Homogenization for rigid suspensions with random velocity-dependent interfacial forces

Abstract
We study suspensions of solid particles in a viscous incompressible fluid in the presence of random velocity-dependent interfacial forces. The flow at a small Reynolds number is modeled by the Stokes equations, coupled with the motion of rigid particles arranged in a periodic array. The objective is to perform homogenization for the given suspension and obtain an equivalent description of a homogeneous (effective) medium, the macroscopic effect of the interfacial forces and the effective viscosity are determined using the analysis on a periodicity cell. In particular, the solutions uωε to a family of problems corresponding to the size of microstructure ε and describing suspensions of rigid particles with random surface forces imposed on the interface, converge H1-weakly as ε→0 a.s. to a solution of a Stokes homogenized problem, with velocity dependent body forces. A corrector to a homogenized solution that yields a strong H1-convergence is also determined. The main technical construction is built upon the Γ-convergence theory. © 2014 Elsevier Inc.

Citation
Gorb, Y., Maris, F., & Vernescu, B. (2014). Homogenization for rigid suspensions with random velocity-dependent interfacial forces. Journal of Mathematical Analysis and Applications, 420(1), 632–668. doi:10.1016/j.jmaa.2014.05.015

Acknowledgements
Y. Gorb and F. Mans were supported by the National Science Foundation grant DMS-1016531; Y. Gorb was also supported by the National Science Foundation grant DMS-1350248. B. Vernescu was supported by the National Science Foundation grant DMS-1109356.

Publisher
Elsevier BV

Journal
Journal of Mathematical Analysis and Applications

DOI
10.1016/j.jmaa.2014.05.015

arXiv
1304.2422

Additional Links
http://arxiv.org/abs/arXiv:1304.2422v1http://arxiv.org/pdf/1304.2422

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