Abstract
Brinkman's filtration equation is usually used to describe the low-Reynolds-number flow in porous media in situations where velocity gradients are non-negligible. In this paper a model problem is analysed to determine the influence of the porosity of the porous medium on the effective viscosity in Brinkman's filtration equation. In the idealized problem we consider axial flow through infinite and streaked arrays of cylindrical rods. Suppose that in such porous medium the flow is described by Brinkman's filtration equation then the effective viscosity can be calculated as a function of porosity. Contrary to the Einstein correction for dilute suspensions it is shown in this paper that the effective viscosity may be less than the viscosity of pure fluid.
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