This work was started via my PhD, under the supervision of Prof. N. Gray. Parts of it were undertaken in collaboration with  M. Shearer and A. Hogg. Now in collaboration with D. Tunuguntla (PhD student) and O. Bokhove (University of Leeds).

This work focused on developing a continuum model of granular size-segregation from a mixture-theory framework. The study will focus on dense granular chute flow where kinetic sieving is the dominant mechanism for particle-size segregation. The basic idea is: that as grains avalanche down-slope, the local void ratio fluctuates and small particles fall into the gaps that open up beneath them, as they are more likely to fit into the available space than the large ones. The small particles, therefore, migrate towards the bottom of the flow and lever the large particles upwards due to force imbalances. This was termed squeeze expulsion by Savage and Lun (1988).

In frictional flows this process is so efficient that segregated layers rapidly develop, with a region of 100% large particles separated by a concentration jump from a layer of 100% fine particles below.  The figure shows the flow of red, large, dense, particles and white, small, less dense, particles from a hopper containing an approximately homogeneous mixture. A region of nearly pure, large, particles is formed near the free-surface, immediately on exiting the gate of the hopper. This layer grows in thickness as the material flows down the slope, due to the downward percolation of the smaller material. As the small material percolates,  squeeze expulsion forces the large particles back upwards, forming a similar growing layer of nearly pure, small particles at the bottom of the flow. This process continues until these pure regions meet and the flow is inversely graded with large material above small.

The continuum model developed is derived based on two key assumptions: firstly, as the different particles percolate past each other there is a Darcy-style drag between the different constituents (i.e., the small and large particles) and, secondly, particles falling into void spaces do not support any of the bed weight. Since the number of voids available for small particles to fall into is greater than for large particles, it follows that a higher percentage of the small particles will be falling and, hence, not supporting any of the bed load, see publication [1], [2].

This segregation theory has been developed and extended in many directions: including the addition of a passive background fluid (see publication [1], [3]) the effect of diffusive remixing, Gray and Chugunov (2006)  and the generalisation to multi-component granular flows by Gray and Ancey (2011).

Additionally, a large number of analytic solutions have been derived from this model, this includes publications [1,2,3,4,5,6,7] plus many more by other authors.

Currently I am involved in using the discrete particle method to perform the micro-macro transition for this model (see separate research page); extending the model to include density [U25] as well as size effects; and using the model to investigate segregation in rotating drums and cylinders.