Journal
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 44, Issue 6, Pages 4835-4857Publisher
WILEY
DOI: 10.1002/mma.7072
Keywords
Darcy' s law; homogenization; micropolar fluid; nonzero spin boundary condition; porous media
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This study examines the flow of a micropolar fluid in a medium perforated by periodically distributed obstacles of size epsilon. A nonhomogeneous boundary condition for microrotation is considered, with microrotation assumed to be proportional to the rotation rate of the velocity on the boundary of the obstacles. The existence and uniqueness of solution are analyzed, and an analog of the classical micropolar Darcy's law in the theory of porous media is derived in the limit as epsilon tends to zero.
We consider a micropolar fluid flow in a media perforated by periodically distributed obstacles of size epsilon. A nonhomogeneous boundary condition for microrotation is considered: The microrotation is assumed to be proportional to the rotation rate of the velocity on the boundary of the obstacles. The existence and uniqueness of solution are analyzed. Moreover, passing to the limit when epsilon tends to zero, an analog of the classical micropolar Darcy's law in the theory of porous media is derived.
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