TY - JOUR

T1 - Homogenization for rigid suspensions with random velocity-dependent interfacial forces

AU - Gorb, Yuliya

AU - Maris, Razvan Florian

AU - Vernescu, Bogdan

N1 - KAUST Repository Item: Exported on 2020-10-01
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.

PY - 2014/5/14

Y1 - 2014/5/14

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/563877

UR - http://arxiv.org/abs/arXiv:1304.2422v1

UR - http://www.scopus.com/inward/record.url?scp=84904180995&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2014.05.015

DO - 10.1016/j.jmaa.2014.05.015

M3 - Article

SN - 0022-247X

VL - 420

SP - 632

EP - 668

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -