The Role of Tortuosity in Upscaling

The concept of tortuosity is an integral part of models that describe transport in multiscale systems. Traditionally, tortuosity is defined as the ratio of an effective path length to the shortest path length in the microstructure. While the shortest path length can be unambiguously specified, the same is not true for the effective path length, since it changes from one type of transport to another. Consequently, it is possible to have different values of tortuosity for different transport processes taking place in the same system. This is convenient since, under this approach, different transport processes can involve the same type of filters of the microscale information, but the nature of such information is what characterizes each type of transport process. In order to avoid running into unclear interpretations, a set of tortuosity rules are proposed, which relate this concept only to the microscale geometry. On the basis of these rules, we examine the pertinence of introducing the tortuosity concept in mass transport. In particular, we study mass diffusion with and without chemical reaction and convection in porous media. Of all these cases, our analysis indicates that the concept of tortuosity is only adequate for passive diffusion, since in the other cases there is an unavoidable coupling of the transport phenomena that determine the effective path of the solute.