Electrokinetic energy conversion of third-grade fluids with slip-dependent zeta potential in nanochannels

This study employs a dual-track strategy combining theoretical analysis and numerical simulation to investigate the electrokinetic flow characteristics and energy conversion mechanisms of third-grade fluids in nanochannels. A semi-analytical framework based on the homotopy perturbation method is established to derive analytical solutions for velocity, streaming potential, and energy conversion efficiency. High-precision numerical solution is achieved through spatial discretization using the Chebyshev spectral method and the formulation of a global Jacobian matrix for the strongly nonlinear coupling effect. Key findings reveal that streaming current diminishes with increasing electrokinetic width and non-Newtonian parameters. However, this attenuation is significantly mitigated when the slip-zeta potential coupling effect is considered. An optimal electrokinetic width maximizes output power and conversion efficiency, with peak values notably enhanced under slip-zeta coupling effect. Increasing the non-Newtonian parameter reduces input and output powers. But, with the enhancement of the non-Newtonian effect, the conversion efficiency initially rises and then declines under three slip conditions, yielding an optimal parameter of the non-Newtonian effect. Moreover, compared to the no-slip case, the optimal parameter increases under slip-independent and dependent-zeta potentials. This work highlights the critical regulatory role of slip-zeta coupling mechanisms in nanochannel energy conversion performance.