Homogenization for rigid suspensions with random velocity-dependent interfacial forces
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Earth Science and Engineering Program
Numerical Porous Media SRI Center (NumPor)
Preprint Posting Date2013-04-08
Embargo End Date2016-05-14
Permanent link to this recordhttp://hdl.handle.net/10754/563877
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AbstractWe 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.
CitationGorb, 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
SponsorsY. 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.