Inter-Particle Forces in Powder Flow

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H M Pollock, R Jones, D Geldart and A Verlinden
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Powder Flow
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United Kingdom


The aim of this Lancaster University-Bradford University collaborative project was to understand the forces between a variety of dry materials at the single-particle level, to relate these to complementary bulk powder flow measurements, and hence to assess how far such-single particle data are able to predict flow behaviour of real value to chemical engineers. In particular, the objectives may be summarised as follows: • At Lancaster, to investigate the forces acting between single dry particles in simple model systems, using atomic force microscope technology; • to acquire a force-curve data bank, using mostly materials already well studied in bulk cohesion testers or of particular interest to IFPRI members; • at Bradford and elsewhere, to standardise the bulk cohesion measurements in an annular shear cell, and to compare the results with those obtained using a variety of other testers; • at Bradford and Lancaster, to clarify the role of particle size and morphology, relative humidity and powder-wall adhesion effects, in the bulk flow behaviour of cohesive powders. For the single-particle work it was necessary to design and construct the required humidity control system within which the atomic force microscope could be operated. Much of the data took the form of normal force as a function of separation between the two surfaces. In addition we broke new ground in devising a reliable method of measuring lateral force (friction) at the single-particle level. To help confirm the basis of theoretical interpretation, simple model systems were studied first, followed by cohesive powders of current interest. Values of pull-off force were surprisingly similar for a range of materials, and strong humidity-dependence was the exception rather than the rule. In the case of alumina, no particle size effects were apparent, in contrast with cohesion test results. Surface treatments of glass or silica- based materials produced clear differences, but not in the case of titania. Clear increases in adhesion were seen for particle-wall contacts in alumina and limestone (in agreement with suggestions from cohesion test results), but not with most of the other materials studied. The data obtained by means of our new single-particle friction technique gave a wealth of information on linear and non-linear load-dependence, the nature of the inter-particle contact (single- or multi-asperity), the occurrence of stick-slip behaviour, and the relevance or otherwise of adhesion in determining friction. In general, the friction technique was considerably more effective in detecting differences in the behaviour of different materials than the normal force curve technique. The Warren Spring-Bradford Cohesion Tester – an annular shear tester - was selected to measure the bulk cohesion of the selected powders. Further study of the topic of bulk powder testers, however, revealed not only that many shear testers are available today but also that the design, measurement procedure and interpretation are topics of great discussion and controversy. For this reason, the programme of bulk powder measurement (unconfined yield strength versus major consolidation stress) were extended to form an experimental study of three different shear testers for measuring the flow properties of bulk solids. A large amount of flowability and cohesion data has enabled us to present a rigorous qualitative comparison of five different types of testing device.

We have attempted a quantitative, if somewhat over-simplified, link between the single-particle and bulk studies. This involves, in the first instance, the simulation of yield loci, making allowance for particle size effects in any approximation of average force per particle in the bulk cohesion experiments. Thus, we have attempted to predict, from single particle normal and friction forces, the results of bulk experiments by suitable scaling, and compare them with the actual bulk data. This has involved deriving a suitable model, and has enabled us to determine the limitations and advantages of the two contrasting testing techniques (atomic force microscope-based and bulk). The single-particle AFM technique is good for the rapid screening of many powders for sensitivity to humidity, and appears to be well suited to studying particle-wall friction: this is important in powder flow where the internal cohesion of the powder is high in comparison with its adhesion to walls (leading to “plug flow”). The roughness studies possible with the AFM are also highly relevant to wall friction and the internal cohesion of powders. However, with the bulk cohesion, particle size effects and consolidation effects, the AFM fails to see many phenomena of interest to chemical engineers simply because they appear to be controlled overwhelmingly by particle geometry rather than the adhesion of single contacts. The single-particle type of experiment is found to explore only the first part of the corresponding bulk experiment, near the origin of the data plots. By plotting the bulk cohesion data as average force/particle rather than as force/unit area, most of the differences between the two types of data disappear. For the finest particles (e.g. 2-4 µm limestone), the average forces per particle coincide between the two types of experiment. Fortunately, many fine powders of interest have particle sizes in the range where overlap occurs and interesting comparisons can be made. Thus, the two experimental approaches appear to be converging at small particle sizes and low consolidation loads, just where we might expect the contacts between individual particles in both studies to be single- or few- asperity contacts. In the pull-off experiments with the AFM, a particle (or group of particles) is pulled away from another particle or group, so that the results are analogous to experiments in which the tensile strength of the powder is measured or deduced. Analysis of the results suggest that the pull-off force is a material, not a particle, property. To explain why the bulk tensile strength falls much less steeply with particle size than expected by simple scaling arguments, it is necessary to assume that the larger particles exhibit multi-asperity contacts. In general, it may be true that friction is more relevant to the particle-wall interface, and adhesion more relevant to the internal shear or cohesion of powders.