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

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.

Debris flows: Experiments and modelling

“…Golick and Daniels [72] and May et al [104] performed ring shear segregation experiments which showed that under a confining pressure both the velocity profile, u = u(z), and the segregation rate, q = q(z), could have a strong height dependence and exact solutions for this case have been constructed [104,105]. Another interesting feature of these experiments is that they measured the degree of segregation based on the rise and fall of the top plate, which was caused by the grains packing denser in a mixed state than in a pure phase.…”

Modelling size segregation of granular materials: the roles of segregation, advection and diffusion

“…In the meantime, a broad theoretical framework for segregation-driven pattern formation in dense flows is emerging (Gray & Thornton 2005;Gray & Chugunov 2006;Thornton et al 2006;May et al 2010;Wiederseiner et al 2011;Marks et al 2011;Thornton et al 2012;Kowalski & McElwaine 2013). This framework incorporates advection due to mean flow, percolation-driven segregation, and diffusion due to random particle collisions, in a continuum transport equation for the volume concentration of species i:…”

The Gray-Thornton Model of Granular Segregation

“…Here, we summarize results that will appear in a pair of papers [6,7]. The experimental setup and protocol are described in detail in [2].…”

“…In [6,7], we considered equation (1) with exponential fiunction u(z) and S(z) = s|u (z)|. However, we restricted attention to solutions independent of x, mimicking conditions in a Couette cell, in which layers of large and small particles are sheared by rotating a lower confining plate.…”