Macrotransport processes: Brownian tracers as stochastic averagers in effective-medium theories of heterogeneous media

Abstract

Macrotransport processes (generalized Taylor dispersion phenomena) constitute coarse-grained descriptions of comparable convective-diffusive-reactive microtransport processes, the latter supposed governed by microscale linear constitutive equations and boundary conditions, but characterized by spatially nonuniform phenomenological coefficients. Following a brief review of existing applications of the theory, we focus-by way of background information- upon the original (and now classical) Taylor-Aris dispersion problem, involving the combined convective and molecular diffusive transport of a point-size Brownian solute “molecule” (tracer) suspended in a Poiseuille solvent flow within a circular tube. A series of elementary generalizations of this prototype problem to chromatographic-like solute transport processes in tubes is used to illustrate some novel statistical-physical features. These examples emphasize the fact that a solute molecule may, on average, move axially down the tube at a different mean velocity (either larger or smaller) than that of a solvent molecule. Moreover, this solute molecule may suffer axial dispersion about its mean velocity at a rate greatly exceeding that attributable to its axial molecular diffusion alone. Such “Chromatographic anomalies” represent novel macroscale non-linearities originating from physicochemical interactions between spatially inhomogeneous convective-diffusive-reactive microtransport processes.