In a bipolar stack, electrochemical cells are electronically connected in series. If the electrolyte resistance between cells through the manifold is insufficient, some current will leak out of the cells. This reduces overall efficiency, an important loss mechanism to consider when designing a stack. Many works exist in the literature that model these shunt currents through an equivalent circuit with resistances R_io into or out of the cells, R_mn in the manifold between cells, and a linearised cell voltage with offset V_lin and resistance R_lin[jls-end-space/]. However, these typically require a numerical solution. We discuss the exact analytical solution, which gives (Formula presented) as a new intuitive, simple approximation for the average manifold shunt current. In an electrolyser, (Formula presented) and shunt currents increase with increasing current I[jls-end-space/]. In a discharging (flow) battery, (Formula presented) and shunt currents are negative, as they run in a direction opposite to the stack current. We use this model to provide clear engineering guidelines for stack design. The exact and approximate solutions are highly practical and insightful results that can be easily used for optimisation and should find widespread use in various industrially relevant applications.

Modulating the potential or current amplitude can improve mass transfer and assist in the bubble removal of electrochemical processes. However, the impact on energy efficiency of water electrolysis requires careful assessment. This study examines an anion exchange membrane (AEM) electrolyser under pulsed and direct current (DC) operating conditions. Two cathode catalysts were tested using square pulses with a duty ratio of 0.5 and 0.9 across 0.005-500 Hz. The pulsed method consumes more or comparable energy compared to the DC case at a time-averaged current density of (Formula presented) (Formula presented) in 1 M KOH. Unlike most studies, we argue that a fair comparison can only be made at an equal average current density to ensure same hydrogen production rate. Using this metric, we find no evidence of any improvement under the tested conditions, highlighting the need for a more rigorous evaluation of the effectiveness of dynamic power strategies.

Modern alkaline water electrolysers for hydrogen production often use a zero-gap configuration in which electrodes are pressed directly against the separator. Counterintuitively, the inclusion of a small electrode-diaphragm gap was previously shown to reduce the cell potential significantly. This work aims to understand, quantify, and model this effect, and take first steps towards optimisation of the gap width. We present experimental measurements and simulations of the cell potential and kinetic and ohmic losses for expanded metal electrodes. We find that the configuration with our smallest used gap, created using a 60µm spacer, yields the lowest cell potential, while the zero-gap configuration incurs additional voltage losses of approximately 80mV at a current density of 10⁴A/m². This can be explained by bubbles and gas films in between the electrode and diaphragm, which block part of the diaphragm and electrode area. We introduce an analytical model that predicts the vertical gas fraction and current density distribution in the electrode-diaphragm gap, which is in good agreement with experimental and simulation results. For a maximum gas fraction below 0.7, the model can explain why there is no optimal gap width based solely on the gap resistance. Instead, the gap allows gas to escape, which mitigates the additional zero-gap overpotential. Our findings confirm, explain, and quantify that intentionally adding a small gap can be an effective way to improve the performance of alkaline electrolysers with perforated plate-like electrodes.

In water electrolysers, gas crossover caused by elevated dissolved gas concentrations poses a major challenge, reducing product purity, safety, and operational stability. However, most existing electrolyser models assume that all generated products leave the electrode in the gaseous phase, neglecting the dynamics of dissolved gas transport. Experimental observations from the literature reveal that bubbles can continue to grow even after detachment, suggesting significant dissolved gas supersaturation. In this work, we develop a computational multiphase flow model that couples the transport of dissolved gas, gas fraction, and volumetric interfacial area to quantify bubble growth within electrogenerated plumes. The model is validated using experimental data extracted from literature videos, where individual bubbles are tracked to determine their size and position over time. The absolute average relative error in predicting bubble diameters is below 7%, demonstrating the model’s accuracy. Results show that at a gas-evolution efficiency of 40%, detached bubbles can grow up to 1.4 times their initial diameter, corresponding to a threefold increase in volume. This confirms that the observed post-detachment bubble growth can be quantitatively explained by the uptake of dissolved gas within the plume. By incorporating this mechanism, the model enables improved prediction of dissolved gas distributions, supporting more reliable design and operation of industrial electrolysers.

The ohmic resistance of an alkaline water electrolyser for green hydrogen production can be reduced by minimising the distance between the electrodes and the diaphragm. A zero-gap configuration requires holes in the electrode to transport the produced gases to the backside of the electrode. Industry typically uses expanded metals and perforated plates with hole sizes of one or a few millimetres, but the optimal hole size is not known. In this study, we experimentally assess the overpotentials as a function of hole size, shape, and open area fraction using a wide variety of electroformed nickel electrodes of 30 cm² up to 10⁴ A/m² in 80 °C 30 w% KOH. We find that for sub-millimetre holes, the overpotentials strongly increase as hole size decreases. The reason is that small hole sizes make it difficult for the gas bubbles to leave effectively, leading to coalescence and clogging. Consequently, a gas film can arise between the electrode and the diaphragm, as shown by through-the-membrane images. Therefore, the increased surface area associated with these small holes is not effectively used. We show that performance can be improved by taking away surface area through additional larger holes in a small hole-size electrode, which allow bubbles to effectively evacuate from the electrodes.

As current densities in alkaline water electrolysers increase, the resistive losses become increasingly important due to the locally high gas fraction around the electrodes, even in zero-gap configurations. Nonetheless, quantitative measurement of the distribution of these high gas fractions is difficult. Consequently, a numerical approach is useful to assess the impact of bubbles on electrolysis. However, models that couple current density and gas fraction distributions in a non-trivial geometry are currently lacking. We show that typically used models in the literature predict unrealistically high gas fractions in electrode-resolved simulations. To improve this, we added to the mixture model equations a solid pressure model similar to that used in simulations of dense granular flows. With the addition of this model, two-dimensional simulations of a lab-scale electrolysis cell accurately reproduce previously reported experimental results. This allows, for the first time, to predict local overpotentials influenced by the bubble distribution, opening the way towards computational optimisation of the electrode geometry.

The rising gas bubbles that are generated in an electrolyser cause electrolyte to flow upwards. By adding a downcomer after separating the gas, the electrolyte will recirculate through natural convection without a pump. We measured the resulting flow rate as a function of current density and electrode–wall distance in a zero-gap alkaline water electrolysis cell. Next, we developed a simple but surprisingly accurate fully analytical model to describe this flow rate as a function of various geometrical and operational parameters. From this model, we derive fully explicit expressions for the optimal electrode–wall distance. For our setup of 0.4 m height we find that values of 1.5–1.9 mm maximise mass transfer, velocity, or minimise the ohmic drop. The electrolyte flow rate is maximised for larger distances, around 6 mm. The accuracy, simplicity, and generality of our analytical model will be useful for the design and optimisation of a variety of gas-evolving electrolysers, including lab-scale as well as industrial reactors.

The high mass transfer to or from gas-evolving electrodes is an attractive feature of electrochemical reactors, which can be partly attributed to the large convective flows that arise due to the buoyancy of bubbles. We derive exact analytical expressions for mass transfer coefficients for the case of constant gas flux boundary conditions. For the mass transport both Dirichlet and Neumann boundary conditions are considered. We deploy a recently derived self-similar solution of laminar two-phase flows, with density, hydrodynamic diffusivity, and viscosity dependent on the local gas fraction. Combining this with the Lévêque approximation, new mass transfer coefficients are obtained analytically. These new results are relevant for various electrochemical processes with gas evolution as well as boiling. The new formulation shows the mass transfer coefficient to scale with the vertical coordinate z proportional to z^−1/5 for short electrodes and low current densities and z^−4/15 for long ones and high current densities. The former limit also applies when buoyancy is due to temperature or concentration differences in the case that density differences are small. We provide a general overview considering all possible gas and mass boundary conditions combinations and a comparison with the Boussinesq approximation of small density differences.

The anodic co-production of hydrogen peroxide (H₂O₂) during alkaline water electrolysis has gained interest as a sustainable alternative for anthraquinone oxidation. However, electrochemical H₂O₂ production is often studied with idealized laboratory setups to determine the H₂O₂ formation kinetics. In this work, we perform the reaction with industrially relevant operating principles using a flow cell with separately recirculating anolyte and catholyte. We then fit the data to an analytical model that we derive based on mole balances that accounts for anodic generation, anodic oxidation, and bulk disproportionation of H₂O₂, as well as electrolyte volumes and electrode surface area. We performed experiments at 100, 200, and 300 mA cm^-2 to derive values for the reaction system. At 200 mA cm^-2, we found a generation rate of 0.037 mmol min^-1 cm^-2 (FE_H2O2 = 59%) and an anodic decomposition rate constant of 0.304 cm min^-1, with a bulk disproportionation rate constant of 1.85 × 10^-3 min^-1. We successfully applied our model to two sources in literature to derive values for their systems as well. In all cases, the contribution of anodic oxidation of H₂O₂ was found to be the larger loss mechanism in comparison to bulk disproportionation. Using the analytical model, we show that decreasing the reservoir volume is a simple way to increase the H₂O₂ concentration over time. Further refinement of the model can be achieved through the use of mass transfer relationships based on electrolyzer geometries to describe the anodic oxidation of H₂O₂ in the mole balance equations.

The electrochemical conversion of CO₂ is a promising method of carbon-neutral chemical production. However, commercial realisation in aqueous electrolytes is challenging, due to competition with the hydrogen evolution reaction (HER), and the propensity for CO₂ to participate in the carbonate equilibrium reactions. These two phenomena are linked through OH⁻ ions, as both the by-product of the catalytic reactions and the culprit behind the parasitic carbonate reactions. By reducing the local catalyst loading where the CO₂ concentration is low, the HER is decreased more than the reactions that are dependent on CO₂ as a reactant. Therefore, it is possible to improve reaction selectivity and reactant utilisation while reducing the capital cost of catalyst. We demonstrate this theory through an analytical solution of a 1D flow electrolyser model. We extend this to a comprehensive model of a contemporary gas-diffusion electrode (GDE) setup. We find that the operation costs are dominated by the electrolyser power consumption and, to a lesser degree, the cost of CO₂ and its recovery at the anode. We numerically obtain the catalyst loading profiles that maximise operating profit. The optimisation process reveals that profits are maximised for high gas flow rates, and consequently, low single pass conversions, where the CO₂ concentration is as high as possible. However, when lower gas flow rates are used for practical reasons, variable catalyst loadings are shown to lead to significant operational improvements, especially in the production of higher C products that require a greater number of electrons transferred. The model is made freely available in MATLAB and its use is encouraged in determining the applicability of variable catalyst loading to future experimental setups.

Poor mass transport to or from vertical gas-evolving electrodes can adversely impact energy efficiency and product purity in the production of hydrogen, chlorine, and various metals. A proper description that combines natural convection with micromixing of growing, coalescing, and departing bubbles is presently lacking. This work develops a simple, physically sound analytical model that includes the influence of bubble size, flow regime, and bubble surface coverage. By comprehensively reviewing mass transfer measurements from the water electrolysis literature, we observe that the surface coverage of oxygen bubbles increases much more strongly with increasing current density than an often-used square root scaling predicts. Strong differences are observed in the degree of micromixing of hydrogen and oxygen bubbles in alkaline and acidic electrolytes. These varied results can all be explained by a combination of electrocapillarity, and coalescence induced by either a high surface coverage or Marangoni flows.

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.

Understanding multiphase flow close to the electrode surface is crucial to the design of electrolyzers, such as alkaline water electrolyzers for the production of green hydrogen. Vertical electrodes develop a narrow gas plume near their surface. We apply the integral method to the mixture model. Considering both exponentially varying and step-function gas fraction profiles, we derive analytical relations for plume thickness, velocity profile, and gas fraction near the electrode as a function of height and current density. We verify these analytical relations with the numerical solutions obtained using two-dimensional mixture model simulations. We find that for low gas fractions, the plume thickness decreases with an increase in current density for an exponentially varying gas fraction profile. In contrast, the plume thickness increases with increasing current density at high gas fractions for an approximately step-function-shaped gas fraction profile, in agreement with experiments from the literature.

Microfluidic fuel cells, electrolyzers, and redox flow batteries utilize laminar flow channels to provide reactants, remove products and avoid their crossover. These devices often also employ porous flow-through electrodes as they offer a high surface area for the reaction and excellent mass transfer. The geometrical features of these electrodes and flow channels strongly influence energy efficiency. We derive explicit analytical relations for the optimal flow channel width and porous electrode volumetric surface area from the perspective of energy efficiency. These expressions are verified using a two-dimensional tertiary current distribution and porous electrode flow model in COMSOL and are shown to be able to predict optimal parameters in commonly used flow-through and interdigitated flow fields. The obtained analytical models can dramatically shorten modelling time and expedite the industrial design process. The optimal channel width and pore sizes we obtain, in the order of 100 microns and 1 micron respectively, are much smaller than those often used. This shows that there is a significant room for improvement of energy efficiency in flow cells that can sustain the resulting pressure drop.

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.

Flow-through electrolyzers, with flow parallel to the current, are used in a wide range of industrial applications. The presence of flow avoids concentration gradients but can also be used to separate evolved gases, allowing membrane-less operation. In this work, we propose a simple multiphase flow-through electrode model. We derive and experimentally validate an analytical expression for the minimum velocity required to ensure effective gas separation. From this relation, we analytically derive design parameters that show that significant energy savings can be made using flow, compared to a physical separator.