Mass Transport Analysis in an Annular Microchannel Driven by a Time-Periodic Oscillatory Electroosmotic Flow for a Maxwell Fluid Under High Zeta Potential

This study investigates characteristics of the mass transport for Maxwell fluids driven by a time-periodic oscillatory electroosmotic flow (EOF) in annular microchannels under high zeta potential conditions. A finite difference method is employed to solve the nonlinear Poisson–Boltzmann equation, the Maxwell fluid momentum equation, the convection–diffusion equation, and the time- and space-averaged mass transport rates are obtained by using the composite trapezoidal rules, and the reliability of the present numerical results for the low zeta potential is verified by comparing the analytical approximate results obtained by using the Debye–Hückel (D–H) linear approximation. The effects of key dimensionless parameters—including electrokinetic width, angular Reynolds number, wall potential ratio, relaxation time, and the inner-to-outer radius ratio—on flow velocity, solute concentration distribution, and average mass transport performance are systematically analyzed. The results show that: (1) a high zeta potential enhances velocity and concentration, while suppressing the spatio-temporal average mass transport rate; (2) the elastic effects of Maxwell fluids, characterized by relaxation time, significantly modulate the structure of velocity and concentration fields under periodic electric forcing, thereby enhancing local mixing or enabling spatially selective separation; (3) at low Reynolds number, the flow remains relatively uniform, facilitating species separation, whereas at higher Reynolds number, amplified elastic responses near the walls lead to increased nonuniformity in velocity and concentration distributions, promoting mixing; (4) asymmetric zeta potentials induce elastic responses in the core region, further intensifying concentration nonuniformity and enabling species separation under specific parameter combinations; and (5) geometric factors such inner-to-outer radius ratio and electrokinetic width significantly affect radial gradient intensity, resulting in switching phenomena between fast- and slow-diffusing species.