Shear-induced diffusion in non-local granular flows

Abstract

We investigate the properties of self-diffusion in heterogeneous dense granular flows involving a gradient of stress and inertial number. The study is based on simulated plane shear with gravity and Poiseuille flows, in which non-local effects induce some creep flow in zones where stresses are below the yield. Results show that shear-induced diffusion is qualitatively different in zones above and below the yield. Below the yield, diffusivity is no longer governed by velocity fluctuations, and we evidenced a direct scaling between diffusivity and local shear rate. This is interpreted by analysing the grain trajectories, which exhibit a caging dynamics developing in zones below the yield. We finally introduce an explicit scaling for the profile of local inertial number in these zones, which leads to a straightforward expression of the diffusivity as a function of the stress and position in non-local flows.Introduction. -Shearing dense granular flows induces diffusion of grains. This mechanism of shearinduced diffusion underpins the rate of mixing [1], heat transfer [2] and segregation [3] in a variety of natural and industrial granular flows. It is usually modelled by a coefficient of self-diffusion, also called diffusivity D [m 2 /s].In homogeneous shear flows, in which there is no gradient of shear rate, three relationships have been established from which diffusivity can be predicted:

Microscopic Origin of Nonlocal Rheology in Dense Granular Materials

“…1(c), the evolution of normalized velocity fluctuations Δ with inertial number I strongly resembles that of the friction coefficient μ. For I > I t , all data points collapse on a single power law: Δ ∼ I 1=2 , consistent with previous studies [3,4,6]. On the contrary, for I < I t , no one-to-one relationship exists between Δ and I, but data points obtained for different values of Ω nevertheless follow parallel trends.…”

“…Numerous studies have, however, revealed the existence of nonlocal effects and deviations from purely rateindependent behavior in the quasistatic regime. In particular, creep as well as strong intermittent velocity fluctuations have been evidenced in quasistatic regions coexisting with inertial layers for different geometrical settings [4,[6][7][8][9][10][11].…”

“…The number I compares a macroscopic deformation timescale 1=_ γ to a microscopic rearrangement timescale d= ffiffiffiffiffiffiffiffi P=ρ p . A one-to-one scaling between velocity fluctuations (or granular temperature) and I is also observed in the inertial regime [3][4][5][6]. This I-controlled rheology is only valid above a yield criterion, which can be defined in terms of a critical friction coefficient μ or of a critical I value [1, 3,4].…”

Force fluctuations at the transition from quasi-static to inertial granular flow

“…Motivated by these shortcomings, non-local rheology theories aim to capture relationships between the stress tensorσ and state variables in addition to the shear rateγ. Three Several such models have been proposed 7,[22][23][24][25][26] , but for the moment there still lacks a universal theory that captures the fundamental physics behind the vast variety of non-local phenomena 27,28 , and that is moreover well-posed 29,30 . In this work we focus on a particular cluster of models based on measures that are accessible to us.…”

Shear-induced diffusion: the role of granular clusters

“…This scaling is verified in diluted granular flows, where the grains' trajectory indeed involves a series of free, ballistic flights interrupted by a binary collision with another grain. However, deviations from that scaling were observed in dense granular flows of cohesionless and cohesive grains [8][9][10]. A qualitative way to understand the origin of these deviations is that grains interact via multiple and sustained contacts in dense granular flows.…”