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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.

Presolar grains originating in oxygen-neon novae may be identified by their sulfur isotopic ratios compared with theoretical estimates. These ratios depend on reliable $^{33}$S($p, \gamma$)$^{34}$Cl and $^{34}$S($p, \gamma$)$^{35}$Cl reaction rates. The latter rate has recently been computed based on experimental input, and many new excited states in $^{35}$Cl were discovered above the proton threshold. The experimental $^{34}$S($p, \gamma$)$^{35}$Cl rate was found to be 2 - 5 times smaller than the theoretical one, and the simulated $^{34}$S/$^{32}$S isotopic ratio for nova presolar grains was thus predicted to be smaller than that of type II supernova grains by up to a factor of 3.7. The present study was performed to confirm the existence of these new resonances, and to improve the remaining uncertainties in the $^{34}$S($p, \gamma$)$^{35}$Cl reaction rate. Energies and spin-parities of the $^{35}$Cl excited levels were investigated with an Enge split-pole spectrograph using the $^{32}$S($\alpha, p$)$^{35}$Cl reaction. Differential cross sections of the outgoing protons were measured at $E_{\alpha}$ = 21 MeV. The existence of the newly discovered states are largely confirmed, although a few states were not observed in this study. The spins and parities of several $^{35}$Cl states were assigned tentatively for the first time. The present $^{34}$S($p, \gamma$)$^{35}$Cl experimental thermonuclear reaction rate is consistent within 1$\sigma$ with the previous evaluation. However, our rate uncertainty is larger due to a more realistic treatment of the experimental uncertainties. The uncertainty in the present rate is up to a factor of 3.5 at nova temperatures. We recommend future work to focus on the unknown properties of four excited states of $^{35}$Cl at 6643 keV, 6761 keV, 6780 keV, and 6800 keV., Comment: 17 pages, 9 figures, accepted to Phys. Rev. C

Background: Discrepancies exist between the observed abundances of argon and calcium in oxygen-neon nova ejecta and those predicted by nova models. An improved characterization of the $^{38}$K($p, \gamma$)$^{39}$Ca reaction rate over the nova temperature regime ($\sim$ 0.1 -- 0.4 GK), and thus the nuclear structure of $^{39}$Ca above the proton threshold (5770.92(63) keV), is necessary to resolve these contradictions. Purpose: The present study was performed to search for low-spin proton resonances in the $^{38}$K $+$ $p$ system, and to improve the uncertainties in energies of the known astrophysically significant proton resonances in $^{39}$Ca. Method: The level structure of $^{39}$Ca was investigated via high-resolution charged-particle spectroscopy with an Enge split-pole spectrograph using the $^{40}$Ca($^{3}$He, $\alpha$)$^{39}$Ca reaction. Differential cross sections were measured over 6 laboratory angles at 21 MeV. Distorted-wave Born approximation calculations were performed to constrain the spin-parity assignments of observed levels with special attention to those significant in determination of the $^{38}$K($p, \gamma$)$^{39}$Ca reaction rate over the nova temperature regime. Results: The resonance energies corresponding to two out of three astrophysically important states at 6154(5) and 6472.2(24) keV are measured with better precision than previous charged-particle spectroscopy measurements. A tentatively new state is discovered at 5908(3) keV. The spin-parity assignments of a few of the astrophysically important resonances are determined. Conclusions: The present $^{38}$K($p, \gamma$)$^{39}$Ca upper limit thermonuclear reaction rate at 0.1 -- 0.4 GK is higher than that determined in [Physical Review C 97 (2018) 025802] by at most a factor of 1.4 at 0.1 GK., Comment: 13 pages, 7 figURes, accepted to Phys. Rev. C

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

A high-resolution study of the electromagnetic response of $^{206}$Pb below the neutron separation energy is performed using a ($\vec{\gamma}$,$\gamma'$) experiment at the HI$\vec{\gamma}$S facility. Nuclear resonance fluorescence with 100% linearly polarized photon beams is used to measure spins, parities, branching ratios, and decay widths of excited states in $^{206}$Pb from $4.9$ to $8.1$MeV. The extracted $\Sigma$$B$(E1)$\uparrow$ and $\Sigma$$B$(M1)$\uparrow$ values for the total electric and magnetic dipole strength below the neutron separation energy are 0.9$\pm$0.2e$^2$fm$^2$ and 8.3$\pm$2.0$\mu_{N}^2$, respectively. These measurements are found to be in very good agreement with the predictions from an energy-density functional (EDF) plus quasiparticle phonon model (QPM). Such a detailed theoretical analysis allows to separate the pygmy dipole resonance from both the tail of the giant dipole resonance and multi-phonon excitations. Combined with earlier photonuclear experiments above the neutron separation energy, one extracts a value for the electric dipole polarizability of $^{206}$Pb of $\alpha_{D}\!=\!122\pm10$mb/MeV. When compared to predictions from both the EDF+QPM and accurately calibrated relativistic EDFs, one deduces a range for the neutron-skin thickness of $R_{\rm skin}^{206}\!=\!0.12$-$0.19$fm and a corresponding range for the slope of the symmetry energy of $L\!=\!48$-$60$MeV. This newly obtained information is also used to estimate the Maxwellian-averaged radiative cross section $^{205}$Pb(n,$\gamma$)$^{206}$Pb at 30keV to be $\sigma\!=\!130\!\pm\!25$mb. The astrophysical impact of this measurement--on both the s-process in stellar nucleosynthesis and on the equation of state of neutron-rich matter--is discussed., Comment: 8 pages and 4 figures. Manuscript accepted for publication in Physics Letters B

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