On the intrinsic nature of jump coefficients at the interface between a porous medium and a free fluid region

In this paper, we discuss the physical nature of the jump parameters that generally appear in the expression for the jump conditions at a fluid/porous interface. These jump parameters are generally thought of as intrinsic interfacial properties, just like surface tension in the case of fluid/fluid interfaces. Based on a two-step up-scaling analysis, we show that jump parameters can be interpreted as surface-excess quantities. The value of a surface-excess quantity is shown to depend linearly on the position of the discontinuous interface and is therefore not an intrinsic property. We propose a theoretical approach that allows to introduce genuine intrinsic interfacial properties and to propose a best choice for the position of the discontinuous interface. We show that these properties are tightly related to the definition of the interfacial zone. This theoretical approach is successfully assessed on three important cases: a laminar flow parallel to a fluid/porous interface, a turbulent flow perpendicular to a porous/fluid interface and heat transfer perpendicular to a fluid/porous interface. It is believed that this approach is general enough to be applied to any interfacial transport phenomenon.