Hydroelectrical energy conversion in narrow confinements in the presence of transverse magnetic fields with electrokinetic effects

In this work, we investigate the combined influences of externally applied axial pressure gradients and transverse magnetic fields on hydroelectrical energy conversion mechanisms in narrow fluidic confinements. This energy conversion is achieved through an exploitation of the electromagnetohydrodynamic effects as a result of electrical double layer formation and the consequent interfacial phenomena. Although no electrical field is externally applied, a reverse electrokinetic transport may be induced on account of the streaming potential field which is spontaneously developed due to the preferential migration of ionic charges with the fluid flow, as modulated by the pressure and the magnetic fields. We explore ranges of surface potentials beyond the traditional Debye-Huumlckel limits by employing nonlinear forms of the Poisson-Boltzmann equation for electrical potential distribution, yet adhering to a semianalytical formalism. Our studies quantitatively depict the explicit implications of the external magnetic field on the overall energy conversion efficiency through the pertinent nondimensional parameters. We also investigate the cases of low surface potentials and thin electrical double layers as special limits of the generalized considerations addressed in this work.