Homogenization for rigid suspensions with random velocity-dependent interfacial forces

Handle URI:
http://hdl.handle.net/10754/563877
Title:
Homogenization for rigid suspensions with random velocity-dependent interfacial forces
Authors:
Gorb, Yuliya; Maris, Razvan Florian ( 0000-0002-7196-6967 ) ; Vernescu, Bogdan
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.
KAUST Department:
Numerical Porous Media SRI Center (NumPor); Earth Science and Engineering Program
Publisher:
Elsevier BV
Journal:
Journal of Mathematical Analysis and Applications
Issue Date:
Dec-2014
DOI:
10.1016/j.jmaa.2014.05.015
ARXIV:
arXiv:1304.2422
Type:
Article
ISSN:
0022247X
Sponsors:
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.
Additional Links:
http://arxiv.org/abs/arXiv:1304.2422v1
Appears in Collections:
Articles; Earth Science and Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorGorb, Yuliyaen
dc.contributor.authorMaris, Razvan Florianen
dc.contributor.authorVernescu, Bogdanen
dc.date.accessioned2015-08-03T12:18:00Zen
dc.date.available2015-08-03T12:18:00Zen
dc.date.issued2014-12en
dc.identifier.issn0022247Xen
dc.identifier.doi10.1016/j.jmaa.2014.05.015en
dc.identifier.urihttp://hdl.handle.net/10754/563877en
dc.description.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.en
dc.description.sponsorshipY. 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.en
dc.publisherElsevier BVen
dc.relation.urlhttp://arxiv.org/abs/arXiv:1304.2422v1en
dc.subjectEffective viscosityen
dc.subjectHomogenizationen
dc.subjectNonlinear Stokes equationen
dc.subjectVelocity-dependent forcesen
dc.titleHomogenization for rigid suspensions with random velocity-dependent interfacial forcesen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.contributor.departmentEarth Science and Engineering Programen
dc.identifier.journalJournal of Mathematical Analysis and Applicationsen
dc.contributor.institutionDepartment of Mathematics, University of Houston, Houston, TX 77204, United Statesen
dc.contributor.institutionDepartment of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Rd., Worcester, MA 01609, United Statesen
dc.identifier.arxividarXiv:1304.2422en
kaust.authorMaris, Razvan Florianen
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