rate to partrcle srze, suspensron volume and ultrasonic power, energy ... restricted cavitation zone around the ultrasonic probe. Mechanical ..... ultrasonic device.
ELSEVIER
Powder
Energy-size Karl A. Kustersa,
reduction Sotiris
Technology
80 (1994) 253-263
laws for ultrasonic
E. Pratsinisap*,
Steven
G. Thornab,
fragmentation Douglas
M. Smithb
‘Depatient of ChemrcaI Engmeenng, Unrversrty of Cmcmnatr, Cmcmnatr, OH 45221-0171, USA bUNMINSF Center for Micro-Engmeered Ceramics, Unrversrty of New Merrco, Albuquerque, NM 87131, USA Recewed 28 December
1993, m revised form 13 May 1994
Abstract The energy requirement 1s a key criterion for the selection and use of a grmdmg process. Ultrasomc drspersron 1s extensively used to disperse submicron agglomerated powders m hqurd suspensions Suspensrons of srhca agglomerates were ground wrth solids concentration up to 50% by weight The fragmentation or grmdmg rate 1s inversely proportronal to suspensron volume Starting from a semrempirrcal expression that relates fragmentatron rate to partrcle srze, suspensron volume and ultrasonic power, energy consumptron laws for both eroding and non-eroding powders are developed Experrmental results supportmg the energy consumption laws are given Lower power input for ultrasomcatron favors efficient energy use. For eroding powders (e g silica, zrrcorna) the energy expendrture per unit powder mass (specrfic energy) by ultrasomc grmdmg IS lower than that of conventronal grinding techniques. In contrast, it IS slightly higher than ball mrlhng for non-erodmg powders (e g. trtama) Kqwordr
Ultrasomc fragmentation,
Grmdmg energy; Ceramic powders
1. Introduction
Ultrasonicatron of liquid suspensions of ceramic powders provides an effectrve tool for the elimination of agglomerates [l] that cause problems in postprocessing and degrade product quality [2]. Aoki et al. [3] showed that ultrasomcally induced cavitatron 1s necessary for deagglomeration to take place. Most likely the intense pressures generated in the vicinity of imploding cavitation bubbles [4] are the primary means of particle degradation. These pressures have been measured with the use of hollow glass bubbles [5,6] and were found to be strong enough to fragment agglomerated powders by cracking [7]. It was shown that agglomerated powders could be well dispersed into their constituent submicron primary particles under the action of these cavitation pressures [7-91. The fragmentation can occur either by fracture or erosion. Erosion refers to particle size reduction due to the loss of primary particles from the surface of the agglomerate, whereas fracture is the partitioning of the original agglomerate mto several smaller agglomerates. Which breakage mechanism dominates may depend on *Correspondmg
author
0032-5910/94/$07 00 0 1994 Elsevler Science S A All rights reserved SSDI 0379-6779(94)02852-F
the apphed ultrasonic intensity, but it is certamly a function of material properties. For erosion to take place, the primary particles have to be freed from the surface of the agglomerates. This means that the cavitation pressure must be larger than the cohesive strength with which the surface primary particles are bound together. Fracture results from cracking of the agglomerate compact [lo]. Stresses exerted on the agglomerate initiate and propagate cracks from flaws on the surface. Resistance agamst fracture (agglomerate strength) depends on the srze of the surface flaws and the fracture toughness of the particle assembly. Recently a population balance model has been developed describmg quantitatively the ultrasonic fragmentation of agglomerate powders [ll]. This model predicts the evolution of the size distribution of agglomerated partrcles during ultrasonication With the model, the required processing times for desired degrees of dispersion can be calculated. The important parameters in the model are the fragmentation rate and the breakage distributron function. The fragmentation rate is defined as the frequency of break-up events, and results from the physical phenomena governing the disintegration of the agglomerate particles. 1.e their interactrons with the collapsing cavities The breakage distribution function is defined as the fragment size
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drstrlbution resulting from each break-up event, and is a distmct powder characteristic. A theoretical expression for the fragmentation rate as a function of particle size and power input was derived and evaluated by examining experimental data on the ultrasonic dispersion of silica and tnama agglomerated powders [ll]. The breakage distributron functions were determined from the self-preserving size distributions these powders developed after a short period of ultrasonication. In the present article, energy consumption laws are derived for ultrasonic dispersion. In order to obtain an energy-size reduction law for non-eroding powders, the similarity solution of the grinding equation has to be combined with the above-mentioned relationship between fragmentation rate and power input [12]. With eroding powders, the energy consumption must be related to the production of fines. Furthermore, to calculate the specific energy for a given size reduction of agglomerated powder, rt is necessary to consider the effects of particle concentration and irradiated suspension volume on the fragmentation rate. Experiments were conducted to elucidate these effects on the energy consumption. Finally, a comparison is presented between the energy efficiency of ultrasomc dispersion and other grinding techniques such as ball milling.
2. Theory
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5
where r, is the cavity radius at maximum expansion, pressure m the suspension and K denotes the cavitation efficiency, defined as the ratio of energy spent for the creation of cavities to the total ultrasonic energy employed [14]. Only particles m the vicinity of the collapsing cavity, 1.e. those close to or at the cavity wall, are exposed to the intense pressures generated by its implosion. Neglecting cavity interaction, the number of agglomerates of radius r, touching the cavity wall at maximum expansion (rbx=-rJ, i.e. prior to collapse, N,, is given by:
P, is the hydrostatic
N,(v, t) = 4mb2r,(v)n(v,
t)
(2)
where n(v, t) is the number concentration of agglomerates of volume 2, at time t. The total number of agglomerates that are fragmented per unit time in the cavitation zone is given by the product of Eqs. (1) and (2). Dividing this product by the total number of particles of size v in the suspension [ =rr(~, t) x V,,,] yields for the fragmentation rate: S(v)-
3KE
ra(v)
V,,,
Phrb
--
For sphencally shaped agglomerates with sohds density 4, the relationship between the agglomerate radius, r,, and volume, V, is:
2.1. Fragmentation rate expremon v=
The fragmentation rate, S(V), represents the relative change m number or volume concentration of particles of volume v per unit time by the disruptive action of collapsmg cavities. These cavities are generated in a restricted cavitation zone around the ultrasonic probe. Mechanical mixing ensures that all the particles in the suspension are exposed to the ultrasonic forces in the cavitation zone. In the beginmng of the ultrasonic treatment, the cavities originate from gas nuclei in the liquid as well as on the particle surfaces. These cavities expand in the dilation half-cycle of the pressure sound wave and collapse violently when the pressure enters the compression half-cycle. Upon collapse the cavities break up into tmy bubbles that can act as new cavitation nuclei. This chain reaction stops when the nuclei become too small for expansion under the applied acoustic pressure. Finally a constant level for the total number of cavities collapsmg per unit time, NC, is reached m about ten pressure cycles [13] The final number of collapsing cavities per unit time is independent of the initial number of gas nuclei in the suspension, but rt is related to the power input, E [ll]:
(1)
7 7rrb3Ph
$
ra(v)3+
(4)
With r,- d” [13,15], the expression for the fragmentation rate reduces to:
dependency on particle size has been verrfied by experimental data on the ultrasonic dispersion of agglomerated silica and trtania particles [ll]. The effect of power input on the fragmentatron rate was found to be slightly less than predrcted:
The
S(V) = 2.0 x 10-3eo ‘“V’“lV,,,
(6)
The fragmentatron rate is also a function of the sohds density, as follows from Eq. (5). The solids density C$J ranged from 0.4 to 0.67 for the employed powders, a variation that was insufficient to significantly affect the fragmentatron rate. Eq. (6) can be also written as a power law [12]: S(d) =A@
(7)
where d represents the equivalent solids volume diameter of the agglomerates. For the particular case
KA
of ultrasonic
dispersion,
Kusters et al I Powder
A = 1.6 x 10-3~o 38/Vlot and
a = 1.
It may seem odd that the agglomerate strength does not enter the fragmentation rate expression. Basically this means that Eq. (6) applies only to those cases where the ultrasonic forces acting on the particles are always strong enough to induce breakage of the particles. It has been observed that for strong materials there is a certain induction period or time lag before fracture occurs [ll]. Apparently, during the time lag, flaws or cracks are created on the particles and grow until they reach the critical crack size, above which fracture contmues uninhibited [16] and is described by Eq. (6). Hence after this time period, the original agglomerates and the resulting fragments are too weak to resist ultrasonic fragmentation. For eroding agglomerates that exhibit no time lag, Eq. (6) can be utilized from t= 0, but a different breakage distribution function should be implemented in the population balance model. Erosion results in the formation of prunary particles and coarse fragments comparable in size with the original particle, i.e. a bunodal breakage distribution function. The extent of erosion is proportional to the external surface area of the agglomerates [ll]. The breakage distribution function resulting from fracture depends on the cracking pattern. Flaws inside the particle determine the final fragment size distrrbution by fracture, because they give rise to multiple branching of the propagating crack [17]. 2.2. Energy-size reduction law
s m
WV, 0 af
-
=
-S(v)q(v,
t) +
p(v, v’)S(v’)q(v’,
t) dv’
(8)
v
Here q(v, t) is the volume concentration of particles of volume V, and p(v, w’) is the breakage drstribution functron. For non-eroding particulate systems, B(v, v’) is usually normalized with respect to parent agglomerate size, i.e. P(v, 2)‘) = P(V/V’)
powders. For eroding powders, the breakage distribution function cannot be normalized because the size of the resulting primary particles is invariant with respect to parent agglomerate size. Here, however, the energy consumption can be related to the production of fines. 2.2.1. Non-eroding powders
In the self-preserving limit, the average particle size changes with time according to Kapur [20]: -d&SO = -AKd,(ty dt
(9)
This may be the result of the similarity of the fracture pattern in particles of different sizes [19]. For such a normalized breakage distrrbution, a self-preserving solution for Eq. (8) has been formulated by Kapur [20]. The self-preserving particle size distribution is usually obtained after a short period of grinding. In the selfpreserving limit, the particle size distribution does not change its form relative to the mass mean diameter, d,. An expression for the reduction in average particle size is available [20]. This expression will be utilized to derive an energy-size reduction law for non-eroding
+
l
where K is a constant determined by the functional forms of the particle size dependency of the fragmentation rate and breakage distribution functions. If the breakage distribution function does not change with power input, K is also invariant to changes in E. For the particular case in which the cumulative fragment size distribution, B(v, v’), is represented by the following power law expression: b
(11) and a = 1, K equals 1/3b. Here we introduce the reduction sionless time 7 as: R_
T=
The fragmentation expression, Eq. (6), is used in the general grinding equation [18] to describe the ultrasonic fragmentation of agglomerate particles:
255
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d”do) 440
ratio R and drmen-
(12)
S[d,(O)]t = Sot
(13)
Substitution of Eqs. (12) and (13) into Eq. (10) and setting a = 1 yields: dR -=
dr
(14)
-K
Integration of Eq. (14) over T in the self-preserving limit gives: R(T) =K(T-
7,) + R(q)
(15)
where rs denotes the time to reach the self-preserving state. For most fragmentation processes, the self-preserving state is attained very raprdly, so T,+O [20]. In that case Eq. (15) can be approximated by: R(T) =KT+ 1
(16)
This grinding law in time domain can be transformed to the energy domain by recognizing that: E(f) = Et
(17)
where E is the consumed ultrasonic energy. Combining Eqs. (7), (12), (13), (16) and (17) gives: [R(t) E(t)= 620VtotEO Kd,(o)
_
11
(18)
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Kusters et al I Powder
Divrding Eq. (18) by the total particle mass ( = p,C, V,,,) gives for the energy consumption per umt particle mass, E,: E,,,(t) = 620 KPP;;m(o) =KJ
1 d,(t)
P(t)-
11
1 - L(O)
(1%
The specific surface area (surface area per unit particle mass), a,, is inversely proportional to average particle size, i.e. uv~dmml. Hence Eq. (19) can be rewritten as:
Technology 80 (1994) 253-263
where x(21’) denotes the volume percentage (fraction) of fine fragments resulting from break-up of agglomerates of size v’, and vp,max represents the upper boundary for the fine fragment size drstribution. Erosion has been shown to be proportional to external agglomerate surface area [ll]: x(z)‘)= --& Substitution
or
x(d’) = g
(23)
of Eqs. (7) and (23) mto (22) yields: q(v’, t) dv’
(24)
vp, msx EO 62 Em(t)
=
620
The integral on the right-hand side equals (1 -f,) C,, where f, denotes the erosion product fraction. Since f,= C,/C,, Eq. (24) reduces to:
&&d,,,(O)
(20) y
Eq. (20) implies that for a constant ultrasonic power input, the specific surface area of the powder increases proportionally to energy expense. Furthermore it shows that more energy is needed to obtain the same increment in surface area at a higher power input. This is in contrast with conventional grinding techniques like ball milhng, where the size reduction is only dependent on the energy expense but not on the applied power [21]. 2.2.2. Eroding powders In the case of erosion, the breakage function is expressed as [22,23]: P(V, 2)‘) =x(z)‘)w(2)) + [l -x(v’)]n(v,
V’)
t) dv’
Integration 1 -&(t)
of Eq. (25) with f,(O) =0 yields:
= exp( --AS)
(26)
Combmmg Eqs. (7) (13), (23) and (26) gives: 1 -f,(~-) = exp( --x07)
(27)
where xo=x[d,,,(0)]. Combining Eqs. (7), (17) and (26) gives, for the energy-agglomerate fraction relationship for eroding powders:
distribution E(t) = - 620 !L?$Y (21)
where x(v’) 1s the mass fraction of produced fines, w(v) represents the fine fragment size distribution and Qv, v’) the size distribution of the coarse fragments. The coarse fragments may result from additional fracture. Hence the coarse part of the breakage drstributron function may again be normalized. With this provision, a particle size reduction law similar to Eq (14) can be derived for eroding powders. However, the particle size reduction becomes a function of the amount of erosion product, which also changes with time. This prevents a simple relationship between energy consumption and size reduction. With erosion, however, it is more appropriate to define the energy consumption with respect to the produced fine fragments rather than the degree of size reduction. If the size distributions of the fine and coarse fragments do not overlap, the increase in the amount of erosion product, C,, is given by:
x(v’)S(v’)q(v’,
=AH(l -f,(t))
(22)
ln(l -_f,)
Hence the energy consumption E,, is given by E,,,(t) = - 620 &
ln(1 -f,) P s
(28) per unit particle mass,
(29)
3. Experimental The above equations are based on the inherent assumption that the fragmentation rate 1s independent of particle concentration This assumption, however, is expected to break down when the particle concentration approaches unity. It is important to establish the particle concentration range for which Eqs. (18) and (28) are applicable. Furthermore, the dependency on total suspension volume stems from theory but has not been thoroughly investigated experimentally. Experiments were conducted to elucidate the effects of these process variables on fragmentation. The experimental data comprise the ultrasonic fragmentation of silica and titania powders made by wet chemistry techniques [8,9]. These powders were sub-
K.A
Kusters et al. / Powder
sequently heat-treated and ground in a mortar until they passed a 105 pm sieve. The silica prunary particles were made by the Stober process [24]. The titania primary particles were produced by thermal hydrolysis or by base precipitation from a tltania solution (1.0 M TiOz and 3.8 M H,SO,) and will be termed hydrolyzed and base-precipitated titania, respectively. Experiments were also conducted with a commercially available zu-conia powder. Sample suspensions were prepared from these powders in a total volume of 40 and 120 cm3 of 0.05 wt.% sodiummetaphosphate-water solution. Ultrasonic fragmentation was accomplished with a 20 kHz Tekmar TSD500 Sonic Disruptor equipped with a VlA horn with OS-inch tip in a water-jacketed glass sonication vessel. Thoma et al. [6] calibrated the ultrasonic force field with hollow glass bubbles of known compression strength. This calibration gave the effective break-up pressure of the collapsing cavities as a function of power input. The applied cavitation pressure varied from approximately 20 to 800 bar between the lowest (2.5 W) and the highest (100 W) power setting of the ultrasonic device. The temperature of the suspension was maintamed at 25 “C with the use of a water bath. The agglomerates were kept m suspension by magnetic stirring The evolution of the particle size distribution during ultrasonic treatment was measured using a Micromcritics Sedlgraph 5100 particle size analyzer. Sedimentation of the particles in the sample suspension 1s measured by X-ray transmission. This particle size analyzer yields mass distributions, Q(r), over 250 geometrical sections in a user-selected size range, usually from 0.1 to 100 pm.
Technology 80 (1994) 253-263
257
100 r
g? -
80
o untreated
OL 05
1
10 Parttcle diameter
(t - 0)
100 (urn)
Fig 1. Cumulative mass dlstrlbutlons of sihca powder (prmary particle size= 1 pm), ultrasomcally treated for 30 mm at 2 5 W m 40 cm3 suspensions of variable sohds concentration The size dlstrlbutlon of the ongmal powder IS also mdlcated
was produced by the grinding process. For solids concentrations of 5, 25 and 50 wt.%, there 1s an identical increase in the percentage of primary particles, namely up to 60%, by ultrasonic treatment. At the same time, the agglomerate size distribution shifts to lower particle size values. Only the result at a solids concentration of 75 wt.% deviates from this behavior. The 75 wt.% suspension was very viscous, and magnetic mixing was insufficient to wet the ultrasonic probe. A small volume around the probe was de-watered, thereby making impossible the proper transmission of ultrasonic waves into the suspension. This explains why no fragmentation was observed with the 75 wt.% solids suspension. At the lower concentrations the suspension is nonviscous and mixing is unhindered. As a result, the breakage rate is independent of solids concentration up to 50% by weight, in agreement with theory.
4. Results 4.1. Effect of solrds concentration
To examine the effect of solids concentration, suspensions of 5, 25, 50 and 75 wt.% solids were treated at a power input of 2.5 W for 5, 10 and 30 min in a 40 cm3 container. The powder that was used consisted of agglomerates (d,= 19.4 pm) of 1 pm silica spheres that were produced by heat treatment at 1100 “C for 5 h. With p,=2000 kg/m3 181, the applied solids concentrations correspond to 2.5, 14, 33 and 60 vol.%, respectively. Fig. 1 presents the cumulative mass distribution curves for each of the suspensions after 30 min of ultrasonication. The steep rise in the curves at a particle size of 1 pm represents the fine fragment peak, whereas the moderate rise starting at approximately 10 ,um corresponds to the agglomerate fraction of the size distribution. There is already a fan amount (ca. 40%) of primary particles present in the ongmal sample which
4.2. Effect of suspension volume Experunents were conducted to elucidate the effect of suspension volume on the ultrasonic fragmentation rate. Base-precipitated titania agglomerates ([9], d,= 22.4 pm) were ultrasonically treated at 2.5 W in 40 and 120 cm3 suspensions. Fig. 2(a) shows that the reduction ratio increases with time faster at the small than at the large suspension volume for equal power input, as predicted by Eq. (6). When these data are plotted as a function of dimensionless time they collapse on a single line, as predicted by Eq. (16), providing further validation of the proposed model. From this analysis we may conclude that the course of the fragmentation process is unaffected by the scale of operation at equal values of the power input per umt volume of suspension. For a constant solids concentration, the power input per unit mass of solids may be used as a scaling parameter
258
IL4 Kusters et al I Powder
0
100
Grinding
200
0
40 ml
7
120 ml
300
Technology 80 (1994) 253-263
J 10
400
25
Reckon
Time (mm)
ratio, it/d)
Rg. 3 Energy consumptton, E, versus size reduction, R for ultrasomc fragmentation of hydrolyzed tltama powder at 25 and 5 W m 40 cm3 suspension of 2.5 ~01%
I
I
I?
p20 Ii
i
h 1.5 4 1.0 q 0
@I 2
Dimensionles~Tlme, 4
10
&s, t
Fig 2. Reductzon factor, R, versus (a) time, t, m mmutes and (b) dlmenslonless time, T, for ultrasomc treatment of base-preapltated C, = 2 5 tltarua powder at 2 5 W m 40 and 120 cm3 suspensions.
vol % 4.3. Energy-sue reduction laws
4.3.1. Non-eroding powders Experimental data on non-eroding thermally hydrolyzed trtama powder [9] were also analyzed. The cumulative fragment size distribution of these powders (d,,,(O) = 12.3 Frn) is normalized and can be described by Eq. (11) with the power law exponent b= 1 [ll]. The size spectra of this powder become self-preserving after a short period of ultrasonic fragmentation. The self-preservmg drstribution is independent not only of the initial size distribution but also of the applied power input. Fig. 3 shows the energy consumption, E, versus size reduction, R, at an ultrasonic power input of ~=2.5 and 5 W. A linear relationship between E and R is obtained, as predicted by Eq. (18). The slopes of the lines in Fig. 3 amount to 9.3 and 14.0 kJ for E= 2 5 and 5 W, respectively. According to Eq. (18) these values are obtained with K=0.37, i.e. a power law exponent, b, equal to 0.9, in close agreement with the previous experimental result. Eq. (18) is only valid if attainment of the self-preserving state is fast. Analysis of the evolution of the measured size distributions showed that this is indeed the case for the hydrolyzed titania [ll].
The hydrolyzed titania powder displayed a distinct time lag prior to fragmentation [ll]. This time lag results m a non-zero abscissa with the vertical axis at R=l in Fig. 3. 4.3.2. Eroding powders Experimental data from fragmentatron of eroding silica [8] and zirconia powders were used to evaluate the functional form of the relationship between the energy consumption and the fraction of produced fines. The silica agglomerates (d,=31.0 pm) consisted of monodisperse spherical primary particles of about 0 3 pm. Fig. 4(a) is a representative scanning electron micrograph SEM of a zirconia agglomerate. The debris on the surface of the agglomerate is the fines that were already present in the untreated powder. They may have resulted from grinding steps in the process of the zirconia powder production. Fig. 4(b) 1s a larger magnification of these particles, which were also of the order of 0.3 ,um but irregular in shape. Fig. 5 shows the evolution of the size distribution of the silica powder at an ultrasonic power mput of 20 W. Ultrasonic treatment results m the formation of a bimodal distribution with a distinct separation between the agglomerate and fine fragment size modes. With increasing processing time, the agglomerate size distribution shifts to lower particle sizes and shrinks in magnitude. The erosion of agglomerates results m the production of fine fragments, as reflected by the increase in the second mode of the size distribution around a particle diameter of 0.3 pm and the final extinction of the initial agglomerate mode. The fraction of primary particles (fine fragments), f,, was calculated by: vp milx s
q(v, t)dv
fpW= $
Jq(v t)dv -0
(30)
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et al / Powder
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0
5
25
Frg 6 Decrease m fraction of agglomerates, 1 -f,, m sihca powder as a functron of dtmensronless trme, r, for vartous power settmgs of ultrasomc devrce
24
ot-
z
0
z20 5 6 1 6 2 212 ; 7J < 0.6 5 0.4 Z ‘00 01
1 Partlcle diameter
(pm)
Frg 7 Evolutron of partrcle srze drstrrbutton, Q(L), of zucoma powder at E= 20 W m 40 cm3 suspensron of 2 5 vol % Partrcle srze range m Sedrgraph IS from 0 15 to 1013 Frn Ftg 4. Scanmng electron mrcrographs of (a) zrrcoma agglomerate and (b) prrmary parttcles of employed zucoma powder
0.1
1 Partlcle diameter
IO (pm)
100
Frg 5 Evolutron of parttcle size dtstrrbutron, Q(r), of srhca powder (prtmary parttcle srze = 0 3 pm) at e=20 W in 40 cm3 suspension of 25 ~01%. (-o-) t=O, (-+-) t=15 mm, (u) t=30 mm., (-V-) t =45 mm, (-A-) t=60 mm , (t) t =90 mm
The upper boundary of the silica fine fragment srze drstribution, d,, ,_, was taken as 1.0 pm, i.e. v,, max= (7r/6) pm3. Fig. 6 shows the corresponding decrease in the fraction of agglomerates, 1 -f,, with processing
time, together with the experimental data for other ultrasonic power inputs: E= 2.5,5, 20 and 55 W. These data are in excellent agreement with the present theory, Eq. (27) for x,=0.1. Fig. 7 shows the change in the particle srze distribution of the zirconia powder (d,(O) = 4.5 pm) under ultrasonic treatment at l=20 W. A behavior similar to that of the sihca powder is observed. The agglomerate and fine fragment modes, however, start to overlap, resulting in a less accurate determination of the fraction of produced fines. As the particle size corresponding to the mmrmum between the two modes seems to be independent of processing time, this value (1.0 pm) was used as d p,maxto determine the fraction of produced fines. Fig. 8 shows the calculated fraction as a function of dimensionless time, 7, for various ultrasonic power inputs. Again, an exponential decrease in the fraction of agglomerates, 1 -f,, is obtained, similar to Eq. (27) with x0 = 0.2. As follows from the constant values for x0 of both powders, the erosion amount is independent of applied ultrasonic power input. The parameter x,, appears to be merely a powder characteristic.
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--._ --._ -..1 -
Ball Mllmg (Rtttmger) Ultrasomc
L
5
5
_-
