A proven methodology to solve multiphase flows is based on the one-fluid formulation of the governing equations, which treats the phase transition across the interface as a single fluid with varying properties and adds additional source terms to satisfy interface jump conditions, e.g., surface tension and mass transfer. Used interchangeably in the limit of non-evaporative flows, recent literature has formalized the inconsistencies that arise in the momentum balance of the non-conservative one-fluid formulation compared to its conservative counterpart when phase change is involved. This translates into an increased sensitivity of the numerical solution to the choice of formulation. Motivated by the fact that many legacy codes using the non-conservative one-fluid formulation have been extended to phase-change simulations, the inclusion of two corrective forces at the interface and a modification of the pressure-velocity solver with an additional predictor-projection step are shown to recover the exact momentum balance in the evaporative non-conservative one-fluid framework for low-viscosity incompressible flows. This has direct implications for obtaining a physically meaningful pressure jump across the interface and is seen to affect the dynamics of two-phase flows. In the high-viscosity domain, the discretization of the viscous term introduces a momentum imbalance which is highly dependent on the chosen method to model the phase transition. In the context of film boiling, this imbalance affects the time scales for the instability growth. Lastly, the need to develop sub-models for heat and mass transfer and for surface tension becomes evident since typical grid resolutions defined as “resolved” in the literature may not be enough to capture interfacial phenomena.@en

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.

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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.

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The development of a bubble plume from a vertical gas-evolving electrode is driven by buoyancy and hydrodynamic bubble dispersion. This canonical fluid mechanics problem is relevant for both thermal and electrochemical processes. We adopt a mixture model formulation for the two-phase flow, considering variable density (beyond Boussinesq), viscosity and hydrodynamic bubble dispersion. Introducing a new change of coordinates, inspired by the Lees–Dorodnitsyn transformation, we obtain a new self-similar solution for the laminar boundary layer equations. The results predict a wall gas fraction and gas plume thickness that increase with height to the power of 1/5 before asymptotically reaching unity and scaling with height to the power 2/5, respectively. The vertical velocity scales with height to the power of 3/5. Our analysis shows that self-similarity is only possible if gas conservation is entirely formulated in terms of the gas specific volume instead of the gas fraction.@en