Transition layer thickness at a fluid-porous interface

Abstract

The length scale of the transition region between a porous layer and its overlying fluid layer is experimentally studied. The experimental setup consists of a rectangular channel, in which a fluid layer flows over a porous bed. Using particle image velocimetry and refractive index matching, two-dimensional velocity measurements in the interfacial region were performed. The thickness of this transition layer, defined by the height below the permeable interface up to which the velocity decreases to the Darcy scale, is measured and compared with the permeability and the matrix grain size. It was observed that the thickness of the transition zone, δ, is of the order of the grain diameter, and hence, much larger than the square root of the permeability as predicted by previous theoretical studies. The Reynolds number and the fluid height over the porous substrate were found to affect the gradient of the horizontal velocity component at the interfacial region while the length scale of the transition layer remains approximately unchanged. The effect of the porous matrix type has been investigated by utilizing spherical glass beads as well as granulates. Scaling the measured velocities by the interfacial velocity near the uppermost solid matrix resulted in a unique velocity distribution in the case of monodisperse glass beads, hinting that the interfacial velocity represents a proper scaling factor. However, for polydisperse granulate material deviation from this behavior was observed.