Applied PDE Group
Nonlinear Partial Differential Equations in Fluid and Solid Mechanics

HT2016bp

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

​Ch. Helzel, A.E. Tzavaras, A comparison of macroscopic models describing the collective response of sedimenting rod-like particles in shear flows, Physica D: Nonlinear Phenomena, 337(1):18-29, 2016
Ch. Helzel, A.E. Tzavaras
macroscopic models rod-like particles
2016
​We consider a kinetic model, which describes the sedimentation of rod-like particles in dilute suspensions under the in uence of gravity. This model has recently been derived by Helzel and Tzavaras in [6]. Here we restrict our considerations to shear ow and consider a simplifed situation, where the particle orientation is restricted to the plane spanned by the direction of shear and the direction of gravity. For this simpli ed kinetic model we carry out a linear stability analysis and we derive two di erent 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