Self-Diffusion Scalings in Dense Granular Flows

TL;DR

This study measures self-diffusion in dense granular flows of inelastic spheres, compares empirical and theoretical predictions, and explores anisotropy and solid fraction effects at high densities.

Contribution

It provides new numerical data on self-diffusion coefficients at high solid fractions and evaluates the accuracy of existing empirical and kinetic theory models.

Findings

Diffusion coefficients depend on solid fraction and shear rate.

Anisotropy is observed in diffusion behavior.

Discrepancies exist between measurements and kinetic theory predictions.

Abstract

We report on measurements of self-diffusion coefficients in discrete numerical simulations of steady, homogeneous, collisional shearing flows of nearly identical, frictional, inelastic spheres. We focus on a range of relatively high solid volume fractions that are important in those terrestrial gravitational shearing flows that are dominated by collisional interactions. Diffusion over this range of solid fraction has not been well characterized in previous studies. We first compare the measured values with an empirical scaling based on shear rate previously proposed in the literature, and highlight the presence of anisotropy and the solid fraction dependence. We then compare the numerical measurements with those predicted by the kinetic theory for shearing flows of inelastic spheres and offer an explanation for why the measured and predicted values differ.