Shear-driven size segregation of granular materials: modeling and experiment

TL;DR

This study investigates size-driven segregation in granular materials under shear, applying a modified Gray-Thornton model to experimental data from an annular Couette cell, revealing the model's strengths and limitations in predicting segregation dynamics.

Contribution

It extends the Gray-Thornton segregation model to exponential shear profiles and compares its predictions with detailed experimental measurements.

Findings

The model captures the initial mixing and slower re-segregation phases.

Re-segregation in experiments occurs exponentially, not finite as the model predicts.

The velocity profile and packing density measurements improve model accuracy.

Abstract

Granular materials segregate by size under shear, and the ability to quantitatively predict the time required to achieve complete segregation is a key test of our understanding of the segregation process. In this paper, we apply the Gray-Thornton model of segregation (developed for linear shear profiles) to a granular flow with an exponential profile, and evaluate its ability to describe the observed segregation dynamics. Our experiment is conducted in an annular Couette cell with a moving lower boundary. The granular material is initially prepared in an unstable configuration with a layer of small particles above a layer of large particles. Under shear, the sample mixes and then re-segregates so that the large particles are located in the top half of the system in the final state. During this segregation process, we measure the velocity profile and use the resulting exponential fit as input parameters to the model. To make a direct comparison between the continuum model and the observed segregation dynamics, we locally map the measured height of the experimental sample (which indicates the degree of segregation) to the local packing density. We observe that the model successfully captures the presence of a fast mixing process and relatively slower re-segregation process, but the model predicts a finite re-segregation time, while in the experiment re-segregation occurs only exponentially in time.