On the apparent slip velocity at fluid–porous interfaces

The primary quantity that characterizes transport phenomena across fluid–porous interfaces is the slip velocity. Traditionally, the dimensionless form of the slip velocity is expressed using the porous medium's (interior) permeability-based length scale. Although commonly used, this form has been known to rapidly vary with volume fraction, interface location, and the geometry of the porous medium. In this paper, we propose to use a length scale based on the interface permeability to non-dimensionalize the slip velocity. Since this quantity contains information about the geometrical structure of the transition layer between the free-fluid region and the porous domain, it serves as an appropriate length scale to capture the physical features in the vicinity of the fluid–porous interface. Using numerical simulations, we investigate the influence of the volume fraction, scale separation parameter, location of the interface, structure of the porous medium, and geometry arrangement on the proposed non-dimensional slip velocity. These results provide substantial evidence that the new scaling overcomes the deficiencies of the interior permeability-based length scale. Moreover, we show that the proposed length scale is also applicable to flows over rough surfaces, while the widely employed interior permeability is undefined for such surfaces.