Effect of solvent depletion on electrokinetic energy conversion in viscoelastic fluids

Abstract

We analyze the electrokinetic energy conversion from the pressure-driven flow of viscoelastic fluids akin to dilute polymer solutions. In contrast to the previously reported results, we account for the reduced differential capacitance over the interfacial layer and the solvent-mediated non-electrostatic interactions, cumulatively represented in an extended continuum framework. We attribute a physical basis of our consideration from the perspective of the formation of a polymer-depleted layer at the channel interface, where the explicit role of the solvent appears to dictate the electromechanics–hydrodynamics coupling over the interfacial scales. By adapting a “box-model” depicting the alterations in the solvent permittivity across the interfacial layer and accommodating a non-electrostatic interaction coefficient concomitantly, the interfacial electrokinetics are coupled with the bulk flow of the polymer-rich medium using the simplified Phan-Thien–Tanner (sPTT) constitutive model. A closed-form theory is obtained that includes only two fitting parameters, namely, the span of the interfacial layer and the strength of the non-electrostatic interactions. These parameters are estimated from comprehensive molecular simulation data. The results of the investigation are analytically tractable and enable rationalizing the “electrokinetic” implications of the polymer-depleted interfacial layer and the possibility that the electrokinetic parameters can be extracted from measurements obtained from experiments. This paves the way toward optimizing the induced streaming potential for the conversion of hydraulic energy to electrical power in polymeric solutions.