Electro-osmotic effect on solute dispersion in viscoelastic fluid through a microchannel with reactive boundaries

The study of solute dispersion in microchannel electro-osmotic flow of viscoelastic fluids is crucial for lab-on-a-chip design, drug delivery, and diagnostics. This paper investigates the dispersion of solutes in a viscoelastic fluid flow driven by electro-osmotic body forces in a microchannel, incorporating the wall reactions. While most studies on Taylor dispersion have focused on Newtonian fluids or inelastic non-Newtonian flows, the viscoelastic behavior of non-Newtonian fluids remains largely unexplored. A mathematical model is developed, and the convection-diffusion equation is solved analytically using Mei's multi-scale homogenization technique. A numerical method validates the current analytical solution. The results show that increased fluid viscoelasticity amplifies solute dispersion due to enhanced elasticity, influencing both longitudinal and transverse patterns. Thicker electric double layers, represented by higher Debye-Hückel parameters, reduce the driving force of electro-osmotic flow, decreasing longitudinal dispersion while slightly increasing transverse diffusion. It dampens the electro-osmotic velocity, reducing longitudinal dispersion while slightly increasing transverse diffusion due to weaker electrokinetic effects near the walls. Increasing the Weissenberg number delays transverse uniformity due to enhanced viscoelasticity, while higher Debye-Hückel parameters accelerate the attainment of uniformity. In the case of a reaction at a single boundary, increasing the reaction parameter enhances transverse non-uniformity, while for reactions at both boundaries, non-uniformity is initially higher but decreases as the reaction parameter increases. The novelty of this work lies in its focus on viscoelastic fluids under electro-osmotic forces, offering a comprehensive analytical framework that accounts for wall reactions, which has not been previously explored in such detail.