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Deterministic solution of the kinetic theory model of colloidal suspensions of structureless particles |
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| Authors: | Guillaume Ma?trejean Amine Ammar Francisco Chinesta Miroslav Grmela |
| Affiliation: | 1. Laboratoire de Rhéologie, UJF-INPG-CNRS, 1301 rue de la piscine, Domaine universitaire, BP 53, 38041, Grenoble cedex 9, France 2. Arts et Métiers ParisTech, 2 Boulevard du Ronceray, BP 93525, 49035, Angers cedex 01, France 3. EADS Corporate Fundation International Chair, Ecole Centrale de Nantes, 1 rue de la Noe, BP 92101, 44321, Nantes cedex 3, France 4. école Polytechnique de Montréal, C.P. 6079 suc. Centre-ville, Montréal, H3C 3A7, QC, Canada |
| Abstract: | A direct modeling of colloidal suspensions consists of calculating trajectories of all suspended objects. Due to the large time computing and the large cost involved in such calculations, we consider in this paper another route. Colloidal suspensions are described on a mesoscopic level by a distribution function whose time evolution is governed by a Fokker–Planck-like equation. The difficulty encountered on this route is the high dimensionality of the space in which the distribution function is defined. A novel strategy is used to solve numerically the Fokker–Planck equation circumventing the curse of dimensionality issue. Rheological and morphological predictions of the model that includes both direct and hydrodynamic interactions are presented in different flows. |
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