Electroosmotic pressure-driven oscillatory flow and mass transport of Oldroyd-B fluid under high zeta potential and slippage conditions in microchannels

Abstract

The appropriate analysis for microscale transport of complex fluids is essential in many scientific and technological devices to establish the accurate theoretical model. For example, the viscoelastic fluid plays a vital role in medical diagnostics to separate biomolecules using the concept of a microchannel flow under time-periodic oscillation effects. The available literature demonstrates no such analysis existed for the time-periodic oscillation of Oldroyd-B fluid subjected to the electroosmotic and slippage flow conditions. The present paper develops a new mathematical approach for an electroosmotic pressure-driven pulsatile-Oldroyd-B fluid flow between two parallel plates in microchannels under slipping actions on the wall surface. The flow takes place in an exponential electric field regime by imposing an exponential pressure gradient with time to simulate the elastic and viscous behaviors of the Oldroyd-B fluid. A finite difference method (MATLAB bvp4c) is employed to solve the strongly non-linear electrical potential and concentration equations. A time-periodic oscillation effect on the velocity profile, concentration distribution, and mass transport is analyzed under low or high zeta potentials at the wall. The results highlight that the elastic nature of fluid increases the oscillatory behavior of flow velocity compared to that of the viscous fluid. The zeta potential (ξ¯)in the flow field is responsible for increasing the flow velocity amplitude. Notably, the flow velocity for a high zeta potential (ξ¯=4) at the wall has increased approximately 142.75% at the peak point compared to the low zeta potential(ξ¯=0.1). The velocity amplitude for a higher elastic fluid (elasticity, E = 0.2) compared to a lower elastic fluid (E = 0.1) amplifies 21.01% at the peak point. Finally, it is noteworthy to demonstrate that for the Oldroyd-B fluid, a resonant behavior of the mass transfer rate is dependent on the combination of the parameters, namely angular Reynolds number and elasticity. In this context, it is evident that the interaction of the fluid elasticity and the oscillatory character of flow enhance the mass transfer rate. This innovative concept can be adapted to amplify the fluid mass transfer rate.