'Blue energy' from ion adsorption and electrode charging in sea and river water

A huge amount of entropy is produced at places where fresh water and seawater mix, for example at river mouths. This mixing process is a potentially enormous source of sustainable energy, provided it is harnessed properly, for instance by a cyclic charging and discharging process of porous electrodes immersed in salt and fresh water, respectively [D. Brogioli, Phys. Rev. Lett. 103, 058501 (2009)]. Here we employ a modified Poisson-Boltzmann free-energy density functional to calculate the ionic adsorption and desorption onto and from the charged electrodes, from which the electric work of a cycle is deduced. We propose optimal (most efficient) cycles for two given salt baths involving two canonical and two grand-canonical (dis)charging paths, in analogy to the well-known Carnot cycle for heat-to-work conversion from two heat baths involving two isothermal and two adiabatic paths. We also suggest a slightly modified cycle which can be applied in cases that the stream of fresh water is limited.