Shear-Rate-Independent Diffusion in Granular Flows.
We computationally study the behavior of the diffusion coefficient D in granular flows of monodisperse and bidisperse particles spanning regions of relatively high and low shear rate in open and closed laterally confined heaps. Measurements of D at various flow rates, streamwise positions, and depths collapse onto a single curve when plotted as a function of γd2, where d is the local mean particle diameter and γ is the local shear rate. When γ is large, D is proportional to γd2, as in previous studies. However, for γd2 below a critical value, D is independent of γd2. The acceleration due to gravity g and particle stiffness (or, equivalently, the binary collision time t(c)) together determine the transition in D between regimes. This suggests that while shear rate and particle size determine diffusion at relatively high shear rates in surface-driven flows, diffusion at low shear rates is an elastic phenomenon with time and length scales dependent on gravity (sqrt d/g) and particle stiffness (t(c)sqrt(dg), respectively.
Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, USA.|The Dow Chemical Company, Midland, Michigan 48667, USA.
Yi
Y
Fan
Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, USA.
Paul B
PB
Umbanhowar
Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, USA.|Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, USA.|The Northwestern Institute on Complex Systems (NICO), Northwestern University, Evanston, Illinois 60208, USA.
Julio M
JM
Ottino
Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, USA.|The Northwestern Institute on Complex Systems (NICO), Northwestern University, Evanston, Illinois 60208, USA.
Richard M
RM
Lueptow