Computer simulation study of the effective viscosity in Brinkman’s equation

Brinkman’s equation is often used to match solutions of Stokes’ equation to solutions of Darcy’s law at free‐fluid:porous medium interfaces by the introduction of an effective viscosity parameter, μ_e. Theoretical predictions of the dependence of μ_e on the porosity of the porous medium have given conflicting results. A finite difference solution of Stokes’ equation in three dimensions was used to study fluid flow near the interface between a free fluid and a porous medium. It was found that in order to match solutions of Brinkman’s equation to the numerical solutions, the value of μ_e had to be greater than the free‐fluid viscosity. Within numerical precision, the effective viscosity μ_e was monotonically increasing with decreasing porosity. Good fits to the numerical fluid velocity profiles were obtained for porosities ranging from 50% to 80%.