This paper extends the analysis of solute dispersion in electrohydrodynamic flows to the case of band broadening in polyelectrolyte-grafted (soft) capillaries by accounting for the effects of ion partitioning, irreversible catalytic reaction and pulsatile flow actuation. In the Debye–Hückel limit, we present the benchmark solutions of electric potential and velocity distribution pertinent to steady and oscillatory mixed electroosmotic–pressure-driven flows in soft capillaries. Afterwards, the mathematical models of band broadening based on the Taylor–Aris theory and generalized dispersion method are presented to investigate the late-time asymptotic state and all-time evolution of hydrodynamic dispersion, respectively. Also, to determine the heterogeneous dispersion behaviour of solute through all spatiotemporal stages and to relax the constraint of small zeta potentials, a full-scale numerical simulation of time-dependent solute transport in soft capillaries is presented by employing the second-order-accurate finite difference method. Then, by inspecting the dispersion of passive tracer particles in Poiseuille flows, we examine the accuracy of two analytical approaches against the simulation results of a custom-built numerical algorithm. Our findings from hydrodynamic dispersion in Poiseuille flows reveal that, compared to rigid capillaries, more time is required to approach the longitudinal normality and transverse uniformity of injected solute in soft capillaries. For the case of dispersion in mixed electrohydrodynamic flows, it is found that the characteristics of the soft interface, including the thickness, permittivity, fixed charge density and friction coefficient of the polymer coating layer, play a significant role in determining the Taylor diffusion coefficient, advection speed and dispersion rate of solutes in soft capillaries.
Aqueous Nanoclusters Govern Ion Partitioning in Dense Polymer Membranes
