An analytical multiphase flow model for parallel plate electrolyzers

Membraneless parallel-plate electrolyzers use electrolyte flow to avoid product crossover. Using a mixture model neglecting inertia, and assuming an exponential gas fraction profile, we derive approximate analytical expressions for the velocity profile and pressure drop for thin plumes. We verify these expressions using numerical solutions obtained with COMSOL and validate them using experimental data from the literature. We find that the wall gas fraction increases rapidly at small heights, but becomes fairly constant at larger heights. These expressions serve as a guiding framework for designing a membraneless parallel-plate electrolyzer by quantifying the maximum possible height. We find that buoyancy driven membraneless parallel-plate electrolyzers with a 3 mm gap can be designed with a maximum height of around 7.6 cm at 1000 A/m² for operation with 98% product purity at atmospheric pressure. For a forced flow at Re=1000, the same electrolyzer can be made around 17.6 cm tall at 1000 A/m². These limits can be further improved with smaller bubbles or higher pressure.