We revisit Morrison and Osterle (1965) who derived a phenomenological expression for the 'figure-of-merit' βEK of the electrokinetic energy conversion (EKEC) of a pressure difference into electric energy (and vice versa) using charged nanotubes, nanopores or ion-exchange membranes. We show the equivalence with Morrison and Osterle of a novel expression of βEK derived by Bentien et al (2013). We analyze two physical models for ionic and solvent flow which directly relate βEK to nanopore characteristics such as pore size and wall charge density. For the uniform potential model, we derive an analytical expression as a function of pore size, viscosity, ion diffusion coefficients and membrane charge density, and compare results with the full space-charge model by Osterle and co-workers as a function of pore size and ion diffusion coefficient. We present a novel expression for βEK for salt solutions with ions with unequal diffusion coefficients (mobilities) and show that to increase βEK the counterion mobility must be low and the coion mobility high.
- charged nanopore
- electrokinetic energy conversion