This study systematically investigates the electrokinetic energy conversion of couple stress fluids through graphene nanochannels with mobile surface charges. A multi-physics model integrating constitutive relations, high-slip boundaries, and surface charge mobility is established. Numerical solutions under high surface potential conditions are obtained using the finite difference method coupled with the fourth-order Runge–Kutta scheme, while analytical solutions are derived for low surface potential validation. The results demonstrate that the surface charge mobility (αs) serves as a critical regulator of system behavior. For slip effects: with αs 0, slip consistently enhances efficiency at high surface charge density but exhibits dual-mode behavior at low density, suppressing efficiency for thick electric double layers (small Debye–Hückel parameter K) while enhancing it for thin layers (large K). When αs = 0, slip provides universal efficiency gains. For couple stress effects, efficiency shows an initial increase followed by stabilization with increasing stress parameter when αs 0, independent of double layer thickness. However, when αs = 0, the response bifurcates, increasing then stabilizing for small K values but decreasing then stabilizing for large K values. Additionally, surface charge mobility itself reduces both streaming potential and conversion efficiency through reverse current induction. This work elucidates the pivotal role of surface charge mobility in mediating slip-stress coupling phenomena, resolves the multi-mode conversion mechanisms under dynamic interface conditions, and provides theoretical foundations for optimizing microfluidic energy harvesting systems and biofluidic transport applications.
Fan et al. (Fri,) studied this question.