In recent years, electrokinetic energy conversion for pressure-driven flow through hydrophobic nanochannels has attracted increasing attention from numerous researchers. However, the reported electrokinetic energy conversion efficiencies may be overestimated owing to neglect of the surface charge mobility effect of hydrophobic nanochannels. In fact, both the effective slip length and the induced streaming potential are influenced by the surface charge mobility. In this paper, a theoretical model for electrokinetic energy conversion through graphene nanochannels is developed with consideration of the influence of surface charge mobility. The surface charge density σ s varies from very low to considerably high. A numerical solution to the electric potential is obtained by using the finite difference method. We also derive analytical solutions for two limiting cases, namely, the case with a low zeta potential and the case without considerable electric double layer overlap. Our results reveal that consideration of the surface charge mobility leads to a 44% reduction in the maximum conversion efficiency. The predicted maximum efficiency is approximately 5.9% at σ s=−0.0162 C/m2. Our results may prove useful for predicting and optimizing the electrokinetic conversion efficiency in hydrophobic nanochannels.

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In microscale systems, hydrodynamic slip is considered to significantly influence the fluid flow field. Existing theories of electromagnetohydrodynamic flow in hydrophobic microchannels have postulated a constant slip length and ignored the effect of the surface charge on slip. In this study, we extended prior models by considering a combined pressure-driven and electromagnetohydrodynamic flow in microchannels with consideration of surface charge-dependent slip. An analytical solution for this simple model was derived. After a detailed discussion of the obtained results, we demonstrate that the more realistic surface-charge-dependent case has smaller velocities and flow rates than the surface-charge-independent slip case. Considering the effect of the surface charge on slip, the flow rate can be reduced by up to 7% in the currently selected parameter range. Our results are useful for optimizing electromagnetohydrodynamic flow models in microchannels.

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