Analytical and Numerical Study of Reactive Solute Transport in Viscoelastic Media Under Combined Electroosmotic and Pressure-Driven Flow

This study investigates reactive solute transport in a viscoelastic solvent flowing through a rectangular microchannel subjected to combined electro-osmotic and pressure-driven forcing. The governing advection–diffusion–reaction equation is solved using two complementary approaches: an analytical multiscale homogenization technique and a fully implicit second-order finite-volume formulation with adaptive time stepping. A systematic stability analysis demonstrates that the numerical method is unconditionally stable and provides accurate long-time predictions with significantly reduced computational effort. The results reveal that the effective dispersion coefficient varies non-monotonically with the pressure-to-electro-osmotic drive ratio parameter ω, exhibiting a distinct minimum at a critical value ωc. This minimum occurs only under adverse pressure gradients and shifts to lower ω with increasing Debye–Hückel parameter K, reflecting the influence of electrostatic screening. Viscoelasticity shifts the critical parameter ωc to higher values relative to Newtonian fluids. Detailed concentration contour analysis shows strong coupling between ω, viscoelasticity, and electro-osmotic strength: favorable pressure gradients confine the solute band, whereas adverse gradients induce upstream stretching, with the transition dependent on K. Boundary absorption further modulates transport by creating asymmetric solute depletion near the plates and reducing overall bulk concentrations, highlighting the interplay between advection, diffusion, and wall reaction kinetics. Overall, the combined analytical–numerical framework provides comprehensive insight into how viscoelasticity, electrokinetic effects, and boundary reactions jointly control reactive solute dispersion in microfluidic systems, offering a reliable basis for the design and optimization of electrokinetically driven microchannel processes.