Unsteady convective diffusion with interphase mass transfer

Abstract

The theory of miscible dispersion is extended to interphase transport systems. As a specific example miscible dispersion in laminar flow in a tube in the presence of interfacial transport due to an irreversible first-order reaction at the wall is analysed by an exact procedure. A new exact dispersion model which accounts for dispersion with interphase transport is derived from first principles. The new concept of an ‘exchange coefficient’ arises naturally. This coefficient depends strongly on the rate of interfacial transport. Such transport also affects the convection and dispersion coefficients significantly. A general expression is derived which shows clearly the time-dependent nature of the coefficients in the dispersion model. The complete time-dependent expression for the exchange coefficient is obtained explicitly and is independent of the velocity distribution in the flow; however, it does depend on the initial solute distribution. Because of the complexity of the problem only asymptotic large-time evaluations are made for the convection and dispersion coefficients, but these are sufficient to give useful physical insight into the nature of the problem. When the rate of the wall reaction approaches zero the exchange coefficient also approaches zero and the other two coefficients approach their proper values in the absence of interfacial transport. At the other extreme of rapid wall reaction rates, the convection coefficient is more than 50 % larger than its value in the absence of interfacial transport and the dispersion coefficient is an order of magnitude smaller than that for zero interphase transport.