CALCULATION OF LAG TIME FOR CONVECTIVE-REACTIVE DIFFUSION

Abstract

Closed form solutions for the steady-state permeability P and the lag time L of a linear diffusion system with concurrent convection and reaction were obtained by two methods. In the first method, we identify the singularity at s = 0 of the Laplace transform of the total amount of diffusant, Q(s), released into the receiver as representation of the asymptotic diffusion behavior. P and L are then obtained from the time-independent coefficients of an expansion of Q(s) about s = 0. In the second method, we transform the convective-reactive diffusion equation into a form that contains only first and second derivatives of the concentration distribution function. By comparison of the resulting equation with that for a heterogeneous diffusion system, relationships of the convection velocity and rate constant with the position-dependent partition coefficient in heterogeneous diffusion is found. Taking advantage of the known solutions for permeabiliy and lag time in heterogeneous diffusion, the corresponding expressions for P and L in convective-reactive diffusion are then obtained by transcription. These methods have the advantage over earlier approaches in that solutions in an infinite form are avoided.