TAYLOR DISPERSION OF MULTICOMPONENT SOLUTES

Abstract

Coupled transport of multicomponent solutes in globally continuous systems is considered in the framework of the Generalized Taylor dispersion theory. Coupling between transports of n different species at the local (or micro-) scale, is considered to result from first-order irreversible surface reactions occurring on the local space boundaries, or from the off-diagonal terms of the solute diffusivity matrices. General expressions are obtained for the global effective (long-time) solute dispersion matrix cofficients: mean global scalar reactivity, velocity vector and dispersivity dyadic. The effect of surface chemical reactions is to partition the matter between different solute constituents. This is manifested in a coupling of the global transport coefficients, which may be mathematically removed by a linear (canonic) transformation applied to the effective global transport equation. This type of coupling does not exist for inert solutes. The second type of the global coupling is represented by the off-diagonal terms of the global velocity and dispersivity matrices. It exists for both reactive and inert solutes. This coupling stems from the convective dispersion process (dependence or the global velocity vector on the local space coordinate). Is shown to be irremovable from the global transport equation by any linear transformation via the solute partition matrix. In the canonic form of the global equation the irremovable coupling is manifested by the traceless parts of the global solute velocity matrix and the global solute dispersivity. The solution scheme is illustrated by calculating the mean global diffusivity of a solute consisting of two components, transport of which is coupled at the microscale via the molecular diffusivity matrix. At the macroscale the coupling is shown to be represented by negative off-diagonal terms of the global diffusivity matrix,