MICROSCOPIC ANALYSIS AND MACROSCOPIC MODELS - DEPOSITION DISPERSION CONTINUUM

The process of Taylor longitudinal dispersion of Brownian particles, s olutes, or heat applies expressly to the case with reflection coeffici ent alpha = 1. Nevertheless, convection-diffusion with loss at the wal l (0 less than or equal to alpha < 1) is often modelled in geophysical and chemical engineering contexts by superposing on macroscopic Taylo r dispersion a macroscopic loss term taken as a function of mean conce ntration. We test this procedure by finding, for flow in narrow channe ls, stationary solutions of the microscopic convection-diffusion equat ion that satisfy the wall condition 0 less than or equal to alpha < 1. The ratio of the longitudinal length scale of deposition predicted by the macroscopic model to that given by the microscopic analysis is 0. 85 for alpha = 0, decreasing monotonically to zero as alpha increases toward 1. The divergence of the two results as alpha --> 1 indicates t he singular place occupied by Taylor dispersion in the full deposition -dispersion continuum 0 less than or equal to alpha less than or equal to 1. Implications for macroscopic models of deposition during Row in porous media are discussed briefly.