Transverse vortices induced by modulated granular shear flows of elongated particles

TL;DR

This study uses simulations and theory to explore how modulated shear flows of elongated particles induce transverse vortices, revealing the influence of particle shape, cell geometry, and stress differences on flow patterns.

Contribution

It introduces a generalized granular rheology for elongated grains and analyzes the linear response to perturbations, linking vortex patterns to cell aspect ratio and stress differences.

Findings

Transverse vortices form in shear flows of elongated particles.

Vortex pattern inversion depends on cell aspect ratio.

Second normal stress difference influences flow pattern transitions.

Abstract

We perform discrete element method (DEM) simulations of elongated grains in a shear cell for various particle aspect ratios and contact frictions, with an additional heterogeneous force perturbation in the flow direction. For a perturbation in the form of a single Fourier mode, we show that the response of the system consists of transverse secondary flows that average onto a pattern of four vortices. We also theoretically studied this phenomenon by generalizing the granular rheology $\mu(I)$ to the case of elongated grains and computing the linear response to such a perturbation. Even if the agreement between theory and simulations remains qualitative only, we can reproduce and understand the inversion of the vortex pattern when the cell aspect ratio is increased from a vertically to a horizontally elongated cell shape, emphasizing the key role of the second normal stress difference as well as the cell geometry.