# Energy conversion by surface-tension-driven charge separation

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## Abstract

In this work, the shear-induced electrokinetic streaming potential present in free-surface electrolytic flows subjected to a gradient in surface tension is assessed. Firstly, for a Couette flow with fully resolved electric double layer (EDL), the streaming potential per surface stress as a function of the Debye parameter and *ζ*-potential is analyzed. By contrast to the Smoluchowski limit in pressure-driven channel flow, the shear-induced streaming potential vanishes for increasing Debye parameter (infinitely thin EDL), unless the free surface contains (induced) surface charge or the flow at the charged, solid wall is permitted to slip. Secondly, a technical realization of surface-tension-induced streaming is proposed, with surface stress acting on the free (slipping) surfaces of a micro-structured, superhydrophobic wall. The streaming potential is analyzed with respect to the slip parameter and surface charge. Finally, the surface tension is assumed to vary with temperature (thermocapillarity) or with surfactant concentration (destillocapillarity). The maximal thermal efficiency is derived and compared to the Carnot efficiency. For large thermal Marangoni number, the efficiency is severely limited by the large heat capacity of aqueous solvents. By contrast, destillocapillary flows may reach conversion efficiencies similar to pressure-driven flow.

## Keywords

Electrokinetic energy conversion Marangoni effect Slip flow Superhydrophobic surface Waste heat recovery Thermodynamic analysis## Notes

### Acknowledgments

This work was in part supported by the German Research Foundation (DFG) through Cluster of Excellence 259, ‘Center of Smart Interfaces.’ Steffen Hardt is acknowledged for fruitful discussion.

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