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arXiv · 2512.19149

A Smoluchowski equation for a sheared suspension of frictionally interacting rods

Genevieve Quiñones·Peter D. Olmsted
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Abstract

In this work we develop constitutive equations for a dense, sheared suspension of frictionally interacting rods by applying Onsager's variational method as formulated by Doi. We treat both solid friction, of the Amontons-Coulomb form; and lubricated friction, which scales with relative tangential velocity at the contact point. Dissipation functions in terms of the rod angular velocity are derived via a mean field approach for each form of friction, and from these, a Rayleighian for dense suspensions of rigid rods under shear constructed. Derivatives of this Rayleighian with respect to rod angular velocity and velocity gradient give a Smoluchowski equation and stress tensor, respectively. We show that these are representable as perturbations to Doi's model for a sheared liquid crystal. We also suggest a form for the average number of contacts between rods as a function of volume fraction, aspect ratio, and nematic order parameter, generalizing Philipse's random contact equation for disordered packings.

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Genevieve Quiñones, Peter D. Olmsted. 2025-12-22. A Smoluchowski equation for a sheared suspension of frictionally interacting rods. https://arxiv.org/abs/2512.19149

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