidization velocity (denoted as Ub) decreases as the non-magnetic mass content ··-·

10% mass

• A»»l 0*17_5kA/m

90% mass

•

FIRST

•

DC- 102mm

Οι(935μπι) average p-S920k£/m1 Fe (1416 Mm) p-TOlkgm1

Ca(934Min) p-S920ki/m' Fe(1086pm) average p-TUlkgm' Si (1086μιη) xvcnê p- 7* la/of Fe3O4 (100-200μιη) p-SlOOkgftn1 Resin (500-800) μιη :p- 760 kg/m' (- assumed as 2670 kx/m'

•

• • • • •

Pressure drop Bedvoidage Ficuufc drop curves Field effects on urf Bedvoidage Picsnnediop curves Fidd effects oo Umf Field effects on the onset of MSB andUtf Bedvoidage

FiddeBectson the onset of MSB and Umf Bed expulsion Bed structures and global stability Data correlations Pressure drop Bed structures and global stability

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Vol. 18, Nos. 4-5. 2002

50

(a) Νί250-350μτη

3800

Si 420-630μτη

3165

§

40

2535

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60

80

100

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iυ 40 30· 20

1000

2000

3000

4000

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468

Arnaldos' experimental result with admixtures in an axial field. Adapted from Amaldos (1986). By courtesy of J.Arnaldos. a) Effect of the mass percentage of the magnetic particles on the fluidization onset (velocity Ub) at different field intensities. The components have different sizes and densities. Composition 1 in Table 25. Original Fig. 11.22 in Arnaldos (1986) b) Field intensity effect on the fluidization onset at various admixture beds. The components have different sizes and densities. Composition 1 in Table 25. Original Fig. 11.23 in Arnaldos (1986)

Jordan Hrislov

U


0

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10 20 30 hbo=10cm

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Phase diagram obtained with the composition studied by Hristov et α/.(2000) in axial fields. Field intensity and composition effects. Here φν = (1-Xy ) vo' %» me concentration of the non-magnetic particles.

different bed weights. Figure 94a demonstrates that effect. Moreover, the arrows in Fig. 94a show that the decrease of the magnetic content decreases the values of both velocities Ue and Umf at a fixed field intensity. Wu et al. (1997a, 1997b) reported that that the pressure drop across the admixture bed with low magnetic content is practically independent of the field intensity. On the other hand, in beds of dominating magnetic particles the increase of the field intensity leads to significant variations of the pressure drop corresponding to the regime of MSB. Wu et al. (1997) also reported that in the field intensity range of 5 - 17 kA/m the copper particles appear preferentially at the upper and outer section of the bed prior to extensive bubbling taking place in the bed while the iron particles remained confined in spike. Thus, the observation of Wu et al. (1997a) clearly indicates that a segregation of the phases occurs in regime of MSB before the onset of fluidization of the bed. The magnetic particles remain stabilized while the non-magnetic ones form a fluidized bed at the top of the magnetic layer. The phenomenon has been described be Hristov et al. (2000) and will be discussed in the next subsection. 469

Vol. 18, Nos. 4-5, 2002


220 2JO

18

OA

0.6

0.8

1.0

0.2

U [m/s] Fig. 94: a)

0.4

0.6

αβ

10

U [m/s]

Results of Hristov et al. (2000) with admixtures of magnetite and ion exchange resin in axial fields, Pressure drop curves. The arrows indicate the onset of MSB (light arrows) at Ue and its breakdown (heavy arrows) at velocity Umf; hbo= 100 mm. H= 7061 A/m; φ = φ", % vol.

b)

Bed expansion curves. Zones: I - stable structure- "total stability"; 11- a formation of "pockets" - "global stability" and IIIan ejection of the non-magnetic particles at the top of the stabilized magnetic bed.

IV.3.1.4. Bedstability Girenko and Hristov (1999) and Hristov et al. (2000) reported the development of the bed structure in an axial magnetic field. The bed expansion curves in Fig. 94b mark three zones. The bed expansion in the range hb/hbo= 1.0-1.3 (zone I) gives a homogeneous bed structure without particle segregation. The magnetic phase forms elongated aggregates that tend to orient themselves parallel to the column axis, while the non-magnetic particles fill the gaps (channels) dividing them.

470

Jordan Hristov


With increasing gas velocity and higher field intensities (1.3 < 1.5) the gaps filled with non-magnetic phase become large and a fluidization in these "pockets" starts. In this state the bed loses its "total stability" and passes into a state called "global stability" in accordance with the terminology introduced by Chetty et al. (1991). At higher gas velocities the segregation of the phases begins. Girenko and Hristov termed this point the "segregation velocity" Usg. The non-magnetic particles form a shallow fluidized layer at the bed top, while the rest is stabilized. Along with the further bed expansion (1.5 < hb/hbo) the underlying stabilized bed rejects all the non-magnetic particles that became more homogeneous (formed almost by magnetic particles). The further bed expansion resembles that observed with totally magnetic beds (Rosensweig, 1979; Hristov, 1996). At low and moderate field intensities there are no "pockets" in the bed and the particle segregation starts at Usg. Thus, within the range of low interparticle magnetic forces the state of "global stability" does not exist. The stabilized mixture expands (with a shallow non-magnetic layer at the top) up to the minimum fluidization point at the velocity Umf. lV.3.2.Results - Transverse field The investigations in a transverse field are not so popular among investigators. Girenko and Hristov (1999) reported recently new results on bed behaviour and critical velocities. In a transverse field the formation of magnetic aggregates and the non-magnetic particle arrangement among them exist too. However, the transverse orientation of the aggregates forms a bed structure that is very different from that observed in an axial field. The expanded bed (Ue0. IV. 3. 3. 3. Data correlations— treatments ofSaxena's group data The approach mentioned above was applied here on the data of Saxena and Wu (1999) available in Table 26. The treatment of the values of with Eq. (57) gives decreasing values of k>din with the increasing non-magnetic

475


Vol. 18, Nos. 4-5, 2002

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