On the Brinkman correction in unidirectional Hele-Shaw flows

We study the Brinkman correction to Darcy's equation for unidirectional flows in a Hele-Shaw cell. Three examples, describing gravity-driven flow with variable density, pressure-driven flow with variable viscosity, and pressure-driven flow in a cell with a specific variation in aperture are discussed. In general, the Brinkman correction involves nonlocal terms, and it is not simply equal to an effective viscous shear stress involving the gap-averaged velocity. The latter is applicable at long wavelengths, however, provided that the viscosity is augmented by a prefactor equal to 12/pi(2). (C) 2003 American Institute of Physics.