We study mathematical models and approximations for the sedimentation in suspensions of rod-like particles. The starting point of our considerations is a coupled system of partial differential equations, previously derived by Helzel and Tzavaras [Multiscale Model. Simul., 15 (2017), pp. 500–536], consisting of a kinetic equation for the rod orientation that is coupled to a macroscopic flow equation. It describes the motion of a suspension of rigid rod-like particles under the influence of gravity. Since the coupled system is high dimensional (five dimensions plus time) we are interested in the derivation of models which can adaptively adjust the level of detail. Here we restrict ourselves to simplified lower dimensional flow situations and derive hierarchies of moment equations which can be interpreted as approximations of the coupled kinetic model. We show that the resulting systems of moment equations are hyperbolic.
Contact persons: Sina Dahm and Christiane Helzel