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Kinetic theory of colloidal suspensions: morphology, rheology, and migration |
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| Authors: | Miroslav Grmela Guillaume Maîtrejean Francisco Chinesta Amine Ammar |
| Institution: | 1. école Polytechnique de Montréal, C.P. 6079 suc. Centre-ville, Montréal, H3C 3A7, Quebec, Canada 2. Mechanical and Materials Engineering Group, Engineering Department, European Organization for Nuclear Research (CERN), 1211, Geneva, Switzerland 3. EADS Corporate Foundation International Chair, Ecole Centrale de Nantes, 1 rue de la Noe, BP 92101, 44321, Nantes Cedex 3, France 4. Arts et Métiers ParisTech, 2 Boulevard du Ronceray, BP 93525, 49035, Angers Cedex 01, France |
| Abstract: | Smoluchowski kinetic equation governing the time evolution of the pair correlation function of rigid sphericalparticles suspended in a Newtonian fluid is extended to include particle migration. The extended kinetic equation takes into account three types of forces acting on the suspended particles: a direct force generated by an interparticle potential, hydrodynamic force mediated by the host fluid, and the Faxén-type forces bringing about the across-the-streamline particle migration. For suspensions subjected to externally imposed flows, the kinetic equation is solved numerically by the proper generalized decomposition method. The imposed flow investigated inthe numerical illustrations is the Poiseuille flow. Numerical solutions provide the morphology (the pair correlation function), the rheology (the stress tensor), and the particle migration. |
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