Electric potentials in cylindrical microchannels using forward osmosis: analytical solution and efficiency

Abstract The growing necessity of harvesting energy from renewable sources has produced several studies in electrokinetic phenomena, specifically in the streaming potential, which arises from a flow that enters into contact with a surface able to acquire charge through the normal distribution of coions in the electric double layer (EDL). The principal obstacle in generating electricity from this phenomenon is the necessity of using an external source to prompt the movement of the fluid. In addition, most analytical works present a model that uses parallel plates, which facilitates computing but restrains a huge number of applications, specifically those that are related to a bundle of microchannels or porous media. In the present work, we develop an analytical model for a cylindrical microchannel with silica surfaces in which an electrolyte is driven by an osmotic flow, where we assume low surface potentials. We determine analytically the velocity profile, the pressure field, the streaming potential, and the conversion efficiency between the pressure-driven flow and the induced streaming potential. The results show that thin electric double layers induce larger magnitudes of streaming potential. In addition, we show that there is a theoretical upper bound for such electric potential. In the same way, the conversion efficiency tends to reach an upper bound that depends on the osmotic pressure, the surface properties, and the electrolyte, giving as a result an efficiency of 0.00118%. It is shown that the pressure field is a superposition of the hydraulic pressure drop due to the length of the microchannel and the electrostatic pressure of the counterions in the electric double layer.