Simulations of mass transport in liquid metal electrodes

Liquid metal electrochemical cells are electrochemical device with at least one liquid metal electrode. They were adopted in electro-metallurgical processing, heat-to-power conversion, and energy storage applications. The electrode's liquid state ensures high current density, resulting in batteries with high power densities and electro-metallurgical reactors with high conversion yields. Mass transport is critical in all liquid metal electrochemical cells, but especially in concentration cells like liquid metal batteries. These are fully liquid three-layer cells where the two electrodes are separated by a thin molten salt electrolyte. There, the positive electrode alloying and de-alloying processes store energy in the cell. Inhomogeneities in the liquid metal electrode reduce cell efficiency and material use. In this work, we are interested in understanding mass transport within this electrode. From a first study of diffusive heat and mass transport, we established that solutal effects are predominant in liquid metal electrodes. Any thermally driven convection can not significantly affect a compositionally stable stratification. A solutal flow will efficiently mix the electrode regardless of the temperature distribution. Following that, we developed a consistent explanation for the differences in the cell resistance between charge and discharge, as observed multiple times in the literature. The latter was based on quantitative analysis of a new experimental result. The voltage evolution was measured during the cycling of a liquid metal battery. During discharge, light elements are electro-deposited at the positive electrode's top interface, forming a gravitationally stable stratification. As only diffusion transports the light element away from the interface, the concentration difference and the mass transport overvoltage increase with time. During charging, the opposite phenomenon (electro-refining) takes place. The flux at the active interface builds up an unstable, asymmetric, and time-dependent buoyancy distribution in the layer. That leads first to a diffusive transient and then to a convective flow in the layer. This solutal convection was studied numerically with finite-volume and spectral-element-method solvers. The two-dimensional axisymmetric simulations performed covered Schmidt numbers from 1.125 to 288 and five orders of magnitude of flux Rayleigh numbers, starting from 10000. Two regimes were identified as a function of the flux Rayleigh number. At low Rayleigh numbers, diffusion affects the full layer height before the onset of convection. This results in a global flow. Instead, convection originates in the thin concentration boundary layer with characteristic plume structures in the high Rayleigh number regime. In this regime, onset time and concentration difference are independent with respect to the layer height. Thanks to the extensive parametric study, we retrieved robust scaling for velocity and concentration differences as a function of the current density and material properties of the layer. These results can be used in the design and operation of liquid metal electrodes. For example, they allow estimating the mass transport overvoltage during charge. Furthermore, we studied numerically solutal convection in three-dimensional cylindrical electrodes. We showed that the two-dimensional approximation captures quite remarkably the evolution of integral quantities observed in fully three-dimensional simulations. This is not due to the axisymmetric nature of the flow. On the contrary, we observed a rich dynamic, with polygonal-shaped cells forming and evolving in the active interface concentration distribution. Finally, the influence of non-uniform current distribution on mass transport in a liquid metal electrode was investigated. Differences with respect to the homogenous configuration are present in pure diffusion and at the onset of convection. The solutal flow is able to reduce the inhomogeneities in the electrode.