  The design and performance of liquid metal batteries, a new technology for
grid-scale energy storage, depend on fluid mechanics because the battery
electrodes and electrolytes are entirely liquid. Here we review prior and
current research on the fluid mechanics of liquid metal batteries, pointing out
opportunities for future studies. Because the technology in its present form is
just a few years old, only a small number of publications have so far
considered liquid metal batteries specifically. We hope to encourage
collaboration and conversation by referencing as many of those publications as
possible here. Much can also be learned by linking to extensive prior
literature considering phenomena observed or expected in liquid metal
batteries, including thermal convection, magnetoconvection, Marangoni flow,
interface instabilities, the Tayler instability, and electro-vortex flow. We
focus on phenomena, materials, length scales, and current densities relevant to
the liquid metal battery designs currently being commercialized. We try to
point out breakthroughs that could lead to design improvements or make new
mechanisms important.
