Pith. sign in

REVIEW 2 major objections 5 minor 43 references

Numerical simulation of rolling pad instability in cuboid liquid metal batteries

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read In a cuboid liquid metal battery, the density-difference ratio sets whether rolling-pad waves grow and whether the electrolyte ruptures.

desk verdict Good cuboid LMB numerics, but the headline equal-density stabilization is an artifact of an arithmetic slip: cases 14-17 are ΔρA/ΔρB ≈ 0.665, not 1. read the letter →

arxiv 1908.01884 v2 pith:6EPDTYJ6 submitted 2019-08-05 physics.flu-dyn

Linyan Xiang , Oleg Zikanov This is my paper · ORCID
classification physics.flu-dyn PACS 47.35.Bb47.65.-d
keywords liquidmetalbatteryrollingpadinstabilityinterfacialwavesmagnetohydrodynamicsdensitystratificationthree-layerflowelectrolyterupturenumericalsimulation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper uses three-dimensional simulations of a cuboid liquid metal battery to isolate the electromagnetic mechanism behind the rolling pad instability—a sloshing of the two metal–electrolyte interfaces that can grow until the metal layers touch and short-circuit the cell. Its central claim is that the ratio between the density differences across the two interfaces decides the outcome: when the upper density jump is much smaller than the lower one, slow antisymmetric waves grow and can rupture the electrolyte, whereas when the two jumps are equal, only fast symmetric waves appear, the electrolyte thickness stays nearly constant, and the instability is suppressed. The same three-layer system was also found unstable when the lower jump is the small one, with the slow mode living on the lower interface. If the claim holds, density matching between the metal–electrolyte pairs is a design lever for making large liquid metal batteries safe, in addition to controlling magnetic field and cell shape.

What carries the argument

The object that carries the argument is the electromagnetically coupled pair of interfacial gravity waves in the three-layer system, together with the feedback loop that feeds them: a long-wavelength deformation of an interface changes the local electrolyte thickness, which perturbs the vertical electric current, producing horizontal currents that interact with the vertical magnetic field to create Lorentz forces that push the interfaces further. The new element is the density-difference ratio, which determines which of the two linear modes of this system—the fast mode with symmetrically coupled, nearly equal-amplitude waves and almost constant electrolyte thickness, or the slow mode with antisymmetrically coupled waves and strongly unequal amplitudes—is the one available to the instability. Only the slow modes modulate the electrolyte thickness strongly enough to close the feedback loop, and the density ratio decides whether they exist and where they live.

What would settle it

Build or simulate a 0.1 m cuboid three-layer cell with the electrolyte density tuned so the two density jumps are equal, apply only a vertical magnetic field up to about 200 mT, and watch the interfaces: the model predicts only small non-growing symmetric oscillations with roughly 0.3 s period, so any growing antisymmetric wave, any strong thinning of the electrolyte, or any short circuit in that configuration would refute the density-ratio claim.

Watch

Extended reading notes

Core claim

The central discovery is that the density-difference ratio, not captured by the magnetic-field strength or the standard instability parameter β alone, selects the stability regime and the type of dominant interfacial wave. In simulations with the light-metal/electrolyte density jump much smaller than the electrolyte/heavy-metal jump (the Mg-Sb material set), the growing disturbance is the slow antisymmetric mode: the upper-interface wave is 20 to 60 times larger than the lower-interface wave, the two oscillate 180 degrees out of phase, and raising the vertical field moves the system from stable decay to finite-amplitude sloshing to electrolyte rupture. When the two density jumps are made equal by raising the electrolyte density, the same cell remains stable even at values of β up to 6; the flow reduces to fast symmetric waves with nearly equal amplitudes on both interfaces, so the local electrolyte thickness and vertical current stay nearly uniform. When the lower jump is the small one, the solution is a superposition of fast symmetric and slow antisymmetric modes, and the slow mode on the lower interface is what drives the instability. These results are presented as properties of the simplified model with a constant vertical magnetic field, insulating sidewalls, and equipotential current collectors.

Load-bearing premise

The load-bearing input is that the magnetic field is purely vertical and uniform, with all horizontal and induced components ignored, and that the top and bottom collectors are equipotential so perturbation currents close inside the cell; if real three-dimensional fields or background melt flows matter, the predicted thresholds and mode selection could change.

Editorial extensions

If this is right

  • For cells with a much smaller upper density jump (Mg-Sb), the threshold of instability is near β ≈ 1, and increasing the vertical field produces saturation then rupture; the instability appears as a rotating slow antisymmetric wave concentrated at the upper interface.
  • For cells with equal density jumps, the model predicts no rolling pad instability up to β ≈ 6; only fast symmetric oscillations remain, with periods of 0.24–0.5 s and amplitudes that do not grow.
  • For cells with a much smaller lower density jump, instability is still possible but is carried by slow antisymmetric waves on the lower interface, superimposed on fast symmetric oscillations of the upper interface.
  • Where the instability saturates rather than ruptures, the sloshing wave lowers the cell's overall impedance and raises the total current, while retaining a finite-amplitude interface deformation; at higher field the electrolyte ruptures near a corner, creating a short circuit.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The density-ratio rule, if it survives contact with more complete physics, suggests a passive safety strategy: tune electrolyte density so the two jumps are comparable, although this must be weighed against electrochemical performance of the cell.
  • A direct testable extension would be to add a weak horizontal magnetic field or background melt flow to the equal-density-jump case; the model implies that the resulting symmetry breaking should reintroduce electrolyte-thickness modulation and possibly instability even at high vertical field.
  • The fast/slow mode classification was originally derived for simpler inviscid systems; these simulations suggest it remains the right organizing principle in viscous, nonlinear, three-dimensional sloshing, so the density ratio could serve as a cheap screening criterion in battery design before expensive multiphysics simulation.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper reports three-dimensional, time-dependent OpenFOAM simulations of the rolling pad instability in a cuboid liquid metal battery with three horizontal layers. The model uses a constant vertical magnetic field, equipotential top and bottom walls, insulating sidewalls, and a one-fluid volume-of-fluid treatment; the electric potential is solved in the quasi-static approximation with harmonic interpolation of conductivity. The authors vary the vertical magnetic field, electrolyte thickness, and electrolyte density, and classify the resulting flows as stable, saturated, or rupturing. They report that for a Mg-Sb cell with ΔρA ≪ ΔρB the instability is a slow antisymmetric upper-interface wave; for a case they label ΔρA = ΔρB they observe only fast symmetric waves with nearly constant electrolyte thickness and no instability; and for ΔρA ≫ ΔρB they find mixed fast/slow behavior with instability associated with slow lower-interface modes. The abstract and conclusions assert that the ratio of the density differences across the two interfaces determines both the stability characteristics and the type of dominant interfacial waves.

Significance. If correct, the main novelty is the prediction that tuning the electrolyte density so that the two density jumps are equal suppresses the rolling pad instability, which would be a practically useful design rule for liquid metal batteries. The paper also demonstrates that the fast/slow mode classification of Ref. 11 can be usefully applied to three-dimensional nonlinear MHD simulations. The strengths of the paper are its direct numerical approach, the grid and time-step sensitivity tests, the verification against the cylindrical-cell results of Ref. 10, and the systematic variation of B0, H0_E, and ρE. These strengths make the quantitative regime classification credible within the stated simplified model. However, the central equal-density result is compromised by an arithmetic error in the densities used in cases 14–17, so the reported simulations do not actually contain the case ΔρA = ΔρB. The applicability to real batteries is also limited by the constant-vertical-field and equipotential-boundary assumptions, which the authors acknowledge in Section VI.

major comments (2)
  1. [V C, Table II, Table I] The cases 14–17 are described as having ΔρA = ΔρB, but the numbers in Tables I and II do not support this. With ρA = 1577 kg/m3 and ρB = 6270 kg/m3, the choice ρE = 3452.2 kg/m3 gives ΔρA = 1875.2 kg/m3 and ΔρB = 2817.8 kg/m3, i.e., ΔρA/ΔρB ≈ 0.665, not equality. A true equal-density case would require ρE = (ρA + ρB)/2 = 3923.5 kg/m3. Since Section V C and Section VI use the equality to explain both the absence of instability and the selection of fast symmetric modes, the headline claim is not supported by the reported runs. Please either re-run the relevant cases at ρE = 3923.5 kg/m3 or correct the density values, and in any case report the actual ΔρA/ΔρB for every case in Table II.
  2. [V C, Fig. 11, Fig. 12, Section VI] Even setting the arithmetic aside, the inference from stable runs at ΔρA/ΔρB ≈ 0.665 to the claim that exact equality suppresses the rolling pad instability is under-supported. In these runs the wave pattern remains correlated with the initial perturbation (Fig. 12), so the observed behavior demonstrates stability of that initial state rather than establishing that no slow antisymmetric mode is available at exact equality. The mechanism stated in Section VI (only fast modes with nearly constant electrolyte thickness are present when ΔρA = ΔρB) would require either a simulation at the true equal-density point or a linear-stability analysis of the model at that point. Please supply the missing equal-density case or rephrase the conclusion to refer to an intermediate range of density ratios.
minor comments (5)
  1. [IV A] The sentence 'the analogy with the Hall-Héroult reduction cells leads us to expect the instability characterized by (i) the threshold much lower than for rectangular cells' is confusing because the cell studied here is itself a square cuboid; please clarify which reference geometry is meant.
  2. [III] The verification against Ref. 10 is described only qualitatively ('consistently good agreement', 'accurately reproduce the period... and the value of the threshold magnetic field'). A quantitative statement of the reproduced period and threshold with relative errors would strengthen the claim.
  3. [Table II, Fig. 11] For cases 14–17, the amplitude ratio ΔηA/ΔηB is listed as 1.0, but the time series in Fig. 11 appear to show slightly different oscillation amplitudes for the two interfaces; please define how this ratio was measured and report its uncertainty.
  4. [References] Reference 25 contains the malformed URL 'http://https://www.openfoam.com'; please correct it.
  5. [Fig. 11 caption] The phrase 'in the Insets' should be lowercase or rephrased, and the caption should state whether the vertical scales for the two interfaces are identical.

Circularity Check

0 steps flagged · score 1.0 of 10

No load-bearing circularity: the stability map is generated by direct time integration of an explicit MHD model, with the fast/slow mode classification imported from an external linear analysis; the equal-density runs in Table II are arithmetically inconsistent with Table I, but that is a correctness issue, not a circular derivation.

full rationale

The paper's central derivation is a direct numerical simulation: the governing equations (4)-(12), boundary conditions (13)-(15), and tabulated material properties (Table I) are integrated forward in time, and stability and coupling type are read off the time signals. No parameter in Section V is fitted to the stability outcome, and the claimed dependence on the density-difference ratio is a parametric observation over the three simulated electrolyte densities (1715, 3452.2, and 5994 kg/m^3), not an equation that encodes the result. The fast/slow mode classification is imported from Ref. 11, an independent linear analysis of a non-electromagnetic three-layer system, and is applied only to label the simulated phase relationships, periods, and amplitude ratios; the label does not by construction force which mode appears. The self-citations (Refs. 9, 12, 35, 37) are prior modeling, validation, thesis, and animation material; Ref. 12 is used as a corroborating comparison for the equal-density case, but the present simulations stand on their own time integration. I therefore find no circular step. A separate, non-circular correctness concern: Section V C states that cases 14-17 use an electrolyte density such that 'the density differences across the lower and upper interfaces are the same,' but Table I values (rho_A = 1577, rho_E = 3452.2, rho_B = 6270 kg/m^3) give Delta rho_A = 1875.2 kg/m^3 and Delta rho_B = 2817.8 kg/m^3, a ratio of about 0.665; equality would require rho_E = 3923.5 kg/m^3. This undermines the headline equal-density stabilization claim, but the discrepancy is an arithmetic/support issue rather than circularity, because the simulated stability at the actually simulated parameters is still produced by the dynamics rather than by construction.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

No numbers are fitted to data in this study; all parameters are set from material properties and the parameter sweep is a direct variation of input quantities. The central claims therefore rest entirely on the stated physical and numerical modeling assumptions, which are explicit.

assumptions (5)
  • domain assumption Quasi-static MHD approximation with neglected induced magnetic field (Rem << 1).
    Section II estimates magnetic Reynolds number 4.5e-2 and neglects field induced by motion in Ohm's law and Lorentz force.
  • domain assumption Magnetic field is constant and purely vertical: B = B0 ey.
    Section II states all components but the vertical are neglected, which removes Tayler instability, electro-vortex flow, and background flows.
  • domain assumption Immiscibility, constant temperature, constant fluid properties, no mass transfer across interfaces.
    Section II lists these simplifications to isolate the rolling pad instability; thermal and Marangoni convection and intermetallic solid formation are ignored.
  • domain assumption Boundary conditions: insulating sidewalls and equipotential top and bottom walls with potential drop fixed to unperturbed state (Eqs. 14-16).
    Section II; this imposes that perturbation currents close entirely within the cell, which differs from Ref. 12's continuous potential adjustment.
  • domain assumption Volume-of-fluid one-fluid model with harmonic interpolation of conductivity accurately resolves the sharp conductivity contrast.
    Section III; the numerical method relies on VOF and a conservative current scheme, with convergence tolerance 1e-20 and about 500 iterations per step.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Numerical simulation of rolling pad instability in cuboid liquid metal batteries." pith.science (2026). https://pith.science/paper/6EPDTYJ6

@misc{pith2026190801884,
  author       = {Pith},
  title        = {Pith review of: Numerical simulation of rolling pad instability in cuboid liquid metal batteries},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6EPDTYJ6}},
  note         = {Machine review of arXiv:1908.01884}
}
read the original abstract

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.

Figures

Figures reproduced from arXiv: 1908.01884 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. An example of the vertical cross-section of the optimal grid determined in the course of the grid [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Stable flow at [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figures from the paper (15 more)
Figure 5
Figure 5. Figure 5: The interfacial waves presented as three-dimensional (in Fig. 5a) and two-dimensional [PITH_FULL_IMAGE:figures/full_fig_p018_5.png]
Figure 4
Figure 4. Figure 4: FIG. 4. Unstable flow with saturation at [PITH_FULL_IMAGE:figures/full_fig_p019_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Typical structure of the saturated unstable flow at [PITH_FULL_IMAGE:figures/full_fig_p020_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Unstable flow with saturation at [PITH_FULL_IMAGE:figures/full_fig_p021_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Unstable flow with rupture of electrolyte layer at [PITH_FULL_IMAGE:figures/full_fig_p022_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Typical structure of the flow at [PITH_FULL_IMAGE:figures/full_fig_p023_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Typical structure of the rupture flow at [PITH_FULL_IMAGE:figures/full_fig_p024_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Effect of [PITH_FULL_IMAGE:figures/full_fig_p026_10.png]
Figure 11
Figure 11. Figure 11: We see that the waves are coupled symmetrically (in-phase with each other) and have [PITH_FULL_IMAGE:figures/full_fig_p026_11.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Effect of [PITH_FULL_IMAGE:figures/full_fig_p027_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Stable flow at [PITH_FULL_IMAGE:figures/full_fig_p028_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13. Effect of [PITH_FULL_IMAGE:figures/full_fig_p030_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14. Rolling pad instability caused by slow modes at [PITH_FULL_IMAGE:figures/full_fig_p031_14.png]
Figure 15
Figure 15. Figure 15: FIG. 15. Effect of the form of initial perturbations illustrated by the results for the case 5 ( [PITH_FULL_IMAGE:figures/full_fig_p032_15.png]
Figure 16
Figure 16. Figure 16: FIG. 16. Effect of the form of initial perturbations illustrated by the result for the case 5 ( [PITH_FULL_IMAGE:figures/full_fig_p033_16.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

43 extracted references · 38 canonical work pages

  1. [1]

    merlin.mbs aapmrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

    FUNCTION id.bst "merlin.mbs aapmrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked" ENTRY address archive archivePrefix author bookaddress booktitle chapter collaboration doi edition editor eid eprint howpublished institution isbn issn journal key language month note number organization pages primaryClass publisher school SLACcitation series title translat...

    2010

  2. [2]

    merlin.mbs aipauth4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

    FUNCTION id.bst "merlin.mbs aipauth4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked" ENTRY address archive archivePrefix author bookaddress booktitle chapter collaboration doi edition editor eid eprint howpublished institution isbn issn journal key language month note number organization pages primaryClass publisher school SLACcitation series title translat...

    2010

  3. [3]

    merlin.mbs aipnum4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

    FUNCTION id.bst "merlin.mbs aipnum4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked" ENTRY address archive archivePrefix author bookaddress booktitle chapter collaboration doi edition editor eid eprint howpublished institution isbn issn journal key language month note number organization pages primaryClass publisher school SLACcitation series title translati...

    2010

  4. [4]

    merlin.mbs apsrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

    FUNCTION id.bst "merlin.mbs apsrev4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked" ENTRY address archive archivePrefix author bookaddress booktitle chapter collaboration doi edition editor eid eprint howpublished institution isbn issn journal key language month note number organization pages primaryClass publisher school SLACcitation series title translati...

    2010

  5. [5]

    merlin.mbs apsrmp4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked

    FUNCTION id.bst "merlin.mbs apsrmp4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked" ENTRY address archive archivePrefix author bookaddress booktitle chapter collaboration doi edition editor eid eprint howpublished institution isbn issn journal key language month note number organization pages primaryClass publisher school SLACcitation series title translati...

    2010

  6. [6]

    \@endnotelabel

    #2 \@endnotetext#1 @relax \@bibdataout @FOOTNOTE \@endnotelabel, key="\@endnotelabel", note="#1" \@bibdataout @relax \( \) \\ \@unexpandable@protect `\^^M @documenthook \@bibdataout@init \@bibdataout@init \@bibdataout @bibdata. @ext \@bibdataout@rev \@bibdataout @CONTROL REVTEX41Control @enable@sw ,eprint="" @filesw \@auxout REVTEX41Control @warn The comm...

    work page 2010

  7. [7]

    Kim , author D

    author author H. Kim , author D. A. \ Boysen , author J. M. \ Newhouse , author B. L. \ Spatocco , author B. Chung , author P. J. \ Burke , author D. J. \ Bradwell , author K. Jiang , author A. A. \ Tomaszowska , author K. Wang , author W. Wei , author L. A. \ Ortiz , author S. A. \ Barriga , author S. M. \ Poizeau , \ and\ author D. R. \ Sadoway ,\ title...

    work page 2013

  8. [8]

    author author D. H. \ Kelley \ and\ author T. Weier ,\ title title Fluid mechanics of liquid metal batteries , \ @noop journal journal Applied Mech. Rev. \ volume 70 ,\ pages 020801 ( year 2018 ) NoStop

    work page 2018

Show all 43 references
  1. [9]

    Seilmayer , author F

    author author M. Seilmayer , author F. Stefani , author T. Gundrum , author T. Weier , author G. Gerbeth , author M. Gellert , \ and\ author G. R\" u diger ,\ title title Experimental evidence for a transient Tayler instability in a cylindrical liquid-metal column , \ @noop jo...

    2012

  2. [10]

    Weber , author V

    author author N. Weber , author V. Galindo , author F. Stefani , \ and\ author T. Weier ,\ title title Current-driven flow instabilities in large-scale liquid metal batteries, and how to tame them , \ @noop journal journal J. Power Sources \ volume 265 ,\ pages 166--173 ( year...

    2014

  3. [11]

    Herreman , author C

    author author W. Herreman , author C. Nore , author L. Cappanera , \ and\ author J.-L. \ Guermond ,\ title title Tayler instability in liquid metal columns and liquid metal batteries , \ @noop journal journal J. Fluid Mech. \ volume 771 ,\ pages 79--114 ( year 2015 ) NoStop

    2015

  4. [12]

    Shen \ and\ author O

    author author Y. Shen \ and\ author O. Zikanov ,\ title title Thermal convection in a liquid metal battery , \ @noop journal journal Theor. Comp. Fluid Dyn. \ volume 30 ,\ pages 275--294 ( year 2016 ) NoStop

    2016

  5. [13]

    author author D. H. \ Kelley \ and\ author D. R. \ Sadoway ,\ title title Mixing in a liquid metal electrode , \ @noop journal journal Phys. Fluids \ volume 26 ,\ pages 057102 ( year 2014 ) NoStop

    2014

  6. [14]

    K\"ollner , author T

    author author T. K\"ollner , author T. Boeck , \ and\ author J. Schumacher ,\ title title Thermal Rayleigh-Marangoni convection in a three-layer liquid-metal-battery model , \ @noop journal journal Phys. Rev. E \ volume 95 ,\ pages 053114 ( year 2017 ) NoStop

    2017

  7. [15]

    Zikanov ,\ title title Metal pad instabilities in liquid metal batteries , \ @noop journal journal Phys

    author author O. Zikanov ,\ title title Metal pad instabilities in liquid metal batteries , \ @noop journal journal Phys. Rev. E \ volume 92 ,\ pages 063021 ( year 2015 ) NoStop

    2015

  8. [16]

    Weber , author P

    author author N. Weber , author P. Beckstein , author W. Herreman , author G. M. \ Horstmann , author C. Nore , author F. Stefani , \ and\ author T. Weier ,\ title title Sloshing instability and electrolyte layer rupture in liquid metal batteries , \ @noop journal journal Phys...

    2017

  9. [17]

    author author G. M. \ Horstmann , author N. Weber , \ and\ author T. Weier ,\ title title Coupling and stability of interfacial waves in liquid metal batteries , \ @noop journal journal J. Fluid Mech. \ volume 845 ,\ pages 1--35 ( year 2018 ) NoStop

    2018

  10. [18]

    Zikanov ,\ title title Shallow water modeling of rolling pad instability in liquid metal batteries , \ @noop journal journal Theor

    author author O. Zikanov ,\ title title Shallow water modeling of rolling pad instability in liquid metal batteries , \ @noop journal journal Theor. Comp. Fluid Dyn. \ volume 32 ,\ pages 325--347 ( year 2018 ) NoStop

    2018

  11. [19]

    Tucs , author V

    author author A. Tucs , author V. Bojarevics , \ and\ author K. Pericleous ,\ title title Magnetohydrodynamic stability of large scale liquid metal batteries , \ @noop journal journal J. Fluid Mech. \ volume 852 ,\ pages 453--483 ( year 2018 ) NoStop

    2018

  12. [20]

    author author S. Molokov ,\ title title The nature of interfacial instabilities in liquid metal batteries in a vertical magnetic field , \ @noop journal journal EPL (Europhysics Letters) \ volume 121 ,\ pages 44001 ( year 2018 ) NoStop

    2018

  13. [21]

    Herreman ,\ author C

    author author W. Herreman ,\ author C. Nore , \ author J-L. Guermond , \ author L. Cappanera , \ author N. Weber , \ and\ author G. M. Horstmann , \ title title Perturbation theory for metal pad roll instability in cylindrical reduction cells , \ @noop journal journal J. Fluid...

    2019

  14. [22]

    author author P. A. \ Davidson ,\ @noop title Introduction to magnetohydrodynamics \ ( publisher Cambridge University Press ,\ year 2016 ) NoStop

    2016

  15. [23]

    Sele ,\ title title Instabilities of the metal surface in electrolyte alumina reduction cells , \ @noop journal journal Met

    author author T. Sele ,\ title title Instabilities of the metal surface in electrolyte alumina reduction cells , \ @noop journal journal Met. Mat. Trans. B \ volume 8 ,\ pages 613 ( year 1977 ) NoStop

    1977

  16. [24]

    author author N. Urata ,\ title title Magnetics and metal pad instability , \ in\ @noop booktitle Essential Readings in Light Metals \ ( publisher Springer ,\ year 2016 )\ pp.\ pages 330--335 NoStop

    2016

  17. [25]

    Bojarevics \ and\ author M

    author author V. Bojarevics \ and\ author M. V. \ Romerio ,\ title title Long waves instability of liquid metal-electrolyte interface in aluminium electrolysis cells: a generalization of Sele's criterion , \ @noop journal journal Eur. J. Mech. B, Fluids \ volume 13 ,\ pages 33...

    1994

  18. [26]

    Sneyd \ and\ author A

    author author A. Sneyd \ and\ author A. Wang ,\ title title Interfacial instability due to MHD mode coupling in aluminium reduction cells , \ @noop journal journal J. Fluid Mech. \ volume 263 ,\ pages 343--360 ( year 1994 ) NoStop

    1994

  19. [27]

    author author P. A. \ Davidson \ and\ author R. I. \ Lindsay ,\ title title Stability of interfacial waves in aluminium reduction cells , \ @noop journal journal J. Fluid Mech. \ volume 362 ,\ pages 273--295 ( year 1998 ) NoStop

    1998

  20. [28]

    Zikanov , author A

    author author O. Zikanov , author A. Thess , author P. A. \ Davidson , \ and\ author D. P. \ Ziegler ,\ title title A New Approach to Numerical Simulation of Melt Flows and Interface Instability in Hall – Heroult Cells , \ @noop journal journal Met. Mat. Trans. B \ volume 31 ,...

    2000

  21. [29]

    Sun , author O

    author author H. Sun , author O. Zikanov , \ and\ author D. P. \ Ziegler ,\ title title Non-linear two-dimensional model of melt flows and interface instability in aluminum reduction cells , \ @noop journal journal Fluid Dyn. Res. \ volume 35 ,\ pages 255--274 ( year 2004 ) NoStop

    2004

  22. [30]

    Sun , author O

    author author S. Sun , author O. Zikanov , \ and\ author B. Finlayson ,\ title title Effect of background melt flow and interface distortion on the stability of hall—herault cells , \ @noop journal journal Magnetohydrodynamics \ volume 41 ,\ pages 273--287 ( year 2005 ) NoStop

    2005

  23. [31]

    @noop title OpenFOAM documentation , \ howpublished http://https://www.openfoam.com NoStop

  24. [32]

    Prosperetti \ and\ author G

    author author A. Prosperetti \ and\ author G. Tryggvason ,\ @noop title Computational methods for multiphase flow \ ( publisher Cambridge university press ,\ year 2009 ) NoStop

    2009

  25. [33]

    author author J. U. \ Brackbill , author D. B. \ Kothe , \ and\ author C. Zemach ,\ title title A continuum method for modeling surface tension , \ @noop journal journal J Comp. Phys. \ volume 100 ,\ pages 335--354 ( year 1992 ) NoStop

    1992

  26. [34]

    Ubbink ,\ title Numerical prediction of two fluid systems with sharp interfaces ,\ @noop Ph.D

    author author O. Ubbink ,\ title Numerical prediction of two fluid systems with sharp interfaces ,\ @noop Ph.D. thesis ,\ school University of London PhD Thesis ( year 1997 ) NoStop

    1997

  27. [35]

    thesis ,\ school National University of the Littoral PhD Thesis ( year 2013 ) NoStop

    author author Santiago M \'a rquez Dami \'a n ,\ title An extended mixture model for the simultaneous treatment of short and long scale interfaces ,\ @noop Ph.D. thesis ,\ school National University of the Littoral PhD Thesis ( year 2013 ) NoStop

    2013

  28. [36]

    author author S. S. \ Deshpande , author L. Anumolu , \ and\ author M. F. \ Trujillo ,\ title title Evaluating the performance of the two-phase flow solver interfoam , \ @noop journal journal Computational science & discovery \ volume 5 ,\ pages 014016 ( year 2012 ) NoStop

    2012

  29. [37]

    author author R. I. \ Issa ,\ title title Solution of the implicitly discretised fluid flow equations by operator-splitting , \ @noop journal journal J. Comp. Phys. \ volume 62 ,\ pages 40--65 ( year 1986 ) NoStop

    1986

  30. [38]

    \ Ni , author R

    author author M.-J. \ Ni , author R. Munipalli , author P. Huang , author N. B. \ Morley , \ and\ author M. A. \ Abdou ,\ title title A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part I : On a rectangular collocated grid...

    2007

  31. [39]

    \ Ni , author R

    author author M.-J. \ Ni , author R. Munipalli , author P. Huang , author N. B. \ Morley , \ and\ author M. A. \ Abdou ,\ title title A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part II: on an arbitrary collocated mesh ...

    2007

  32. [40]

    Patankar ,\ @noop title Numerical heat transfer and fluid flow \ ( publisher CRC Press ,\ year 1980 ) NoStop

    author author S. Patankar ,\ @noop title Numerical heat transfer and fluid flow \ ( publisher CRC Press ,\ year 1980 ) NoStop

    1980

  33. [41]

    author author L. Xiang ,\ title Metal pad instability in Liquid Metal Batteries ,\ @noop Master's thesis ,\ school University of Michigan - Dearborn ( year 2018 ),\ note URL : http://hdl.handle.net/2027.42/143526 NoStop

    2018

  34. [42]

    Lukyanov , author G

    author author A. Lukyanov , author G. El , \ and\ author S. Molokov ,\ title title Instability of MHD-modified interfacial gravity waves revisited , \ @noop journal journal Physics Letters A \ volume 290 ,\ pages 165--172 ( year 2001 ) NoStop

    2001

  35. [43]

    Xiang ,\ @noop title Metal pad instability in Liquid Metal Batteries

    author author L. Xiang ,\ @noop title Metal pad instability in Liquid Metal Batteries. Animations of computed flow regimes , \ ( year 2019 ),\ note URL : https://doi.org/10.7302/xpjk-0t20 NoStop

    2019 doi

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.