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Influence of the viscoelectric effects on the electrokinetic power generation controlled by an osmotic semi-membrane placed on a parallel-plate microchannel

In the present work, we develop a theoretical study for predicting the streaming potential and, therefore, the electric power generation in a system composed of a semi-permeable osmotic membrane inserted in a slit microchannel. Both physical systems are communicated through the forced microcirculation of an electrolyte employing the use of a saline gradient, which is established between the external faces of the membrane, creating the suction force needed to induce a hydrodynamic flow. In this manner, we externally impose a uniform volumetric flow rate to promote simultaneous hydrodynamic and electrokinetic fields, replacing the usual external pressure gradient with an equivalent osmotic pressure force. The viscoelectric effects of the electrolyte solution are included in the present analysis. The resulting non-linear governing equations for the motion are written in dimensionless form and permit us to derive an integro-differential equation for the velocity field, which is solved by an iterative method. With the aid of these previous results, the electric energy, in terms of an electrokinetic streaming potential and the streaming current, is generated for this combined system. This proposed electric power generation technique converts the energy of a saline gradient into electrical energy, avoiding the mechanical use of an external pressure gradient.