  The rolling pad instability is caused by electromagnetic interactions in
systems of horizontal layers with strongly different electric conductivities.
We analyze the instability for a simplified model of a liquid metal battery
(LMB), a promising device for large-scale stationary energy storage. Numerical
simulations of the flow and the dynamics of electromagnetically coupled
interfacial waves are performed using OpenFOAM. The work confirms the earlier
conclusions that the instability is a significant factor affecting battery's
operation. The critical role played by the ratio between the density
differences across the two interfaces is elucidated. It is found that the ratio
determines the stability characteristics and the type (symmetrically or
antisymmetrically coupled) of dominant interfacial waves.
