Analysis of the laminar flow in a transition layer with variable permeability between a free-fluid and a porous medium

The transport problem in a three-layer channel consisting of a noticeable transition layer sandwiched by a free-fluid region and a homogeneous porous medium is investigated analytically. The heterogeneous transition layer is characterized by the continuous variation of porosity and permeability, which are specifically described by applying two sets of functions. The Brinkman model is employed in the transition layer, and the analytical velocity profile is obtained in terms of the Airy function. Consistency is found between the computation results and the PIV data measured by Goharzadeh et al. (Phys. Fluids 17:057102, 2005). After comparing the estimated permeability variations with the calculated variation, we find the former predicted permeability values are two orders of magnitude larger than the latter ones. The velocity discrepancy in the transition layer is ascribed to the effectiveness of the empirical permeability function: although the well-known Kozeny– Carman formula can precisely predict the permeability of the monodisperse spherical packing bed with constant porosity, it will overestimate the permeability in the transition layer. Then, the exact permeability variation is expressed by an exponential function, and a more general formula is needed to model the gradual change of permeability along the transition layer region.