The effective viscosity of a channel-type porous medium

Abstract

An expression for the effective viscosity (μe) of a homogeneous channel-type porous medium has been derived by matching the Brinkman solution for the macroscopic flow with the volume average of the corresponding Stokes solution for the microscopic flow. In a least-squares error sense, the optimal value for μe is equal to μ(ϵ−3∕7)∕2 for ϵ⩾3∕7 and 0 for ϵ<3∕7, where ϵ is the porosity and μ is the fluid viscosity. Thus, μe<μ for all ϵ. For μe=0, the Brinkman equation reduces to Darcy’s law.