Flow of Micropolar and Viscoplastic Fluids in a Hele–Shaw Cell
V. V. Shelukhin1,2, V. V. Neverov1,2
1Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: micropolar viscoplastic fluid, yield stress, Hele–Shaw cell, extension of Darcy's law
Abstract
A generalization of Darcy's law relating the velocity averaged over the transverse coordinate and the pressure gradient is obtained for flows in a thin layer. A nonlinear Darcy's law with a limiting gradient is derived taking into account microrotations and the yield stress. It is shown that the micropolarity of fluids manifests itself as an increase in the apparent viscosity and the limiting pressure gradient. A generalization of Darcy's law for the case of pseudo–plastic and dilatant Herschel—Bulkley fluids is obtained.
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