Load-dependent Taylor dispersion in a compliant electroosmotic pump conveying a simplified Phan-Thien-Tanner fluid

Abstract

We develop a coupled model for electroosmotic pumping and passive-solute dispersion of a solvent-free simplified Phan-Thien-Tanner fluid in a compliant slit microchannel. Pressure, wall deformation, axial field, velocity, and dispersion are evaluated self-consistently along the finite-throughput pump characteristic. Lubrication theory, Debye-Huckel electrostatics, an elastic-foundation wall law, and Taylor-Aris macrotransport yield a closed-form flux relation for combined electroosmotic and pressure-driven forcing. Because the shear rate depends cubically on the total shear stress, the two contributions cannot be superposed. The flux decreases monotonically with pressure gradient, ensuring a unique inversion at prescribed throughput. Current conservation couples the axial field to the deformed gap under constant-current and constant-voltage operation. In pressure-free flow, thinning the electric double layer produces a plug-like profile and the Newtonian Taylor coefficient decays as the inverse square of the Debye parameter. Under hydraulic loading, an adverse pressure gradient drives a sheared core counterflow that persists in the thin-double-layer limit, causing the coefficient to approach a finite plateau. At fixed nonzero throughput, partial cancellation between electroosmotic and pressure-driven shear yields a maximum plate number at finite double-layer thickness. This optimum is conditional: joint optimization over throughput and double-layer thickness shifts the overall optimum toward free-flow, thin-double-layer operation. Viscoelasticity can enhance or suppress loaded dispersion, while compliance shifts the pump characteristic and separation optimum. Brownian dynamics validates the reduced model. The resulting load-resolution relation identifies conditions that balance pressure delivery and separation performance.