During the last fifteen years there has been a paradigm shift in the continuum modelling of granular materials, most notably with the development of rheological models, but also with significant advances in theories for particle segregation.
Professor Nico Gray from the University of Manchester has developed new theoretical and numerical frameworks which couple granular flows with particle segregation. Using a series of advection-diffusion-segregation equations, he describes the evolving concentrations of the particles in the flow: these may be of different sizes and have different frictional properties. By also including an excess air phase, which segregates away from the granular material, he also models the complex evolution of the free surface of the flow.
Three primary coupling mechanisms are identified: (i) advection of the particle concentrations by the bulk velocity, (ii) feedback of the particle-size and/or frictional properties on the bulk flow field and (iii) influence of the shear rate, pressure, gravity, particle size and particle-size ratio on the locally evolving segregation and diffusion rates.
The numerical method developed by professor Gray has been extensively tested and used to compute the petal-like segregation pattern that spontaneously develops in triangular rotating drums such as the one illustrated below. You can read more about professor’s Gray’s work here.
Segregation of particles of different sizes in a rotating triangular drum. The image on the left-hand side illustrates the outcome of numerical modelling, while that on the right-hand side is a laboratory experiment, in which a mixture of coarse green particles, intermediate white particles and fine red particles were located in a triangular cell.