Time-periodic electroosmotic flow of non-Newtonian fluid through a polyelectrolyte-grafted circular microchannel

The present research investigates the characteristics of flow dynamics and heat transfer of couple stress fluid through a circular microtube grafted with a polyelectrolyte layer. An alternating current electric field is applied to influence the fluid flow and heat transfer. A mathematical framework is established to describe the phenomenon of time-periodic alternating current electroosmotic flow by incorporating the Poisson–Boltzmann equations, couple stress fluid momentum equations, and energy equations for both polyelectrolyte and electrolyte layers. In the beginning, the Poisson–Boltzmann equation is solved analytically under the Debye–Hückel approximation to obtain the electric potential distribution. Subsequently, momentum equations of the couple stress fluid are then established for both the polyelectrolyte and electrolyte layers, and analytical solutions for these equations are obtained. Finally, the energy equation is discretized numerically using the finite difference scheme with Thomas algorithm. The primary results of this study indicate that velocity oscillation increases, but it is confined to the region near the interface of polyelectrolyte-electrolyte layers, while the amplitude of velocity oscillation decreases with higher oscillating Reynolds numbers. Temperature magnitude increases with the Debye–Hückel parameter, thickness of polyelectrolyte layer, couple stress parameters, and Brinkman number, while the drag parameter decreases it. Further, as the oscillating Reynolds number increases, the core region of the microtube experiences more frequent temperature oscillations, while the amplitude of the time-periodic temperature decreases. These findings provide deeper insights into electrokinetic transport phenomena, which hold potential for particle manipulation, enhancement techniques, biochip drug delivery, and biomedical engineering advancements.