Control of Mass Flow-Rate of Viscoelastic Fluids Through Time-Periodic Electro-Osmotic Flows in a Microchannel

Abstract

In the present research, we address the implications of the pulsating electric field on controlling mass flow rate characteristics for the time-periodic electro-osmotic flow of a viscoelastic fluid through a microchannel. Going beyond the Debye–Hückel linearization for the potential distribution inside the electric double layer, the Phan–Thien–Tanner constitutive model is employed to describe the viscoelastic behavior of the fluid. The analytical/semi-analytical expressions for the velocity distribution corresponding to a steady basic part and a transient perturbed part are obtained by considering periodic pulsations in the applied electrical field. Our results based on sinusoidal pulsations reveal that enhanced shear thinning characteristics of the viscoelastic fluids show the higher amplitude of pulsations with the oscillations in the velocity gradients primarily contrived within the Electric Double Layer region. The amplitude of mass flow rates increases with increasing the viscoelastic parameter εsWi2, whereas, the phase lag displays a reverse trend. The analysis for an inverse problem is extended where the required magnitude of electric field pulsations for a target mass flow rate in the form of sinusoidal pulsations. It is found that with increasing shear-thinning characteristics of the viscoelastic fluid, there is a progressive reduction in the required electric field strength to maintain an aimed mass flow rate. Besides, required electric fields for controlled mass flow with triangular and trapezoidal pulsations are also determined.