Transient dispersion in a channel with crossflow and wall adsorption

Dispersion of substances with reactive boundaries is relevant to a wide range of chemical, biological, and geophysical processes. A supplied crossflow, or equivalently sedimentation of the substance, is also expected to affect the dispersion process. We consider a setting with two infinite parallel plates, where the diffusive substance is adsorbed at the lower plate, simultaneously advected longitudinally by a main flow and vertically by a crossflow. Although the same configuration has been studied previously with the generalized Taylor dispersion (GTD) theory [M. Shapiro and H. Brenner, AIChE J. 33, 1155 (1987)10.1002/aic.690330710] and a dual-perturbation method [T. Y. Lin and E. S. G. Shaqfeh, Phys. Rev. Fluids 4, 034501 (2019)10.1103/PhysRevFluids.4.034501], both of them focused on the long-time asymptotic dispersion regime, exclusive of the important transient dispersion process. As an extension of these works to the transient dispersion process, we utilize the classical method of moments along with the eigenfunction expansion to calculate the moments up to fourth order, and thus the effects of non-Gaussian properties can be reflected. Compared with the result of Brownian dynamics simulations, the present work is shown sufficient to cover the preasymptotic dispersion regime out of reach of the GTD and dual-perturbation method. Strong non-Gaussian properties are found in the preasymptotic regime, as reflected by the nonzero skewness and kurtosis as well as asymmetric longitudinal concentration distribution. Additionally, it is found that the duration of the preasymptotic regime is extended in the presence of both the crossflow and wall adsorption. Considering that most of the substance may have been adsorbed during the preasymptotic regime, it is necessary to use higher-order dispersion models such as the one presented herein.