Convective-diffusive transport of a chemically reactive solute is studied analytically for a general model of a multiphase system composed of ordered or disordered particles of arbitrary shapes and sizes. Use of spatially periodic boundary conditions permits analysis of particulate multiphase systems of effectively infinite size. Solute transport occurs in both the continuous and discontinuous bulk phases, as well as within and across the interfacial phase boundaries separating them. Additionally, the solute is allowed to undergo generally inhomogeneous first-order irreversible chemical reactions occurring in both the continuous and discontinuous volumetric phases, as well as within the interfacial surface phase. Our object is tha t of globally describing the solute transport and reaction processes at a macro- or Darcy-scale level, wherein the resulting, coarse-grained particulate system is viewed as a continuum possessing homogeneous material transport and reactive properties. At this level the asymptotic long-time solute macrotransport process is shown to be governed by three Daruy-scale phenomenological coefficients: the mean solute velocity vector dispersivity dyadic D, and apparent volumetric reactivity coefficient K. A variant of a Taylor-Aris method-of-moments scheme (Brenner & Adler 1982), modified to include solute disappearance via chemical reactions, is used to express these three macroscale phenomenological coefficients in terms of the given microscale phenomenological data and geometry. The general solution technique, illustrated here for a simple, ordered geometrical realization of a two-phase system, reveals the competitive influences of the respective volumetric/surface-excess transport and reaction processes, as well as the solute adsorptivity, upon the three macroscale transport coefficients.
|Number of pages
|Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
|Published - 1990