Homogenization for rigid suspensions with random velocity-dependent interfacial forces

Yuliya Gorb, Razvan Florian Maris, Bogdan Vernescu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)632-668
Number of pages37
JournalJournal of Mathematical Analysis and Applications
Volume420
Issue number1
DOIs
StatePublished - May 14 2014

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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