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

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