Several reasons may be invoked that could result in the inappropriateness of assuming the continuum approach when dealing with transport phenomena in porous media. Probably the most serious of these may be the violation of the length scale constraints. In an attempt to explore this, experimental and numerical investigations were conducted to study the significance of violating the length scale constraints when modeling transport phenomena in porous media based on the continuum approach. Initially, a porous system was constructed that complied with all length scale constraints such that it may be safe to assume the medium as a continuum. Then, in successive experimental setups, the system was allowed to violate the length scale constraints in one of its regions, and the behavior of the system in each case was analyzed. It was found that in situations when the length scale constraints are violated, it may not generally be appropriate to model the system using the macroscopic properties. Moreover, the experiments showed that for the cases under study, when the length scale characterizing the domain was not very much larger than the size of the representative elementary volume, REV (i.e., violating the second length scale constraint), significant variations were observed between measurements and simulation, assuming the continuum approach. As the system's size continued to diminish to be in the order of the size of the REV (i.e., violating the first length scale constraint), a surprisingly better match was observed. It was concluded that the boundary effects become significant as the length scale characterizing the domain gets smaller. However, further decrease in length scale incorporates mixing processes that compensate for the effects of the boundary region.

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Journal Journal of Porous Media
Salama, A. (Amgad), & van Geel, P. (2008). Flow and solute transport in saturated porous media: 2. Violating the continuum hypothesis. Journal of Porous Media, 11(5), 421–441. doi:10.1615/JPorMedia.v11.i5.10