Myths about later-day extensions of Darcyʹs law

Low intensity mass and energy transport processes in porous solids historically have been treated as though they are adequately described by Darcyʹs long-ago empirical relationship (Darcy, H., 1856. Les Fountaines Publique de la Ville Dijon, Dalmont, Paris). Almost a hundred years had elapsed, however, before Yuster (Yuster, S.T., 1951. Theoretical consideration of multiphase flow in idealized capillary systems. Proceedings of the Third World Petroleum Congress, 2, 437–445) inferred that coupling effects might be involved during the ensuing pore-space fluid flows; therefore, Yuster in effect hypothesized that the Onsager (Onsager, L., 1931. Reciprocal relations in irreversible processes. Physical Reviews, 37, 405–426; 38, 2265–2279) formulations probably should be considered. This is because of the way the latter take into explicit account the fact that entropy production rates for decaying irreversible processes inherently are positive-definite quantities. In this paper, it is specifically suggested that Yusterʹs watershed ideas preferably should be employed for cases where there is a significant momentum transfer across the interstitial no-slip fluid–fluid interfaces of contact. And here, it will be further suggested that these ideas can also be applied to describe the nature of other categories of porous media-coupled transport processes. Accordingly, the purpose of this paper is to call attention to what is believed to be a growing need to clarify the ongoing dispute about what still remains as a fractious issue. The hope is, of course, that future workers eventually will be able to anticipate if and when the so-called Onsager (i.e. O/Dogma) models should be employed rather than the superficial empirical Darcian (D/Dogma) ones. Thereby, perhaps the validity of simulation outputs can be significantly enhanced. In other words, the intended goal here will be to establish a coherent way to examine if and when two or more contiguous mass/energy fluid particle streams will couple with each other in ways governed by the dictates of the famous Onsager Reciprocity Relationships (ORR). This approach was first proposed by Lars Onsager, and eventually, in 1968, he was awarded for it the Nobel Prize in Physics. Accordingly, it is the intention in what follows to suggest that whenever traditional modeling algorithms do not seem to provide adequate forecasts for future process states, then other more solidly-based means must be developed to replace what here are being referred to as somewhat suspect later-day extensions of Darcyʹs Law.