Abstract
We 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.
Original language | English (US) |
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Pages (from-to) | 18-29 |
Number of pages | 12 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 337 |
DOIs | |
State | Published - Jul 23 2016 |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledgements: Research supported in part by the King Abdullah University of Science and Technology and by the Aristeia program of the Greek Secretariat for Research.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Condensed Matter Physics