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arXiv · 1510.03972

A comparison of macroscopic models describing the collective response of sedimenting rod-like particles in shear flows

Christiane Helzel·Athanasios E. Tzavaras
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Abstract

We consider a kinetic model, which describes the sedimentation of rod-like particles in dilute suspensions under the influence of gravity. This model has recently been derived by Helzel and Tzavaras in \cite{HT2015}. Here we restrict our considerations to shear flow and consider a simplified situation, where the particle orientation is restricted to the plane spanned by the direction of shear and the direction of gravity. For this simplified kinetic model we carry out a linear stability analysis and we derive two different macroscopic models which describe the formation of clusters of higher particle density. One of these macroscopic models is based on a diffusive scaling, the other one is based on a so-called quasi-dynamic approximation. Numerical computations, which compare the predictions of the macroscopic models with the kinetic model, complete our presentation.

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Christiane Helzel, Athanasios E. Tzavaras. 2015-10-14. A comparison of macroscopic models describing the collective response of sedimenting rod-like particles in shear flows. https://doi.org/10.1016/j.physd.2016.07.004

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