Solute dispersion in an electroosmotic flow of Carreau and Newtonian fluids through a tube: analytical study

Abstract

The study presents a comprehensive theoretical analysis of solute transport under the electroosmotic flow of a two-fluid model consisting of Carreau–Newtonian fluids in a cylindrical tube, to predict more accurate dispersion dynamics. To accommodate the broader physical situation, the induced streaming potential resulting from a gradient in ion accumulation along the flow direction owing to the convective transport is considered. The analysis specifically accounts for the effect of slip and no-slip boundary conditions at the tube wall, addressing hydrophobic and hydrophilic properties of the Newtonian fluid, respectively. For the hydrophobic case, the influence of slip flow on the solid–liquid interface is considered, leading to the slip-dependent zeta potential. The closed-form solution of the velocity profile is obtained using the perturbation technique, assuming the Weissenberg number as the small perturbation parameter for both slip and no-slip formulations. The combined advection–diffusion equation for solute transport is addressed using a hybrid method incorporating Gill’s approach and the Hankel transformation to obtain the analytical expressions for the dispersion coefficient, mean concentration, and concentration distributions. The apparent slip-dependent zeta potential within the electric double layer due to the slip flow at the wall is shown to have a significant impact on the dispersion dynamics. The study examines the impact of various dynamic parameters, namely the Carreau fluid parameters (Weissenberg number and power law index), zeta potential at the wall, inverse Debye length, viscosity ratio parameter, and slip length, on the concentration distribution through convection, ultimately affecting the dispersion coefficient. The effect of wall slip condition on the solute plume distribution is more pronounced at the higher time level. It is noted that the effect of all the dynamical parameters on solute dispersion is observed to be more significant for the slip-dependent zeta potential at the wall compared to the no-slip condition at the wall. The findings of this work have broad implications in biomedical engineering, drug delivery systems, chemical mixing, and separation processes.