Shear flow over a porous layer: Velocity in the real proximity of the interface via rheological tests

In this paper, we have experimentally investigated the velocity profile of a fluid undergoing simple shear above a porous medium. To this end, we used for the first time rheological tests performed with a constant stress rheometer equipped with parallel plate geometry with a real porous medium glued on the lower plate. The velocity at the interface between the porous layer and the free fluid was inferred by extrapolating the linear velocity profile in the free fluid to the interface. These data were nicely compared with predictions obtained integrating the Brinkman extension of Darcy law in the porous medium together with Stokes equations in the free fluid coupled at the interface by the continuity of velocity and by the momentum balance suggested by Ochoa-Tapia and Whitaker [Int. J. Heat Mass Transfer 38(14), 2635 (1995)]. In the literature, the physical origin of the stress jump imposed by Ochoa-Tapia and Whitaker at the interface has been attributed to a perturbation of the velocity profile in the vicinity of the interface, both in the porous medium and in the free fluid. For the first time, the disturbance in the free fluid has been measured and quantified resulting in a satisfactory agreement with theoretical predictions.