The concept of tortuosity is an integral part of models that describe trans- port in multiscale systems. Traditionally, tortuosity is dened as the ratio of an eective path length to the shortest path length in a representative sample of the porous medium microstructure. While the latter can be unambiguously specied, the same is not true for the eective path length, since it changes from one type of transport to another. Consequently, it is possible to have dierent tortuosity values for dierent transport processes taking place in the same system. In order to avoid running into unclear interpretations, we pro- pose a set of tortuosity rules, which relate this concept only to the microscale geometry. On the basis of these rules, we examine the pertinence of introduc- ing the tortuosity concept in mass diusion with and without chemical reaction and convection in porous media. The upscaling process is achieved using the method of volume averaging. The results from this analysis show that eective transport coecients (including tortuosity) can be expressed in terms of lters of the microscale information. Indeed, dierent transport processes can involve the same type of lters, but the nature of the information that passes through them is what characterizes each type of transport. The role of tortuosity in upscaling is therefore a lter that should only capture the information related to the microstructure of a system.
Available at: http://works.bepress.com/francisco_j_valdes_parada/38/