Self-diffusion in inhomogeneous granular shearing flows

TL;DR

This paper investigates how flow inhomogeneity influences self-diffusion in granular shearing flows, revealing that granular temperature-based scaling better collapses data, thus aiding modeling of mixing and segregation.

Contribution

It introduces measurements of self-diffusion in inhomogeneous granular flows and compares scaling laws, highlighting the effectiveness of granular temperature-based scaling over shear rate-based scaling.

Findings

Granular temperature scaling better collapses diffusion data.

Flow inhomogeneity significantly affects self-diffusion behavior.

Results provide a foundation for diffusion models in inhomogeneous flows.

Abstract

In this letter, we discuss how flow inhomogeneity affects the self-diffusion behavior in granular flows. Whereas self-diffusion scalings have been well characterized in the past for homogeneous shearing, the effect of shear localization and nonlocality of the flow has not been studied. We therefore present measurements of self-diffusion coefficients in discrete numerical simulations of steady, inhomogeneous, and collisional shearing flows of nearly identical, frictional, and inelastic spheres. We focus on a wide range of dense solid volume fractions, that correspond to geophysical and industrial shearing flows that are dominated by collisional interactions. We compare the measured values first, with a scaling based on shear rate and, then, on a scaling based on the granular temperature. We find that the latter does much better than the former in collapsing the data. The results lay the foundations of diffusion models for inhomogeneous shearing flows, which should be useful in treating problems of mixing and segregation.