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.Comment: Keywords: rod-like particles, sedimentation, linear stability, moment
closure, quasi-dynamic approximation, diffusive scalin
