The wall shear rate distribution for flow in random sphere packings
Patrick B. Warren, Frantisek Stepanek
TL;DR
This study analyzes the distribution of wall shear rates in pressure-driven Stokes flow through random sphere packings, revealing how the distribution changes with packing density and providing an exact result for isolated spheres.
Contribution
It introduces a detailed analysis of wall shear rate distribution in sphere packings and derives an exact result for flow around isolated spheres.
Findings
P(gamma) is approximately exponential for dense packings.
P(gamma) shows additional structure at low packing fractions.
A simple force-balance based expression for mean wall shear rate is provided.
Abstract
The wall shear rate distribution P(gamma) is investigated for pressure-driven Stokes flow through random arrangements of spheres at packing fractions 0.1 <= phi <= 0.64. For dense packings, P(gamma) is monotonic and approximately exponential. As phi --> 0.1, P(gamma) picks up additional structure which corresponds to the flow around isolated spheres, for which an exact result can be obtained. A simple expression for the mean wall shear rate is presented, based on a force-balance argument.
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