An expression for the effective viscosity (mu_e) 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 mu_e is equal to mu*(epsilon - 3/7)/2 for epsilon geq 3/7 and 0 for epsilon < 3/7, where epsilon is the porosity and mu is the fluid viscosity. Thus mu_e < mu for all epsilon. For mu_e = 0 the Brinkman equation reduces to Darcy\'s law.
WP Breugem. The effective viscosity of a channel-type porous medium.
published, Physics of Fluids, 2007, 19