Theory of ion transport with fast acid-base equilibrations in bioelectrochemical systems

Bioelectrochemical systems recover valuable components and energy in the form of hydrogen or electricity from aqueous organic streams. We derive a one-dimensional steady-state model for ion transport in a bioelectrochemical system, with the ions subject to diffusional and electrical forces. Since most of the ionic species can undergo acid-base reactions, ion transport is combined in our model with infinitely fast ion acid-base equilibrations. The model describes the current-induced ammonia evaporation and recovery at the cathode side of a bioelectrochemical system that runs on an organic stream containing ammonium ions. We identify that the rate of ammonia evaporation depends not only on the current but also on the flow rate of gas in the cathode chamber, the diffusion of ammonia from the cathode back into the anode chamber, through the ion exchange membrane placed in between, and the membrane charge density.