Year: 2017
Type: article
Abstract: This Letter introduces unexpected diffusion properties in dense granular flows and shows that they result from the development of partially jammed clusters of grains, or granular vortices. Transverse diffusion coefficients $D$ and average vortex sizes $\ensuremath{\ell}$ are systematically measured in simulated plane shear flows at differing inertial numbers $I$ revealing (i) a strong deviation from the expected scaling $D\ensuremath{\propto}{d}^{2}\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\gamma}}$ involving the grain size $d$ and shear rate $\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\gamma}}$ and (ii) an increase in average vortex size $\ensuremath{\ell}$ at low $I$, following $\ensuremath{\ell}\ensuremath{\propto}d{I}^{\ensuremath{-}\frac{1}{2}}$ but limited by the system size. A general scaling $D\ensuremath{\propto}\ensuremath{\ell}d\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\gamma}}$ is introduced that captures all the measurements and highlights the key role of vortex size. This leads to establishing a scaling for the diffusivity in dense granular flow as $D\ensuremath{\propto}{d}^{2}\sqrt{\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\gamma}}/{t}_{i}}$ involving the geometric average of shear time $1/\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\gamma}}$ and inertial time ${t}_{i}$ as the relevant time scale. Analysis of grain trajectories is further evidence that this diffusion process arises from a vortex-driven random walk.
Source: Physical Review Letters
Authors: Prashidha Kharel, Pierre Rognon
Institution: The University of Sydney
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2620394352