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' β_EK 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 β_EK derived by Bentien et al (2013). We analyze two physical models for ionic and solvent flow which directly relate β_EK 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 β_EK for salt solutions with ions with unequal diffusion coefficients (mobilities) and show that to increase β_EK the counterion mobility must be low and the coion mobility high.