Cell voltage model for Li-Bi liquid metal batteries

TL;DR

This paper introduces a simple, fast quasi-one-dimensional voltage model for Li-Bi liquid metal batteries, combining equilibrium potential, ohmic drop, and mass transport effects, validated across various experiments.

Contribution

A novel, comprehensive voltage model for Li-Bi liquid metal batteries that integrates equilibrium, ohmic, and mass transport phenomena with analytical and numerical solutions.

Findings

Model accurately predicts cell voltage in different configurations.

Equilibrium potential fitted from multi-study data and phase diagram.

Mass transport effects modeled via diffusion equations.

Abstract

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.