Transient solute dispersion in electro-osmotic viscoplastic flow in a microchannel

The transport of a neutral solute in incompressible electro-osmotic flow of Bingham plastic non-Newtonian liquid flowing through a microchannel is studied theoretically. The flow is driven by a constant axially applied electric field. The non-dimensional conservation equations with associated boundary conditions are solved with Gill's series expansion technique. The whole transport process is analyzed using three transport coefficients, namely, advection coefficient, dispersion coefficient and the apparent asymmetry coefficient, respectively. The mean concentration distribution of the solute is calculated via a third-order approximation of the series expansion. The study investigates the collective effects of yield stress and electric double layer (EDL) thickness (inverse Debye length) on the transport of solute. The long-term behaviour of mean concentration distribution is shown to be accurately predicted by second-order approximations; however, utilizing third or higher order approximations in Gill's series expansion enables a more refined analysis of the small and moderate time behavior of transport coefficients. The present analysis is relevant to emerging applications in bio-microfluidics exploiting electroviscous fluent media.