Numerical simulation for electrokinetic energy conversion during couple stress fluid flow in microtube

Abstract

The severe energy constraints of modern healthcare sensors, actuators, and diagnostic instruments necessitate an in-depth analysis of electrokinetic energy conversion. In this context, this study investigates the interplay between streaming potential generation and its subsequent impact on electrokinetic energy conversion efficiency during a pressure-driven flow in a microfluidic tube. The mathematical model employs Nernst–Planck equation for the ionic distribution, Poisson equation for the electric potential, and Navier–Stokes equation for the fluid flow. To account the complex interactions and internal rotations within charged biomolecules and electrolytes, the model incorporates the non-Newtonian couple stress effect. A comprehensive analysis for a wide range of relevant parameters has been performed using a numerical solution approach. The results elucidate the influence of the associated parameters on the fluid velocity, steaming potential, and electrokinetic energy conversion efficiency. The outcomes demonstrate that, within the specified parameter range, increase in couple stress and decrease in Debye length lead to an enhancement in streaming potential. Increasing the electrokinetic parameter enhances both the flow rate and electrokinetic energy conversion efficiency, thereby facilitates efficient cooling. Explicit analytical solutions for the fluid velocity, streaming potential, and electrokinetic energy conversion efficiency are obtained as a limiting case for a Newtonian fluid under the combined circumstances of low advection and the Debye–H\(\ddot{u}\)ckel electrostatic framework. Furthermore, the investigation has been extended to optimize the electrokinetic energy conversion efficiency using statistical analysis based on the response surface method.