The ion-partitioning effects on solute transport phenomena of time-periodic electro-osmotic flow in fractional Jeffrey fluid are investigated through a polyelectrolyte layer (PEL)-coated conical nanopore within a reactive wall whose ends are connected with two large reservoirs. By considering the ion-partitioning effects, analytical solutions for the induced potential and the axial velocity are presented, respectively, from the modified Poisson–Boltzmann equation and the Cauchy momentum equation with the proper constitutive equation of the fractional Jeffrey fluid model in the exterior and interior of the PEL. The analytic solution of the convection–diffusion for solute transport is established in the entire domain. The influence of the oscillating Reynolds number Rew, permittivity ratio εr between two mediums, relaxation time [Formula: see text], retardation time [Formula: see text], phase partitioning coefficient σp, PEL fixed charge density qfix, Debye–Hückel parameter κa, and softness parameter λs are investigated in this study. Asymptotic solution for the axial velocity was also presented for low-oscillating Reynolds numbers and validated. The maximum axial velocity occurs when the permittivity between the PEL and electrolyte is the same for all models. The volumetric flow rate decreases with the increase in the PEL thickness, positive PEL charge density, and softness parameter in our study. The volume flow rate of the Newtonian fluid increased 24.07% for Maxwell fluid ([Formula: see text], α = 1) and 11.56% for Jeffrey fluid ([Formula: see text], α = 1, and [Formula: see text]), when [Formula: see text], Rew = 10, qfix = 5, d = 0.2, [Formula: see text], and [Formula: see text]. The mass transport rate increases with relaxation time, tidal displacement, and permittivity ratio between these layers.

The theoretical analysis for the mass transfer process of an oscillatory electroosmotic flow (EOF) in the fractional Jeffrey fluid model is studied through the polyelectrolyte layer (PEL) coated cylindrical annulus...

The time-dependent electroosmotic flow (EOF) and heat transfer characteristic of a generalized Maxwell fluid through the polyelectrolyte layer (PEL) grafted nanopore are investigated while considering different permittivity between the PEL and electrolyte solution. The ion partitioning effects arise due to the different permittivity among these regions. Taking the ion partitioning effects, the analytic solution for the induced potential is established within and outside the PEL from the modified Poisson–Boltzmann equation assuming the Debye–Hückel approximation for a low surface charge. The Cauchy momentum equation with a suitable constitutive equation for fractional Maxwell fluids is derived, and the corresponding analytic solution is presented to provide the axial fluid flow distribution in the full domain. The energy fluxes that have major contributions to the energy equation mainly depend on axial conduction, convection due to electrolyte transport, and Joule heating effects for the external electric field. The analytical solutions of the energy equation for hydro-dynamically fully developed flow with constant thermophysical properties are presented to provide the temperature distribution considering constant heat flux at the nanopore wall. The influence of several important factors for characterizing heat transfer behavior is investigated in the present study. The maximum fluid velocity occurs when the permittivity between the PEL and electrolyte region is the same. The increasing values of fluid velocity imply higher convective heat transfer and make the Nusselt number higher. This study makes a conscious effort toward highlighting the modality controlling the heat transfer characteristics for the ion partitioning effects.

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