J. Bridgwater

Fundamental powder mixing mechanisms

Abstract Traditional methods of seeking to understand powder mixing are evaluated and it is found that few fundamentals generalisations have emerged. This is ascribed to a reluctance to come to terms with and understand the unique properties of powders. This reluctance stems from difficulty in performing reliable experiments free of sampling uncertainties and the inability to understand the influence of sample size on sample concentration. The limitations that have been found in more fundamental studies on equipment are outlined. It is pointed out that powder behaviour depends on whether the powder can be considered cohesive or cohesionless. Cohesionless powders do not form agglomerates capable of withstanding tension, and are particularly susceptible to bulk and free surface segregation. Also, the evaluation of mixing depends on the process requirement: a duty may be macroscopic, demanding, say, compatible residence time distributions of the components, or may be microscopic, demanding satisfactory detailed distributions. Particular consideration is given to processes occurring in bulk powders; for example, the influence of consolidation, the development and spacing of failure zones, the inherent time and position dependence of powder composition and strength, and segregating effects of individual cohesionless particles or individual cohesive agglomerates. It is proposed that two key length scales may be sufficient to describe a powder mixer, namely the failure zone spacing and the failure zone height. More generally, it is concluded that laboratory tests for mixers are of restricted value and that work in future should concentrate on industrial scale studies and on fundamentals.

A review of attrition and attrition test methods

Abstract The sources of attrition during the use of particulate materials are described and the mechanisms which cause breakdown discussed. A wide variety of techniques for testing the susceptibility of particles to attrition has been reported. These techniques aim either to characterise and compare attrition of different materials or to predict particle behaviour during powder use. The majority involve some form of mechanical means for inducing attrition under standard, if undefined, conditions. Other means have been suggested as the basis of test procedures but there is little quantitative knowledge and there are few established tests. The mechanical tests fall into two categories, namely single particle and multi-particle. The multi-particle tests more closely relate to powder use but they are primarily empirical in nature, whereas the single particle tests enhance the understanding of particle breakage but are difficult to compare with attrition observed in practice. The use of tests for predictive purposes currently presents difficulties, especially under diverse conditions of application.

The extrusion mechanics of pastes—the influence of paste formulation on extrusion parameters

Abstract Paste rheology has been studied with a ram extruder in which there is convergent flow followed by extrusion through a tube of constant diameter, the die-land. Pastes have been made from particles of known size distribution and liquids of known rheology. The flow has been described successfully by regarding the convergent flow to be governed by a yield mechanism and the plug flow in the die-land by wall resistance. This gives rise to two important extrusion parameters, namely the yield value and wall stress. The seven different α-alumina pastes which have been studied all comply with this pattern. Both the yield value and wall stress are dependent on velocity. In each instance, the velocity effect is proportional to the effective viscosity of the liquid phase. Particle size distribution and liquid phase content each have a substantial effect on the extrusion parameters.

Simulated and measured flow of granules in a bladed mixer—a detailed comparison

Abstract Experimental measurements and simulations of a granular flow system have been compared in detail. Positron emission particle tracking (PEPT) was used to study the motion of glass beads in a vertical axis mixer with slowly rotating flat blades. Unlike conventional techniques which are restricted to measuring the flow at the surface or a transparent wall, PEPT revealed the motion of material throughout the entire bed. The flow produced was three dimensional with vortices, and is more complicated than other granular flows that have been described previously. Discrete element method (DEM) was employed to simulate the same system using various sets of parameters for the bed material. As there are extensive three-dimensional flow data from both the experiment and the simulations, it has been possible to make comprehensive quantitative comparisons. This enabled the accuracy of the sets of assumptions for the DEM simulations to be examined. The simulations predicted the overall motion of the bed well. However no one set of assumptions was best, but that different sets predicted the detailed motion more accurately in different parts of the bed. None the less, it is evident that DEM models can now be used with some confidence to explore mixer design and performance.

The mechanisms of free surface segregation

Abstract When a heap is formed by pouring, free surface segregation is the process by which free flowing particles separate. Experiments were conducted in an apparatus in which all variables could be controlled and the results could be expressed in dimensionless form. Data were obtained principally for small quantities of a tracer component in a close-sized bulk material. Both diameter and density had a significant effect on the spatial probability distribution of the tracers. Those larger than the bulk or less dense would float down to the bottom of the free surface, whereas those smaller than the bulk or more dense would sink into the heap close to the pouring point. Improvement in distribution could be achieved by balancing the effects of size and density. Increase in the velocity of impact onto the surface affected the influence of size but not of density. The spatial distribution of the tracer in the feed material was also significant.

On the modelling of the packing of fine particles

Abstract It is postulated that the effect of absolute particle size on particle packing be modelled by use of (i) an initial porosity to take into account the packing of mono-sized particles and (ii) the concept of packing size ratio as a measure of the particle-particle interaction in forming a packing of mixed powders. This hypothesis is tested by the experimental measurements of the standard poured and tapped packing densities of white fused alumina powders. The results indicate that simple measurements can lead to the formulation of equations to quantify initial porosity and the packing size ratio. The porosity of multicomponent mixtures of powders can be predicted by the modified linear packing model as facilitated by the equations formulated.

Particle mixing and segregation in failure zones—theory and experiment

Abstract During the motion of powders, it is found that such of the material moves as blocks with regions of high strain, termed failure zones, between. For free-flowing materials, it is shown how a general theory of particle motion can be developed in order to understand mixing and segregation in failure zones. The theory shows how complete segregation can arise. It can also be applied to systems of low concentrations of small particles, employing previously obtained data on inter-particle percolation rates, to give a model free of adjustable parameters; this shows satisfactory agreement with experiment.

Bubble coalescence in viscous liquids

Abstract When a gas is bubbled into a viscous liquid, coalescence of the bubbles occurs. This in turn influences the bubble-induced liquid flow and the mass transfer rate, matters of considerable practical importance. Experiments have been conducted on the relative motion of vertically aligned bubble pairs, each having volumes from 10 to 40 cm 3 , in a 67 per cent wt solution of sucrose in water. The Reynolds numbers encoutered were 40–90. It was demonstrated that bubbles up to 70 cm apart initially, coalesced, even when the difference in the infinite fluid rise velocities of single bubbles would suggest that coalescence is impossible. Although more detailed information upon wake structure and the motion of bubbles in such wakes is required before a full explanation is possible, a theoretical treatment relying on an asymptotic wake velocity profile provides a general explanation of the phenomenon.

A phenomenological study of a batch mixer using a positron camera

Abstract Particulate motion within a Lodige mixer has been analysed using a refinement of the nuclear imaging technique, positron emission tomography. The detailed tracking of a single, in this case large, radioactive tracer particle has revealed information on the detailed flow behaviour in the mixer, by determining not only axial, radial and angular locations but also axial, radial and angular velocity distributions. The mixer had a five litre mixing bowl containing two ploughshare blades and two end scraper blades mounted upon a horizontal mixing shaft rotating at a fixed frequency of 4Hz. Three active mixing regions separated by boundaries coinciding with the axial positions of the ploughshare blades were found, and residence time distributions in these regions of the mixer determined. Assessment was performed for eight powder fill proportions ranging from 7% to 70% by volume; the results show a great influence of detailed mixer geometry on behaviour. This application of the positron emission particle tracking technique demonstrates its potential for powder mixing studies.

Attrition of particulate solids under shear

Abstract Eleven granular materials of various sizes and internal structures were tested in an annular attrition cell that models the breakage occurring in a failure zone of a deforming powder. The cell permits the stress and the strain to be determined and controlled. For none of these materials were the traditional laws of comminution correct, nor was a first-order kinetic model of degradation generally found. A description of the rate of attrition following an empirical form due to Gwyn was the most effective. The product size distribution was well described by the Schuhmann formulation and this in turn led to a means of modifying the Gwyn approach. Using an experimentally measured parameter to describe the influence of normal stress on attrition rate, the data for a given sample could be unified.