Change in macroscopic concentration at the interface between different materials: Continuous or discontinuous

Abstract

There have been conjectures that a spatial average could result in a volume‐average concentration which is no longer continuous at sharp interfaces between different materials. However, convincing experimental evidence showing the existence of such a discontinuity is not available because of the difficulty associated with measuring solute concentration in the void space within a porous medium. In this paper we used pore‐scale simulations to explore the change in macroscopic concentration when solute moves from one material into another. Water flow through the void space was assumed to be laminar, and solute transport consisted of molecular diffusion and advection; both were simulated using the lattice Boltzmann equation methods. To accurately represent the fluid‐solid interface, the multiple‐relaxation‐time lattice Boltzmann equation method was used to simulate fluid flow. We first simulated solute transport in a 3D column with one half packed with fine glass beads and the other half with coarse glass beads. The simulated solute concentration and solute flux at pore scale were then spatially averaged to produce volume‐average and flux‐average concentration profiles, respectively, in attempts to understand if solute accumulates at the media interface when moving from one medium into another. The results revealed that, when solute migrated from the coarse medium into the fine medium, it did accumulate at the media interface; we also found mass accumulation at the reservoir‐column interface. Such accumulations made solute take more time to break through the column when flowing from the coarse medium to the fine medium than from the fine medium to the coarse medium. We also simulated solute movement in an idealized 2D column packed with different rectangular solids and with high porosity; the results indicated that, although the dispersive properties of the two media differed considerably, there was no mass accumulation and the macroscopic concentration was found to be continuous at the media interface. These simulated results suggest that a sharp change in material properties with moderate porosity will likely lead to a mass accumulation, but knowing the transport properties of the two materials alone is not sufficient to determine if a mass accumulation could develop. What causes mass accumulations appears to be some microstructures in the vicinity of the interface, which cannot be accounted for by the macroscopic transport parameters of each of the two media.