We present a mathematical model to study the electroosmotic flow of a viscoelastic fluid in a parallel plate microchannel with a high zeta potential, taking hydrodynamic slippage at the walls into account in the underlying analysis. We use the simplified Phan-Thien–Tanner (s-PTT) constitutive relationships to describe the rheological behavior of the viscoelastic fluid, while Navier’s slip law is employed to model the interfacial hydrodynamic slip. Here, we derive analytical solutions for the potential distribution, flow velocity, and volumetric flow rate based on the complete Poisson–Boltzmann equation (without considering the frequently used Debye–Hückel linear approximation). For the underlying electrokinetic transport, this investigation primarily reveals the influence of fluid rheology, wall zeta potential as modulated by the interfacial electrochemistry and interfacial slip on the velocity distribution, volumetric flow rate, and fluid stress, as well as the apparent viscosity. We show that combined with the viscoelasticity of the fluid, a higher wall zeta potential and slip coefficient lead to a phenomenal enhancement in the volumetric flow rate. We believe that this analysis, besides providing a deep theoretical insight to interpret the transport process, will also serve as a fundamental design tool for microfluidic devices/systems under electrokinetic influence.

We discuss the entropy generation minimization for electro-osmotic flow of a viscoelastic fluid through a parallel plate microchannel under the combined influences of interfacial slip and conjugate transport of heat. We use in this study the simplified Phan-Thien–Tanner model to describe the rheological behavior of the viscoelastic fluid. Using Navier’s slip law and thermal boundary conditions of the third kind, we solve the transport equations analytically and evaluate the global entropy generation rate of the system. We examine the influential role of the following parameters on the entropy generation rate of the system, viz., the viscoelastic parameter (εDe2), Debye–Hückel parameter κ¯, channel wall thickness (δ), thermal conductivity of the wall (γ), Biot number (Bi), Peclet number (Pe), and axial temperature gradient (B). This investigation finally establishes the optimum values of the abovementioned parameters, leading to the minimum entropy generation of the system. We believe that results of this analysis could be helpful in optimizing the second-law performance of microscale thermal management devices, including the micro-heat exchangers, micro-reactors, and micro-heat pipes.

We study the effect of viscoelasticity on the transportation of neutral solutes through a porous microchannel. The underlying transport phenomenon, modelled using the simplified Phan-Thien-Tanner constitutive equation, is actuated by the combined influence of pressure gradient and electroosmosis. Here, we obtain the closed form solution for the velocity distribution inside the flow domain and calculate the concentration profiles of the neutral solutes within the mass transport boundary layer by invoking the similarity solution approach. To establish the efficacy of viscoelastic solvents in the transportation of neutral solutes, which may find relevance in transdermal drug delivery applications, here we show the variations in the local solute concentration, the length averaged solute concentration at the wall, and the Sherwood number with the viscoelastic parameter. The present study infers that the shear-thinning nature of the viscoelastic fluid enhances the convective mass transfer as well as the permeation rate in the porous membranes. A complex interplay between the fluid rheology and the porous structure of the walls influenced by the electrochemistry at the interfacial scale modulates the mass transfer boundary layer of neutral solutes, implicating an effective method of mass transport in transdermal drug delivery applications.

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