Deterministic solution of the kinetic theory model of colloidal suspensions of structureless particles

Guillaume Maîtrejean (1) , Amine Ammar (2) , Francisco Chinesta (3) , Miroslav Grmela (4)

1 LR - Laboratoire de rhéologie
2 LAMPA - Laboratoire Angevin de Mécanique, Procédés et InnovAtion
3 ECN - École Centrale de Nantes
4 EPM - École Polytechnique de Montréal

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-Plancklike 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.

Mots clés: Colloidal suspensions; Smoluchowski equation; Proper generalized decomposition

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Guillaume Maîtrejean, Amine Ammar, Francisco Chinesta, Miroslav Grmela. Deterministic solution of the kinetic theory model of colloidal suspensions of structureless particles. Rheologica Acta, 2012, 51 (6), pp.527-543. ⟨10.1007/s00397-011-0609-3⟩. ⟨hal-01061268⟩