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We present a novel laboratory setup for studying the fluid dynamics in liquid metal batteries (LMBs). LMBs are a promising technology suited for grid-scale energy storage, but flows remain a confounding factor in determining their viability. Two important drivers of flow are thermal gradients, caused by internal heating during operation, and electrovortex flow (EVF), induced by diverging current densities. Our setup explores thermal gradients and electrovortex flow separately and in combination in a cylindrical layer of liquid gallium, simulating the behavior in a single layer of an LMB. In this work, we discuss the design principles underlying our choices of materials, thermal control, and current control. We also detail our diagnostic tools - thermocouple measurements for temperature and Ultrasonic Doppler Velocimetry (UDV) probes for velocities - and the design principles which go into choosing their placement on the setup. We also include a discussion of our post-processing tools for quantifying and visualizing the flow. Finally, we validate convection and EVF in our setup: we show that scaling relationships between the nondimensional parameters produced by our data agree well with theory and previous studies., Comment: 13 pages, 9 figures

Humankind produced 63.7 million metric tons of aluminium in 2019, nearly all via an electrochemical process in which electrical current liberates molten Al from dissolved alumina. That year, Al production required 848 TWh of electricity1, 3% of the worldwide total, and caused 1% of human greenhouse gas emissions. Much of the electricity and emissions originate from energy loss in the poorly conducting electrolyte where aluminum oxide is dissolved. Thinning the electrolyte layer could decrease loss but has been limited by the Metal Pad Instability (MPI), which causes Al cells to slosh out of control if the electrolyte is not sufficiently thick. Here we show that adding an oscillating component to the current disrupts the MPI in realistic simulations, allowing stable operation with electrolyte layers at least 12% thinner. This occurs when oscillation excites standing waves, which decouple the resonance that drives a growing traveling wave, characteristic of the MPI. Maintaining oscillation can prevent MPI; initiating oscillation can halt an MPI in progress. Our findings could significantly increase the efficiency of virtually all aluminium refining cells without the need for expensive reconstruction, thereby decreasing energy use by 34 TWh/year (2.1 MJ/kg Al) or more and greenhouse gas emissions by 13 Mton/year or more.

Liquid metal batteries are proposed for low-cost grid scale energy storage. During their operation, solid intermetallic phases often form in the cathode and are known to limit the capacity of the cell. Fluid flow in the liquid electrodes can enhance mass transfer and reduce the formation of localized intermetallics, and fluid flow can be promoted by careful choice of the locations and topology of a battery's electrical connections. In this context we study four phenomena that drive flow: Rayleigh-B\'enard convection, internally heated convection, electro-vortex flow, and swirl flow, in both experiment and simulation. In experiments, we use ultrasound Doppler velocimetry (UDV) to measure the flow in a eutectic PbBi electrode at 160{\deg}C and subject to all four phenomena. In numerical simulations, we isolate the phenomena and simulate each separately using OpenFOAM. Comparing simulated velocities to experiments via a UDV beam model, we find that all four phenomena can enhance mass transfer in LMBs. We explain the flow direction, describe how the phenomena interact, and propose dimensionless numbers for estimating their mutual relevance. A brief discussion of electrical connections summarizes the engineering implications of our work.

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., Comment: 31 pages, 16 figures, 206 references

Low-cost coin vibrational motors, used in haptic feedback, exhibit rotational internal motion inside a rigid case. Because the motor case motion exhibits rotational symmetry, when placed into a fluid such as glycerin, the motor does not swim even though its vibrations induce steady streaming in the fluid. However, a piece of rubber foam stuck to the curved case and giving the motor neutral buoyancy also breaks the rotational symmetry allowing it to swim. We measured a 1 cm diameter coin vibrational motor swimming in glycerin at a speed of a body length in 3 seconds or at 3 mm/s. The swim speed puts the vibrational motor in a low Reynolds number regime similar to bacterial motility, but because of the vibration it is not analogous to biological organisms. Rather the swimming vibrational motor may inspire small inexpensive robotic swimmers that are robust as they contain no external moving parts. A time dependent Stokes equation planar sheet model suggests that the swim speed depends on a steady streaming velocity $V_{stream} \sim Re_s^{1/2} U_0$ where $U_0$ is the velocity of surface vibrations, and streaming Reynolds number $Re_s = U_0^2/(\omega \nu)$ for angular vibrational frequency $\omega$ and fluid kinematic viscosity $\nu$., Comment: See the movie: https://youtu.be/0nP2MgzaOyU

Approximate empirical models of thermal convection can allow us to identify the essential properties of the flow in simplified form, and to produce empirical estimates using only a few parameters. Such "low-dimensional" empirical models can be constructed systematically by writing numerical or experimental measurements as superpositions of a set of appropriate basis modes, a process known as Galerkin projection. For three-dimensional convection in a cylinder, those basis modes should be vector-valued, mutually orthogonal, and defined in cylindrical coordinates. Here we construct such a basis set and demonstrate that it has these desired properties and boundary conditions when the exact constraint of incompressibility is relaxed. We show its use for representing sample simulation data and point out its potential for low-dimensional convection models., Comment: 9 pages; 8 figures, (revised to include fundamental improvements that result from eliminating the constraint of incompressibility), submitted to Physical Review Fluids

Although understanding the collective migration of cells, such as that seen in epithelial sheets, is essential for understanding diseases such as metastatic cancer, this motion is not yet as well characterized as individual cell migration. Here we adapt quantitative metrics used to characterize the flow and deformation of soft matter to contrast different types of motion within a migrating sheet of cells. Using a Finite-Time Lyapunov Exponent (FTLE) analysis, we find that - in spite of large fluctuations - the flow field of an epithelial cell sheet is not chaotic. Stretching of a sheet of cells (i.e., positive FTLE) is localized at the leading edge of migration. By decomposing the motion of the cells into affine and non-affine components using the metric D$^{2}_{min}$, we quantify local plastic rearrangements and describe the motion of a group of cells in a novel way. We find an increase in plastic rearrangements with increasing cell densities, whereas inanimate systems tend to exhibit less non-affine rearrangements with increasing density., Comment: 21 pages, 7 figures This is an author-created, un-copyedited version of an article accepted for publication in the New Journal of Physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at doi:10.1088/1367-2630/15/2/025036

We present a method for reconstructing two-dimensional velocity fields at specified length scales using observational data from tracer particles in a flow, without the need for interpolation or smoothing. The algorithm, adapted from techniques proposed for oceanography, involves a least-squares projection of the measurements onto a set of two-dimensional, incompressible basis modes with known length scales. Those modes are constructed from components of the velocity potential function, which accounts for inflow and outflow at the open boundaries of the measurement region; and components of the streamfunction, which accounts for the remainder of the flow. All calculations are evaluated at particle locations, without interpolation onto an arbitrary grid. Since the modes have a well-defined length scales, scale-local flow properties are available directly. The technique eliminates outlier particles automatically and reduces the apparent compressibility of the data. Moreover the technique can be used to produce spatial power spectra and to evaluate the spatial effects of open boundaries; it also holds promise for direct calculation of scale-to-scale transfer of enstrophy and energy.