Effects of variable slip length over induced electric potentials in microchannels

Abstract

The exploration of new alternatives in renewable energy has embraced several branches: from solar, hydroelectric, and wind energy on the macro scale, up to those more recently such as to harvest power from some electrokinetic phenomenon, for instance, the well-known electric generation by means of the induced streaming potential process. This electric potential is found in micro and nano scales, where the physicochemical properties of surfaces have fundamental importance, such as the slippage effect. Most works oriented to determine induced electric potential in micro and nanochannels assume constant Navier slip length, which quantifies the hydrophobic degree of the surface. This assumption could overestimate the performance of the so-called electrokinetic batteries. For this reason, it is necessary to enlarge the analysis of variable slip over electrokinetics in micro and nanoscale.In the present analysis, we develop an analytical procedure to estimate the electric potentials induced in a microchannel by a flowing laminar solution due to osmotic gradients, whose configuration is better known as an electrokinetic forward osmosis battery. Assuming a non-linear dependence of Navier slip as a function of the pressure, we obtain regular perturbative series solutions for velocity, pressure, and the streaming potential. For this purpose, we use the dimensionless decay parameter ϵ̃, which measures the decrease of slippage due to the pressure at the wall as the perturbation parameter. We conclude that the velocity field has not only a longitudinal component if not also a transverse component normal to the surfaces as a consequence of the variable slippage, showing that the classical assumption of fully developed flow is no longer possible. In addition, our data shows that constant slip overpredicts the electric potentials up to 5% in comparison with the case of exponential slip. Finally, the results show that induced electric potentials are benefited from variable slippage; however, the influence of the decay parameter that appears in the boundary condition (32) associated with the variable slip decreases the induced potentials.