Cell voltage model for Li-Bi liquid metal batteries

Lithium-bismuth bimetallic cells are amongst the best explored liquid metal batteries. A simple and fast quasi-one-dimensional cell voltage model for such devices is presented. The equilibrium cell potential is obtained from a complex two-dimensional fit of data drawn from multiple studies of equilibrium cell potential and rendered congruent with the phase diagram. Likewise, several analytical and fit functions for the ohmic potential drop across the electrolyte are provided for different battery geometries. Mass transport overpotentials originating from the alloying of Li into Bi are modelled by solving a diffusion equation, either analytically or numerically, and accounting for the volume change of the positive electrode. The applicability and limitations of the model are finally illustrated in three distinct experimental settings. •A one-dimensional cell voltage model for Li-Bi cells is developed.•The open-circuit potential is obtained by a complex fit of measurement data.•Ohmic overpotential models for different geometries are provided.•Volume change is accounted for when computing the mass transport losses.