Streaming potential generated by a pressure-driven flow over superhydrophobic stripes

Abstract

The streaming potential generated by a pressure-driven flow over a weakly charged slip-stick surface [the zeta potential of the surface is smaller than the thermal potential (25 mV)] with an arbitrary double layer thickness is theoretically studied by solving the Debye–Huckel equation and Stokes equation. A series solution of the streaming potential is derived. Approximate expressions for the streaming potential in the limits of thin double layers and thick double layers are also given in excellent agreement with the full solution. To understand the impact of the slip, the streaming potential is compared against that over a homogeneously charged smooth surface. Our results indicate that the streaming potential over a superhydrophobic surface can only be enhanced under certain conditions. Moreover, as the double layer thickness increases, the advantage of the superhydrophobic surface diminishes. In addition, the Onsager relation which directly relates the magnitude of electro-osmotic effect to that of the streaming current effect has been explicitly proved to be valid for thin and thick double layers and homogeneously charged superhydrophobic surfaces. Comparisons between the streaming current and electro-osmotic mobility for an arbitrary electric double layer thickness under various conditions indicate that the Onsager relation seems applicable for arbitrary weakly charged superhydrophobic surfaces although there is no general proof. Knowledge of the streaming potential over a slip-stick surface can provide guidance for designing novel and efficient microfluidic energy-conversion devices using superhydrophobic surfaces.