Revisiting Morrison and Osterle 1965: the efficiency of membrane-based electrokinetic energy conversion

We revisit Morrison and Osterle (1965) who derived a phenomenological expression for the 'figure-of-merit' [Formula: see text] 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 [Formula: see text] derived by Bentien et al (2013). We analyze two physical models for ionic and solvent flow which directly relate [Formula: see text] 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 [Formula: see text] for salt solutions with ions with unequal diffusion coefficients (mobilities) and show that to increase [Formula: see text] the counterion mobility must be low and the coion mobility high.