Mixing indices in up-scaled simulations

Mixing and segregation of granular materials are important industrial processes. Their accurate simulation via discrete simulations requires a large number of particles with high computational demand, which can make it infeasible for industrial scale applications. One way to solve this challenge is the usage of up-scaled simulations, where groups of small particles are replaced by larger particles, while the relevant features of the process are conserved.
In order to help improve the mixing evaluation, we review numerous mixing indices and investigate their sensitivity to factors relevant to up-scaled mixing process simulations. We test the indices in a simplified 2D model system. We focus on system-specific and statistical features.
As the main output, we provide guidelines for selecting appropriate indices and their parameters to analyse a given mixing process. We show that: (i) the average height method is simple to calculate and useful for evaluating mixing in different directions; (ii) the Lacey index performs well when the solid fraction is homogeneous; (iii) the neighbour distance method allows evaluation of mixing even without selecting a subset of particle types to trace.