technique, sample preparation and presentation to the optical system is a critical element of the analysis .... Size (D50 ,µm by laser diffraction). 6.45. 5.1. 5.35.
A PRELIMINARY INVESTIGATION CONCERNING THE EFFECT OF PARTICLE SHAPE ON A POWDER’S FLOW PROPERTIES By: Mark Bumiller Malvern Instruments, Inc. Vice President
John Carson, Ph.D. Jenike & Johanson, Inc. President
James Prescott Jenike & Johanson, Inc. Senior Consultant
Introduction The particle size distribution and shape of powders and suspensions can affect basic unit operations including size reduction, classification, mixing, filtration, crystallization, and flow through hoppers and Y-branches. As a result, particle characterization is often demanded by regulatory agencies and purchasing contracts. Everything from incoming raw materials to final products may have size specifications, and once a size specification is written the material must be carefully analyzed in an analytical laboratory that typically contains one or more particle characterization techniques for determining the size distribution, shape and flow characteristics of powders, suspensions and emulsions. Recently, attention has been given to trying to understand the complex relationship between particle size, shape, and powder flow (1). Powder flow is a complex subject, influenced by other factors besides particle size and shape, including density, moisture content, temperature, consolidation pressure, and time of storage at rest (2). Although shape is expected to influence powder flow, the relationship between size, shape and flow is not thoroughly understood, especially in the fine particle regime below 15 µm. To further complicate the situation, the shape of the particles also influences the size measurement, and is dependent on the sizing technique used for the analysis. The effect of particle shape on size measurements Many different sizing techniques are used and shape affects each differently. Several researchers have investigated how the shape of particles influences size analysis results (3,4). The differences are often accentuated at the tails of the distribution – the D10 and D90 more than at the median, the D50. Since the differences appear at the tails of the distribution, the spans (defined as (D90-D10)/D50) are often dissimilar. Consider the example of needle shaped particles measured by sieves and a light scattering system (sometimes called laser diffraction). Depending on both the aspect ratio and the size of the longest dimension, the fibers will often tumble through the laser beam at random orientations to the light source. At times the laser sees the maximum projected area, at other times the minimum projected area (essentially a sphere with a diameter equal to the thickness of the needle) and every orientation in-between. Therefore the distribution recorded by this technique could be a broader distribution than results measured by sieves, microscopy or other techniques. Using light scattering to measure shape Light scattering can also provide morphology data for certain specific particle shapes. Several researchers (5,6) have described techniques for determining a shape characteristic known often as the chunkiness ratio for plate-like particles. In addition to the size distribution,
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instruments can take a zero angle turbidity (obscuration) measurement that can be used to calculate the volume concentration of particle present using the following equation derived by combining the Mie theory of light scattering with the Beer-Lambert law: c=
100 loge (1- Obscuration) -3 ViQi b∑ 2 di
(1)
where c is the concentration (%), b is the beam length, Vi is the volume in size band I, Qi is the extinction coefficient of size band I and d i is the mean diameter of size band I. The extinction coefficient is a measure of how efficient a particle of a particular size is at scattering light. Equation (1) shows the relationship between volume concentration and the obscuration measured as part of a normal experiment and is quite accurate for nearly spherical particles. As particles become less spherical and more plate-shaped, errors in the calculated volume concentration arise from an increase in obscuration observed from plate shaped particles when compared to an equal volume of a spherical material. The ratio between the actual volume concentration and the volume concentration calculated by the particle size analyzer is used to calculate a three-dimensional shape value known as the chunkiness ration as shown in equation (2). Chunkiness ratio =
Ds 0.5 h
(2)
Where Ds0.5 = Median diameter of the distribution based on surface area h = Thickness of the plate The chunkiness ratio and thickness of plate-shaped particles can be determined through a relatively simple experiment by weighing a sample of known density and adding this sample to a known volume of diluent in the analyzer. This same experiment can be performed on more spherical particles as a method to confirm the choice of refractive index for the sample material. A more accurate choice of refractive index will result in a more accurate calculated volume concentration. There is a long tradition of interpreting a plot of light intensity versus scattering angle to obtain shape information on particles (7). The shape of the curve has been used to provide information on polymer conformation, and derivatives such as the Guiner plot (for globular structures), the Kratky plot (for Gaussian coils and chains) and the bending rod plot for semi flexible chains. The same idea has now been applied to examining the structure of aggregates to obtain the fractal dimension. Raper and Amal (8,9) have published numerous articles where light scattering instruments were used to quantify the fractal numbers of floc structures. The fractal number then comes from the negative slope of the linear portion of a log-log plot of scattering intensity versus wave number. These studies have proven useful for characterizing flocculated systems where fractal numbers provide important information in addition to the size distribution. A loose aggregate will have a low fractal dimension, while a more compact aggregate will have a higher fractal dimension.
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Other particle shape measuring techniques Although light scattering instruments can provide useful shape information in a few specific circumstances, this is not a common technique used by industry. Particle shape analysis is commonly performed using a variety of techniques including microscopy, image analysis and other automated or semi-automated optical techniques. Just as a variety of methods are used for particle shape analysis, a plethora of calculations are currently used in attempts to quantify the shape of particles (10). Unfortunately, there is little harmonization in the world of particle shape characterization. Although microscopy can be used for qualitative particle shape analysis, image analysis is often required to automate the complex task of assigning shape values to large numbers of particles. Both microscopy and image analysis investigate particle morphology by examining the two dimensional projection of the particle. As with any particle characterization technique, sample preparation and presentation to the optical system is a critical element of the analysis routine. One reason light scattering systems are affected by particle shape is the fact that particles moving through the optical system in turbulent flow typically arrange themselves in random orientation to the light source and detection system. This “tumbling” effect results in particles exposing their minimum and maximum projected areas to the instrument optics (along with every other conceivable orientation). This random orientation broadens the reported size distribution. Since random particle orientation causes difficulties when analyzing particle shape, it follows that it would be beneficial to align the particle flow through an automated image analysis system. The flow particle (wet) image analysis data presented in this study was collected on a Sysmex FPIA-2100 image analysis instrument where the particles are suspended in a liquid and hyrodynamically focused through a shear cell during data acquisition. Since the particles are subject to shear forces in the cell, the maximum projected area is exposed to the imaging camera for analysis. Particles were assigned both a particle size and shape value. The size is an equivalent spherical diameter and the shape number is the circularity defined in equation (11) below. Circularity = perimeter of circle w/same area (11) image perimeter of particle outline Some powders are best analyzed in their natural dry state. The dry image analysis data in this study was generated using a Pharma Vision 830 system that uses a sample preparation device that disperses the particles evenly and randomly on a glass slide or plate. T he slide is then placed on a bench where the objective stages across the sample area and collects the images for analysis. One of the shape values assigned by this system is defined as roundness. Roundness is a measurement of the length – width relationship, with a value in the range [0.0, 1.0]. A perfect circle has roundness 1.0, while a very narrow elongated object has roundness close to 0. Intuitively the roundness is a comparison between the “strength” of the major axis and the “strength” of the minor axis. For a circle or a square, the “strength” of the major and minor axis is about the same. However, for a rod shaped object the “strength” of the major axis is considerably greater than the “strength” of the minor axis. Formally, this roundness R is defined as:
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R = λ 1 − λ 2 λ 1 + λ 2
(12)
where λ1 and λ2 are the eigenvalues of the covariance matrix M. I xx I xy M = I xy I yy I xx = ∑ xi x j
(13) (14)
i, j
I xy = ∑ xi y j
(15)
I yy = ∑ yi y j
(16)
i, j
i, j
where xi and yi are the co-ordinates of pixel pij of the object relative to the center of gravity of the object. The major axis of the object is the eigenvector of the maximum eigenvalue of matrix M, and is essentially the principal component of the object. Powders studied The materials studied in this investigation are glass spheres, calcium carbonate crystals and plate-shaped talc powders (shown in Figures 1, 2 and 3). These powders are similar in size but have quite different morphologies. They also are quite different in particle hardness. Glass is roughly six times as hard as talc on the moh scale. Calcium carbonate is roughly in the middle between these two extremes.
Figure 1: Glass Spheres
Figure 2: CaCO3
Figure 3: Talc
The size distributions were analyzed using light scattering (Malvern Mastersizer2000) and, both wet (Sysmex FPIA) and dry (Pharma Vision 830) image analysis. Particle shape is defined by circularity described in equation (11) and roundness as described in equation (12). The chunkiness ratio and thickness of the talc sample was determined using the Malvern Mastersizer2000 as described earlier in this paper. Table 1 summarizes the size and shape characteristics of the powders in this study and Figures 4 and 5 present size and shape summaries.
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Glass Calcium spheres carbonate 0.914 0.808 0.902 0.677
Circularity (wet image analysis) Roundness (dry image analysis)
Talc 0.626 0.575
Size (D50 ,µm by wet image analysis)
6.44
5.75
4.97
Size (D50 ,µm by dry image analysis)
8.44
5.912
7.79
Size (D50 ,µm by laser diffraction) Chunkiness ratio Thickness
6.45
5.1
5.35 2.44 1.88
Table 1 Dv50 by Technique 9 8 7 6 5 4 3 2 1 0
wet image analysis dry image analysis laser diffraction
Glass
CaCO3
Talc
Figure 4
Circularity/Roundness 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
Circularity (wet image analysis) Roundness (dry image analysis)
Glass spheres
Calcium carbonate
Talc
Figure 5
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After determining the size and shape distributions of the samples, the powders were exposed to a series of powder flow tests to investigate any possible relationships between particle shape and flow properties. Characterizing powder flowability The term “powder flowability” can be thought of simply as the ability of a powder to flow. Using such a definition, powder flowability is sometimes thought of as a one -dimensional characteristic of a powder, whereby powders can be ranked on a sliding scale from “freeflowing” to “non-flowing”. Unfortunately, this simplistic view lacks science and understanding sufficient to address common problems encountered by the formulator and equipment designer. Flowability is not an inherent material property, but the result of the combination of material physical properties that affect material flow AND the equipment used for handling, storing, or processing the material. Equal consideration must be given to both the material characteristics and the equipment. The same powder may flow well in one hopper but poorly in another; likewise, a given hopper may handle one powder well but cause another powder to hang-up. Therefore, a more accurate definition of powder flowability is the ability of powder to flow in a desired manner in a specific piece of equipment. The specific bulk characteristics and properties of a powder that affect flow, which can in principle be measured, are known as flow properties. These flow properties refer to the behavior of the bulk material, and arise from the collective forces acting on individual particles, such as van derWaals, electrostatic, surface tension, interlocking, friction, etc. For more information on underlying particle properties that contribute to flow behavior, refer to Rumpf (11), or more recently, Podczeck (12). Armed with the flow properties of a powder, engineers can optimize the selection of transfer equipment. These same properties can be used as a basis for retrofitting existing equipment to correct flow problems. Formulators can use these properties during product development, to predict flow behavior in existing equipment. The flow properties that are generally of most interest include: Cohesive Strength. The consolidation of powder may result in arching and ratholing within transfer equipment. These behaviors are related to the cohesive strength of the powder, which is a function of the applied consolidation pressure. In a lab, cohesive strength can be measured accurately by a direct shear method. The most universally accepted method utilizes the Jenike shear tester and is described in ASTM standard D 6128 (13). By measuring the required shear force for various vertical loads, a relationship describing the cohesive strength of the powder as a function of the consolidating pressure can be developed (2). This relationship, known as a flow function, can be analyzed to determine the minimum outlet diameters for bins, press hoppers, blender outlets, etc. to prevent arching and ratholing (14). Internal Friction. Internal friction values are important when characterizing the flow properties of a powder. Such friction is caused by solid particles flowing against each other, and is expressed as an angle of internal friction. This angle can be measured via the cohesive strength tests described above.
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Wall Friction. Used in a continuum model, wall friction (or particles sliding along a surface) is expressed as the wall friction angle or coefficient of sliding friction. The lower the coefficient of sliding friction, the less steep hopper or chute walls need to be for powder to flow along them. This friction coefficient can be measured by sliding a sample of powder in a test cell across a stationary wall surface using a shear tester (2, 13). The coefficient of sliding friction is the ratio of the shear force required for sliding to the normal force applied perpendicular to the wall material coupon. A plot of the measured shear force as a function of the applied load generates a relationship known as the wall yield locus. This flow property is a function of the powder handled and the wall surface in contact with it. Variations in the material, or the wall surface finish, can have a dramatic effect on the resulting friction coefficient (15). Wall friction can be used to determine the hopper angles required to achieve mass flow. Bulk Density. The bulk density of a given powder is not a single or even a dual value, but varies as a function of the consolidating pressure applied to it (2,14). By measuring the degree to which a powder compacts as a function of the applied pressure and expressing the results as a straight line on a log-log plot, the slope of this line represents the material’s “compressibility”. The resulting data can be used to accurately determine capacities for storage and transfer equipment, as well as to provide information to evaluate wall friction and feeder operation requirements. Permeability. Flow rate limitations may occur when handling fine powders, due to the expansion and contraction of voids during flow creating air pressure gradients within the powder bed. The permeability of a powder, or its ability to allow air to pass through it, will have a controlling effect on the discharge rate that can be achieved. Permeability is measured as a function of bulk density (2). The method typically employed involves measuring the flow rate of air at a specific pressure drop through a sample of known density and height. Once this relationship is determined it can be used to calculate critical powder discharge rates that will be achieved for steady flow conditions though various orifice sizes. Test results and analysis All tests were run at room temperature on samples at their as received moisture content (0.3% for talc, 0.1%. for the other two). Only continuous flow conditions were analyzed. Wall friction was measured on a coupon of 2B finish stainless steel sheet. The flow tests results can be summarized in many different ways. Cohesive strength can be used to calculate the minimum outlet diameter, BC, in a conical mass flow hopper to prevent arching. A powder’s bulk density/pressure relationship can be described either by the range of bulk density values or by the slope, β, of this relationship on a log-log plot. Wall friction can be represented by the recommended hopper wall angle θc (measured from vertical) to achieve mass flow in hopper fabricated from the tested wall material and for a particular outlet size (chosen at 12 in. for Table 2). A powder’s permeability can be used in conjunction with its bulk density/pressure relationship to calculate critical steady state flow rates through the outlet of a mass flow hopper. An outlet size of 2 ft. and an Effective Head of 5 ft. were used to tabulate the values in Table 2. Finally, a powder’s internal friction can be represented by its effective angle of internal friction, δ. Using these means to characterize the flow properties of the powders studied, the results are shown in Table 2.
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Talc Calcium Carbonate BC (ft.) 0.4 0.6 Bulk density range [pcf] 13 to 43 35 to 75 0.16 0.11 β 4* 12 θc [deg] Critical flow rate [tph] 0.3 9.1 35 38 δ [deg] *Flow questionable along any sloping hopper surface Table 2
Glass Spheres 0.1 53 to 84 0.06 23 2.8 36
Looking at this data in an attempt to find possible correlations between flow property values and particle size or shape, several hypotheses can be developed: 1. The higher the mean circularity the lower the wall friction angle, and hence the larger θc. This relationship holds for the three materials tested on 2B finish stainless steel sheet. It seems reasonable to expect that more spherical particles are, in general, less frictional. However, particle hardness may also be affecting this correlation, since the hardness of these three materials increases as mean circularity increases. Since harder particles deform less under load, their surface area in contact with the wall surface may be less than with softer particles. If so, this would result in lower wall friction and in turn, larger values of θc. 2. The higher the mean circularity the lower the value of β. This relationship holds for all three powders studied. While there is some reason to expect that more spherical particles may be less compressible, a stronger driving force is probably particle hardness. 3. The higher the mean diameter the higher the permeability, and hence the higher the critical steady state flow rate. This relationship does not hold well for all three materials. While the talc has the smallest mean diameter and the lowest critical flow rate, the glass spheres have the highest mean diameter but a lower critical flow rate than the calcium carbonate. The calcium carbonate has an intermediate value of mean particle diameter but the highest critical flow rate. Undoubtedly, there are other variables besides mean diameter that affect critical flow rate, e.g. the complete particle size distribution, compressibility, cohesiveness, and more. It is also important to bear in mind that the differences in mean particle diameter between the three powders studied are quite small. 4. The higher the mean circularity the higher the critical steady state flow rate. As with hypothesis 3, this works well for the talc (lowest mean circularity, lowest critical flow rate), but not for the other two. 5. The higher the mean circularity the lower the cohesive strength, and hence the smaller the value of BC. This works for the glass spheres (highest circularity, smallest BC), but does not work for the other two powders that were analyzed. Undoubtedly, there are other significant factors besides mean circularity that affect a powder’s cohesive strength.
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6. The higher the mean particle diameter and the lower the particle diameter standard deviation, the higher the critical flow rate. There is too little data to evaluate this hypothesis. Conclusions This study has focused on three powders having approximately the same particle size but quite different shapes. We have found a possible correlation between mean circularity and two measures of powder flowability: wall friction angle and compressibility parameter β. Correlation with other measures of flowability were either very weak or the data was too limited. Clearly, much more data of this type must be generated before any firm conclusions can be drawn. However, it is encouraging to see the possible correlations that have been developed so far. Acknowledgements The authors wish to thank Specialty Minerals of Bethlehem, PA for donating the calcium carbonate used in this study and Luzenac of Englewood, CO for donating the talc sample. References 1. F. Podczeck, Y. Miah, “The influence of particle size and shape on the angle of internal friction and the flow factor of unlubricated and lubricated powders”, Int. J. Pharm., 144 (1996) 2. J.W. Carson and J. Marinelli, “Characterize Bulk Solids to Ensure Smooth Flow,” Chemical Engineering, 101 (4), 78-90 (April 1994). 3. M. Naito et. al, “Effect of particle shape on the particle size distribution measured with commercial equipment”, Powder Technology, 100 (1998) 4. B. Kaye, D. Alliet, L. Switzer, C. Turbitt-Daoust, “The effect of shape on intermethod correlation of techniques for characterizing the size distribution of powder”, Part. Part. Syst. Charact., 14 (1997) 5. Baudet, G., M. Bizi, J. Rona, “Estimation of the average aspect ratio to lamellae-shaped particles by laser diffractometry”, Part. Sci. & Technol., 11 (1993) 6. Lips, A., Hart P., Evans D., Proceedings to the fifth European symposium in particle characterization (1992) 7. Denkinger, P., Burchard, W., J. Polymer Science, Part B, 29 8. Jung, S., Amal, R., Raper, J., Part. Part. Syst. Charact., 12 (1995) 9. Bushell, G., Amal, R., Raper, J., Part. Part. Syst. Charact., 15 (1998) 10. F. Podcek, “The Shape of Powder particles and its Influence on Powder Handling, IFPRI Review Report (1999)_ 11. H. Rumpf, and W. Herrmann, “Properties, Bonding Mechanisms and Strength of Agglomerates,” Processing Preparation, 11 (3), 117-127, (1970). 12. F. Podczeck, Particle-particle Adhesion in Pharmaceutical Powder Handling, (Imperial College Press. London, 1998). 13. Standard Shear Testing Method for Bulk Solids Using the Jenike Shear Cell, ASTM Standard D6128-97, American Society for Testing and Materials (1998).
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14. A.W. Jenike, Storage and Flow of Solids (Bulletin 123 of the Utah Engineering Experimental Station), 53 (26), (1964, Revised 1980). 15. J.K. Prescott, D.A. Ploof and J.W. Carson, “Developing a Better Understanding of Wall Friction,” Powder Handing and Processing, 11 (1), 27-35 (January/March 1999).
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