In flow-by capacitive deionization (CDI) brackish water flows between two electrodes that capacitively remove salt. We assume low inlet concentrations so “salt shocks” appear in the electrodes and the process becomes diffusion-limited. For unit charge efficiency, a simplified model is derived consisting of two coupled partial differential equations. We obtain approximations, and exact solutions in terms of the Lambert W function, for the salt concentration as a function of time and space and for the equilibrium charge-voltage relation. These surprisingly simple solutions compare well with the results from comprehensive two-dimensional simulations. Useful analytical expressions are obtained for optimal geometrical and operational parameters that maximize the productivity and minimize the specific energy losses. By making cells much thinner the productivity can be increased an order of magnitude compared to typical values in the literature. The optimal electrode is found to be roughly six times thinner than the spacer. The associated pressure drop is around 0.4 bar per 1 mM of inlet salt concentration, making our recommendations practically feasible only for relatively low concentrations. The obtained model and analytical expressions provide useful guidance to strongly improve the design process.

The use of gas diffusion electrodes that supply gaseous CO₂ directly to the catalyst layer has greatly improved the performance of electrochemical CO₂ conversion. However, reports of high current densities and Faradaic efficiencies primarily come from small lab scale electrolysers. Such electrolysers typically have a geometric area of 5 cm², while an industrial electrolyser would require an area closer to 1 m². The difference in scales means that many limitations that manifest only for larger electrolysers are not captured in lab scale setups. We develop a 2D computational model of both a lab scale and upscaled CO₂ electrolyser to determine performance limitations at larger scales and how they compare to the performance limitations observed at the lab scale. We find that for the same current density larger electrolysers exhibit much greater reaction and local environment inhomogeneity. Increasing catalyst layer pH and widening concentration boundary layers of the KHCO₃ buffer in the electrolyte channel lead to higher activation overpotential and increased parasitic loss of reactant CO₂ to the electrolyte solution. We show that a variable catalyst loading along the direction of the flow channel may improve the economics of a large scale CO₂ electrolyser.

The electrochemical reduction of CO₂ on planar electrodes is limited by its prohibitively low diffusivity and solubility in water. Gas-diffusion electrodes (GDEs) can be used to reduce these limitations, and facilitate current densities orders of magnitude higher than the limiting current densities of planar electrodes. These improvements are accompanied by increased variation in the local environment within the cathode, with significant effect on Faradaic efficiency. By developing a simple and freely available analytical model of a cathodic catalyst layer configured for the production of CO, we investigate the relationships between electrode reaction kinetics, cell operation conditions, catholyte composition and cell performance. Analytical methods allow us to cover parameter ranges that are intractable for numerical and experimental studies. We validate our findings against experimental and numerical results and provide a derivation and implementation of the analytical model.