A comparison of macroscopic models describing the collective response of sedimenting rod-like particles in shear flows
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
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AbstractWe consider a kinetic model, which describes the sedimentation of rod-like particles in dilute suspensions under the influence of gravity, presented in Helzel and Tzavaras (submitted for publication). 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 nonlinear 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.
CitationA comparison of macroscopic models describing the collective response of sedimenting rod-like particles in shear flows 2016 Physica D: Nonlinear Phenomena
SponsorsResearch supported in part by the King Abdullah University of Science and Technology and by the Aristeia program of the Greek Secretariat for Research.
JournalPhysica D: Nonlinear Phenomena