Analytical asymptotic solutions for longitudinal dispersion with dead zones

Abstract

Analytical solutions for the asymptotic behaviour of two-dimensional flow with dead zones have been obtained using the Aris method of moments. These spatial and temporal solutions demonstrate the relative contributions of main flow shear dispersion and dead zone trapping to the total rate of longitudinal dispersion. A general solution for spatial distributions was recently given in the literature but was not applied to a specific dead zone geometry. Good agreement is found with the dead zone experiments of Valentine [30] and previous numerical solutions. Steady-state equilibrium profile solutions for the variations in mass, centroid and variance over the flow cross-section au derived for both spatial and temporal distributions. While the centroid, variance and skew all increase linearly during the equilibrium period, the kurtosis increase quadratically, consistent with an eventual asymptote of the kurtosis coefficient to the Gaussian value of 3.0.