کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6418308 | 1339325 | 2014 | 37 صفحه PDF | دانلود رایگان |
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 uÏϵ 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 ϵâ0 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 Î-convergence theory.
Journal: Journal of Mathematical Analysis and Applications - Volume 420, Issue 1, 1 December 2014, Pages 632-668