Derivation of Complete Jump Boundary Conditions Between Homogeneous Media

The modeling of transport phenomena between homogeneous regions requires the derivation of jump boundary conditions. These conditions account for the rapid spatial variations of the transport properties taking place near the dividing surface of the media. There has been a long debate in the literature about whether the discontinuity should apply to the fields (e.g., velocity, temperature, concentration) or to their fluxes. In this work, a general methodology giving rise to jump conditions for both the fields and the fluxes is proposed. This method, besides using a microscopic closure, introduces macroscopic deviation fields that lead to closure schemes for both jump conditions. The methodology is applied first to the diffusive mass transport of a passive solute between a porous medium and a plain fluid and second to the classical problem of momentum transport in a channel partially filled with a porous medium. In both cases, it is required to account for the spatial variations of effective transport coefficients as well as the width and position where the jump conditions must be satisfied. One attractive feature of this methodology is related to its ability to provide the necessary length-scale constraints under which the jump conditions can be applied.