Dispersion in Laminar Flow Through Tubes by Simultaneous Diffusion and Convection

Abstract

The dispersion of a small quantity of a solute initially injected into a round tube in which steady-state laminar flow exists is critically examined. It is shown that the mean solute concentration profile is far from being symmetric at small dimensionless times after injection. The mean concentration and the axial location at the peak of the profile are presented in detail as functions of time for flow with various Peclet numbers. It is suggested that such results may be useful for determining either the molecular diffusion coefficient or the mean flow velocity or both from experimental measurements. A previously established criterion in terms of the Peclet number for determining the minimum dimensionless time required for applying Taylor’s theory of dispersion is graphically illustrated. Although the complete generalized dispersion equation of Gill’s model is exact, the truncated two-term form of it with time-dependent coefficients is exact only asymptotically at large values of time; however, at small Peclet numbers, the two-term approximation is shown graphically to be reasonably satisfactory over all values of time. The exact series solution is compared with the solution of Tseng and Besant through the use of Fourier transform.