COMPUTER-SIMULATION STUDY OF THE EFFECTIVE VISCOSITY IN BRINKMAN 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, mu(e). Theoretical predictions of the dependence Of mu(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 mu(e) had to be greater than the free-fluid viscosity. Within numerical precision, the effective viscosity mu(e) was monotonically increasing with decreasing porosity. Good fits to the numerical fluid velocity profiles were obtained for porosities ranging from 50% to 80%.