Mixing cohesionless materials

When solid particles of different types are mixed together, a random distribution of the components is rarely produced and deterioration of the mixture can occur on subsequent handling. Among the microscopic processes responsible, one important mechanism for free-flowing materials is thought to be interparticle percolation, the drainage of particles through the interstices between larger ones. If the larger particles are stationary this is called spontaneous percolation, whereas if it is produced by shear strain the term strain-induced percolation is used. Here a quantitative evaluation of both and some consequences are described.
A practical application of spontaneous percolation has been the design and construction of a new static mixer or distributor, consisting of rows of angle bars mounted horizontally in a vertical channel. Material fed to the top of a unit bounces off the bars and is distributed across the channel. Two mixers were built; one dispersed material in one lateral direction only and could be used for feeding material onto a belt or distributing seed from a moving vehicle. The other produced a two-dimensional dispersion and would be useful in distributing material flowing into hoppers or whenever a good mixture were required. Optimisation of the design was investigated using a computer program which simulated the motion of a spherical particle as it fell through such a mixer. Design data was deduced from the record of the position of the particle. The mixers were not suitable for use with fine materials.
Interpretation of experimental results from this equipment requires suitable statistical indices and two were developed here. One related the variance of sample compositions to the number of particles fed to the mixer by assuming that the distributions of material were ordered. The second, using the correlation coefficient between samples, related the variance to the sample size in those situations where two orthogonal processes are in operation. Both techniques are generally applicable to fields other than that of powder mixing.
On the theoretical side, an existing model of spontaneous percolation for inelastic materials has been extended and improved. The original form did not account for the motion of a particle between collisions with bulk particles but this has now been included. An entirely new semi-empirical model for partly elastic materials has also been proposed. Both predict percolation velocities which agree with experimental data.
In order to extend earlier experimental studies on strain-induced percolation, a simple shear cell was modified by installing a hydraulic drive which enabled the cell to be driven at a constant speed. Advantages of the use of such a cell include the possibility of detecting a percolating particle on entry to and exit from the bed and the constant strain throughout the material. Reliable and accurate readings of residence times of percolating particles were recorded and percolation velocities and both lateral and axial diffusion coefficients were calculated. These were functions of the relative particle size and density, the material properties of the percolating particle and bed conditions such as strain rate and normal stress Denser and softer particles percolated faster. Decreasing the diameter ratio between percolating and bulk particles from 0.67 to 0.27 caused a twenty-five fold increase in the percolation rate. The dependence of this rate on particle diameter was interpreted using statistical mechanics. The percolation rate has been shown to reach a constant value as the strain rate increases, in contrast to the deductions drawn in earlier work by Scott, whose procedure has been proved to be unsound.

Advisor: Bridgwater, J