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arXiv · 1309.4069

A Mean Field Model of Layering Instability in Shearing Suspensions

J. I. Katz
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Abstract

Concentrated suspensions may shear-thin when the suspended particles form planar sheets that slide over one another with less friction than if the particles are randomly distributed. In a naïve model the suspension is described by a mean effective viscosity, and particles that collide with each other redistribute the mean density in the shearing direction. This leads to a diffusion equation for the particle density. If the viscosity in the unthinned state is a steeply increasing function of particle density the effective diffusion coefficient is negative and the diffusion equation, meaningful only on scales larger than the particle separation, is ill-posed. This singularity corresponds to the formation of planar sheets of particles and defines a critical particle density for the onset of shear thinning.

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J. I. Katz. 2014-02-23. A Mean Field Model of Layering Instability in Shearing Suspensions. https://doi.org/10.1103/physreve.89.021003

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