Boundary Layer Thickness in Dual Potential Fluid Flow through Porous Medium

A transient, two-dimensional fluid flow through porous medium in a dual potential field has been studied analytically and experimentally. The field in a rectangular domain is created by placing two inlets: manifold along one of the edges at potential φ1, and the other inlet is a channel placed in the center of the domain perpendicular to the first inlet on the top surface at potential φ2(x). For any location in the domain with potential φ(x),x=(x,y), we define two potential differences Δφ1=φ(x)−φ1 and Δφ2=φ(x)−φ2(x) with respect to the two inlets. Therefore, two distinct sub-regions of the porous medium exist, where Δφ1<Δφ2 and Δφ1>Δφ2. The interface between the regions satisfies Δφ1=Δφ2 which we define as a boundary layer of thickness δ(x). In the experiments, we varied: the channel cross-sectional area, medium width, and thickness. The same fluid of very high viscosity (to reduce mixing) was used at both inlets with one stream dyed; thus, visualizing the flow and the two distinct sub-regions. We have also developed an analytical model to predict the boundary layer thickness, δ(x). Both, implicit and explicit solutions are found, where the explicit solution is given in the form of the inverse Lambert function. The solution has only one physical constant which is a function of the pressure gradient and the directional permeabilities of the porous medium. A comparison between experimental and analytical results reveals an excellent agreement.