Solution of Gill's generalized dispersion model: Solute transport in Poiseuille flow with wall absorption

Previous applications of Gill's generalized dispersion model in the description of solute transport in Poiseuille flow with wall absorption used only the long-time asymptotic values of dispersion coefficients. They are also limited to the simplest second order equation, which resembles Taylor's classic model with a Gaussian distribution for cross-sectional mean concentration. To obtain the time-dependent dispersion coefficients, in this work the coefficients of dispersion model are concretely related to the moments of concentration distribution. With the readily obtained higher order dispersion coefficients, solution of the Taylor-Gill expansion equation is presented up to the fourth order, accounting for the asymmetry (skewness) and heavy tails (kurtosis) of the cross-sectional mean concentration distribution.