Transverse concentration distribution in Taylor dispersion: Gill’s method of series expansion supported by concentration moments

•Initial transition of the transverse concentration distribution in Taylor dispersion.•Fourth-order series expansions of mean concentration supported by fourth-order concentration moments.•Convergence analysis of Gill’s series expansions.

Presented in this paper is an analytical study of initial transition of the transverse concentration distribution in Taylor dispersion in a laminar tube flow. Gill’s method of series expansion originally for the solution of the cross-sectional mean concentration is rigorously developed to obtain the transverse concentration distribution. Existing result by homogenization technique is analytically recovered as the special asymptotic expression of the finding by the present series expansion. With the mean concentration given by a Hermite polynomial based on the first four concentration moments to fully reflect the skewness and kurtosis, fourth-order series expansions are performed with sound convergence to detail the initial transition of the transverse distribution. Due to the velocity non-uniformity, the distribution of the transverse concentration in the central cross-section of the cloud appears as a “saddle” and attenuates gradually with the contribution of diffusion but does not disappear even at large time. The transition in transverse distribution is confirmed as one order of magnitude slower than that to longitudinal normality.