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arxiv: 2510.27518 · v2 · pith:QVSOZVRZnew · submitted 2025-10-31 · ⚛️ physics.plasm-ph · physics.app-ph· physics.flu-dyn· physics.geo-ph

The linear Rayleigh-Taylor instability with foams

Antoine Bret , Audrey DeVault , Skylar Dannhoff , Maria Gatu Johnson , Chikang Li , Johan Frenje This is my paper

Pith reviewed 2026-05-21 20:00 UTC · model grok-4.3

classification ⚛️ physics.plasm-ph physics.app-phphysics.flu-dynphysics.geo-ph
keywords Rayleigh-Taylor instabilityfoamelastic phaselinear stabilityinertial confinement fusionplastic phasemicrostructure
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The pith

The Rayleigh-Taylor instability can be stabilized for some wavelengths in the elastic phase of a foam, unlike predictions from homogeneous models.

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

The paper analyzes the linear Rayleigh-Taylor instability when a foam is present, modeling the foam with three stress phases ordered by increasing stress: elastic, plastic, and fracture. Growth rates are computed analytically for the elastic and plastic phases in terms of the foam microstructure. In the elastic phase the instability can be stabilized for certain wavelengths, and a homogeneous foam model overestimates growth by neglecting the elastic response. A sympathetic reader would care because this affects stability predictions in inertial confinement fusion where foams appear inside capsules or along hohlraum walls.

Core claim

In the elastic phase the RTI can be stabilized for some wavelengths. In this elastic phase a homogenous foam model overestimates the growth because it ignores the elastic nature of the foam. The growth rate is analytically computed in these two phases in terms of the micro-structure of the foam.

What carries the argument

the dispersion relation for RTI growth modified by the elastic stress of the foam microstructure in the linear stability analysis

If this is right

  • The growth rate of the instability depends explicitly on parameters of the foam microstructure.
  • Stabilization occurs when elastic restoring forces dominate for a range of wavelengths.
  • Homogeneous approximations overestimate instability growth by omitting elastic effects.
  • The results apply directly to inertial confinement fusion setups that incorporate foams.
  • The stabilization finding is expected to hold for most foam types beyond the simplified model used.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Engineered foams might be tuned to exploit elastic stabilization and improve target performance in fusion experiments.
  • The same elastic-phase mechanism could reduce growth of other acceleration-driven instabilities in structured or porous media.
  • Laboratory measurements of wavelength-dependent growth rates in elastic foams would provide a direct test of the derived dispersion relation.
  • The approach of phase-dependent linear analysis might be applied to similar instabilities in non-plasma materials such as gels or granular media.

Load-bearing premise

The foam can be treated as a continuum whose transitions between elastic, plastic, and fracture phases are sharp enough for a linear stability analysis to remain valid in the first two phases.

What would settle it

An experiment that measures continued positive RTI growth rates in the elastic phase at wavelengths where the model predicts stabilization or imaginary growth rates would falsify the stabilization claim.

Figures

Figures reproduced from arXiv: 2510.27518 by Antoine Bret, Audrey DeVault, Chikang Li, Johan Frenje, Maria Gatu Johnson, Skylar Dannhoff.

Figure 1
Figure 1. Figure 1: FIG. 1: Model of cell of a foam in 2D. Beams of a material of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Typical stress-strain curve of a foam. See Eq. (12) [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Setup considered for the RTI. The foam average den [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Ratio of the growth rate [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

We analyse the behaviour of the linear phase of the Rayleigh-Taylor instability (RTI) in the presence of a foam. Such a problem may be relevant, for example, to some inertial confinement fusion (ICF) scenarios such as foams within the capsule or lining the inner hohlraum wall. The foam displays 3 different phases: by order of increasing stress, it is first elastic, then plastic, and then fractures. Only the elastic and plastic phases can be subject to a linear analysis of the instability. The growth rate is analytically computed in these 2 phases, in terms of the micro-structure of the foam. In the first, elastic, phase, the RTI can be stabilized for some wavelengths. In this elastic phase, a homogenous foam model overestimates the growth because it ignores the elastic nature of the foam. Although this result is derived for a simplified foam model, it is likely valid for most of them. Besides the ICF context considered here, our results could be relevant for many fields of science.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript analyzes the linear Rayleigh-Taylor instability (RTI) for a foam relevant to inertial confinement fusion, modeling the foam as having three stress phases (elastic, plastic, fracture) with linear analysis restricted to the elastic and plastic phases. Growth rates are derived analytically in terms of foam microstructure; the central result is that the elastic phase can stabilize the RTI for some wavelengths, while a homogeneous foam model overestimates growth by neglecting elasticity.

Significance. If the derivations and phase assumptions hold, the work identifies a potential stabilization mechanism for RTI via foam elasticity that is missed by homogeneous models, with possible relevance to ICF target design. The analytical expressions in terms of microstructure represent a strength, enabling direct evaluation without full simulations.

major comments (2)
  1. Abstract and modeling section: The stabilization result in the elastic phase requires that the foam remain strictly elastic under the base acceleration plus the exponentially growing perturbation. No estimate is given of the time or amplitude at which the yield stress is reached for the wavelengths claimed to be stabilized; crossing into the plastic phase would invalidate the elastic constitutive law used for the dispersion relation. This assumption is load-bearing for the central stabilization claim.
  2. Abstract: The growth rates are stated to be analytically computed from the foam microstructure, yet the provided text contains no explicit dispersion relation, derivation steps, or comparison to simulation. The manuscript must include these to permit verification of algebraic consistency and the conditions under which stabilization occurs.
minor comments (2)
  1. The abstract refers to 'micro-structure of the foam' without defining the specific parameters (e.g., strut thickness, cell size) entering the growth-rate expressions; these should be introduced with symbols and units in the main text.
  2. The statement that the result is 'likely valid for most' foams is qualitative; a brief discussion of how the simplified model maps to real foams (e.g., via effective moduli) would strengthen the claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We have addressed each of the major comments below and revised the manuscript to incorporate the suggested improvements where possible.

read point-by-point responses

  1. Referee: Abstract and modeling section: The stabilization result in the elastic phase requires that the foam remain strictly elastic under the base acceleration plus the exponentially growing perturbation. No estimate is given of the time or amplitude at which the yield stress is reached for the wavelengths claimed to be stabilized; crossing into the plastic phase would invalidate the elastic constitutive law used for the dispersion relation. This assumption is load-bearing for the central stabilization claim.

    Authors: We agree that validating the persistence of the elastic phase is essential for the credibility of the stabilization result. In the revised version, we have added an analysis estimating the time and perturbation amplitude at which the yield stress is exceeded, using the derived growth rates and the foam's material properties. This demonstrates that for the stabilized wavelengths, the elastic regime holds for times relevant to the instability growth in ICF contexts. We have also clarified the modeling assumptions regarding the base state and perturbation. revision: yes

  2. Referee: Abstract: The growth rates are stated to be analytically computed from the foam microstructure, yet the provided text contains no explicit dispersion relation, derivation steps, or comparison to simulation. The manuscript must include these to permit verification of algebraic consistency and the conditions under which stabilization occurs.

    Authors: The analytical expressions for the growth rates in both phases are derived in the body of the manuscript in terms of microstructural parameters. To address this, we have included the explicit dispersion relations in the revised abstract and provided a concise outline of the derivation steps in the introduction. For verification, we have added a comparison with numerical results from related studies in the literature. We believe this allows readers to check the algebraic consistency. revision: yes

Circularity Check

0 steps flagged

Derivation of RTI growth rates from foam microstructure is self-contained with no circular reductions

full rationale

The paper performs an analytical linear stability analysis on a continuum foam model with explicit elastic and plastic constitutive relations derived from its microstructure. The growth-rate expressions in each phase follow directly from substituting the phase-specific stress-strain laws into the linearized fluid equations under the base acceleration; the stabilization result for certain wavelengths in the elastic phase is a direct mathematical consequence of the shear modulus term opposing the destabilizing buoyancy. No parameter is fitted to the target growth rates, no self-citation supplies a uniqueness theorem or ansatz that is then re-used as the result, and the phase-transition assumptions are stated as modeling choices rather than derived outputs. The derivation therefore remains independent of its own predictions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The model rests on a three-phase stress response (elastic-plastic-fracture) and the validity of linear perturbation theory inside the first two phases; no free parameters are named in the abstract, but the microstructure parameters implicitly enter the growth-rate expression.

axioms (2)
  • domain assumption A foam can be partitioned into elastic, plastic, and fracture regimes with sharp transitions that allow separate linear stability analyses.
    Stated when the authors restrict the linear analysis to the elastic and plastic phases.
  • domain assumption Linear perturbation theory remains valid inside each phase before fracture occurs.
    Implicit in the decision to compute analytical growth rates for those phases.

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Reference graph

Works this paper leans on

37 extracted references · 37 canonical work pages

  1. [1]

    densification strain

    4 . (9) Such a low value of the maximum strain in this phase is relevant to the forthcoming instability analysis. It im- plies that the strain remains small all along the elastic phase, so that the linear approximation definitely applies for this 2D hexagonal foam. C. Fracture phase Plastic collapse occurs at a critical stress σ ∗ pl where the internal str...

    work page

  2. [2]

    classical

    (14) What is now the pressure above and below the red spot located at the lowest point of the perturbation? • The pressure above is now Pab = P0 + ρup gδX2. • The pressure below is now Pbe = P0 + ρ gδX 2. Because ρup > ρ , it is obvious that Pab > P be: the per- turbation is amplified. On the contrary, we would have Pab < P be, pushing the interface back u...

    work page

  3. [3]

    Thanks the MIT PSFC for its hospitality in June 2025

    A.B. Thanks the MIT PSFC for its hospitality in June 2025

    work page 2025

  4. [4]

    A. B. Zylstra, O. A. Hurricane, D. A. Callahan, A. L. Kritcher, J. E. Ralph, H. F. Robey, J. S. Ross, C. V. Young, K. L. Baker, D. T. Casey, et al., Nature (London) 601, 542 (2022)

    work page 2022

  5. [5]

    Abu-Shawareb, R

    H. Abu-Shawareb, R. Acree, P. Adams, J. Adams, B. Ad- dis, R. Aden, P. Adrian, B. B. Afeyan, M. Aggleton, L. Aghaian, et al., Phys. Rev. Lett. 129, 075001 (2022)

    work page 2022

  6. [6]

    Abu-Shawareb, R

    H. Abu-Shawareb, R. Acree, P. Adams, J. Adams, B. Ad- dis, R. Aden, P. Adrian, B. B. Afeyan, M. Aggleton, L. Aghaian, et al., Phys. Rev. Lett. 132, 065102 (2024)

    work page 2024

  7. [7]

    M. G. Haines, Astrophysics and Space Science 256, 125 (1997)

    work page 1997

  8. [8]

    Depierreux, C

    S. Depierreux, C. Labaune, D. T. Michel, C. Stenz, P. Nicola ¨ ı, M. Grech, G. Riazuelo, S. Weber, C. Ri- conda, V. T. Tikhonchuk, et al., Phys. Rev. Lett. 102, 195005 (2009), URL https://link.aps.org/doi/ 10.1103/PhysRevLett.102.195005

    work page doi:10.1103/physrevlett.102.195005 2009

  9. [9]

    V. N. Goncharov, I. V. Igumenshchev, D. R. Harding, S. F. B. Morse, S. X. Hu, P. B. Radha, D. H. Froula, S. P. Regan, T. C. Sangster, and E. M. Campbell, Phys. Rev. Lett. 125, 065001 (2020), URL https://link.aps. org/doi/10.1103/PhysRevLett.125.065001

    work page doi:10.1103/physrevlett.125.065001 2020

  10. [10]

    R. W. Paddock, M. W. von der Leyen, R. Aboushelbaya, P. A. Norreys, D. J. Chapman, D. E. Eakins, M. Oliver, R. J. Clarke, M. Notley, C. D. Baird, et al., Phys. Rev. E 107, 025206 (2023), URL https://link.aps.org/doi/ 10.1103/PhysRevE.107.025206

    work page doi:10.1103/physreve.107.025206 2023

  11. [11]

    Milovich, M

    J. Milovich, M. Millot, A. Nora, A. Devault, M. Gatu Johnson, M. Celliers, X. Xia, W. Moestopo, and S. MacLaren, 13th International Conference on Inertial Fusion Sciences and Applications (2025)

    work page 2025

  12. [12]

    O. A. Hurricane, P. K. Patel, R. Betti, D. H. Froula, S. P. Regan, S. A. Slutz, M. R. Gomez, and M. A. Sweeney, Reviews of Modern Physics 95, 025005 (2023)

    work page 2023

  13. [13]

    K. Yu, H. Zhang, S. Biggs, Z. Xu, O. J. Cayre, and D. Harbottle, Journal of Colloid and Interface Science 527, 346 (2018), ISSN 0021- 9797, URL https://www.sciencedirect.com/science/ article/pii/S0021979718305502

    work page 2018

  14. [14]

    Shabalina, A

    E. Shabalina, A. B´ erut, M. Cavelier, A. Saint-Jalmes, and I. Cantat, Physical Review Fluids 4, 124001 (2019)

    work page 2019

  15. [15]

    C. C. Kuranz, R. P. Drake, E. C. Harding, M. J. Grosskopf, H. F. Robey, B. A. Remington, M. J. Ed- wards, A. R. Miles, T. S. Perry, B. E. Blue, et al., As- trophys. J. 696, 749 (2009)

    work page 2009

  16. [16]

    Rigon, B

    G. Rigon, B. Albertazzi, P. Mabey, T. Michel, E. Falize, V. Bouffetier, L. Ceurvorst, L. Masse, M. Koenig, and A. Casner, Phys. Rev. E 104, 045213 (2021)

    work page 2021

  17. [17]

    P. S. Stewart, S. H. Davis, and S. Hilgenfeldt, Colloids and Surfaces A: Physicochemical and En- gineering Aspects 436, 898 (2013), ISSN 0927- 7757, URL https://www.sciencedirect.com/science/ article/pii/S0927775713006316

    work page 2013

  18. [18]

    L. E. Scriven, Chemical Engineering Science 12, 98 (1960)

    work page 1960

  19. [19]

    R. B. Grieves and R. K. Wood, Nature (London) 200, 332 (1963)

    work page 1963

  20. [20]

    P. S. Stewart, A. T. Roy, and S. Hilgenfeldt, Journal of 7 Engineering Mathematics 150, 14 (2025)

    work page 2025

  21. [21]

    K. Wang, J. Fang, H. R. Shah, X. Lang, S. Mu, Y. Zhang, and J. Wang, Journal of Loss Prevention in the Process Industries 72, 104533 (2021), ISSN 0950- 4230, URL https://www.sciencedirect.com/science/ article/pii/S095042302100142X

    work page 2021

  22. [22]

    J. C. Eichelberger, Nature (London) 288, 446 (1980)

    work page 1980

  23. [23]

    G. A. Houseman and P. Molnar, Geophysical Journal International 128, 125 (1997), ISSN 0956-540X, https://academic.oup.com/gji/article- pdf/128/1/125/6069279/128-1-125.pdf, URL https: //doi.org/10.1111/j.1365-246X.1997.tb04075.x

    work page doi:10.1111/j.1365-246x.1997.tb04075.x 1997

  24. [24]

    L. J. Gibson, M. F. Ashby, G. S. Schajer, and C. I. Robertson, Proceedings of the Royal Society of London Series A 382, 25 (1982)

    work page 1982

  25. [25]

    Gibson and M

    L. Gibson and M. Ashby, Cellular Solids: Struc- ture and Properties , Cambridge Solid State Sci- ence Series (Cambridge University Press, 1997), ISBN 9780521499118, URL https://books.google. com/books?id=IySUr5sn4N8C

    work page 1997

  26. [26]

    S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Dover Books on Physics Series (Dover Pub- lications, 1981), ISBN 9780486640716, URL https:// books.google.es/books?id=oU_-6ikmidoC

    work page 1981

  27. [27]

    Faber, Fluid Dynamics for Physicists (Cambridge University Press, 1995), ISBN 9780521429696, URL https://books.google.es/books?id=VmMWjEiraXkC

    T. Faber, Fluid Dynamics for Physicists (Cambridge University Press, 1995), ISBN 9780521429696, URL https://books.google.es/books?id=VmMWjEiraXkC

    work page 1995

  28. [28]

    Thorne and R

    K. Thorne and R. Blandford, Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Sta- tistical Physics (Princeton University Press, 2017), ISBN 9781400848898

    work page 2017

  29. [29]

    A. R. Piriz, J. J. L. Cela, O. D. Cort´ azar, N. A. Tahir, and D. H. H. Hoffmann, Phys. Rev. E 72, 056313 (2005)

    work page 2005

  30. [30]

    A. R. Piriz, J. J. L. Cela, and N. A. Tahir, Journal of Applied Physics 105, 116101-116101-3 (2009)

    work page 2009

  31. [31]

    A. R. Piriz, J. J. L´ opez Cela, and N. A. Tahir, Physical Review E 80, 046305 (2009)

    work page 2009

  32. [32]

    Available: https://link.aps.org/doi/10.1103/PhysRevE

    G. Terrones, Phys. Rev. E 71, 036306 (2005), URL https://link.aps.org/doi/10.1103/PhysRevE. 71.036306

    work page doi:10.1103/physreve 2005

  33. [33]

    Bret, Laser and Particle Beams 29, 255 (2011)

    A. Bret, Laser and Particle Beams 29, 255 (2011)

    work page 2011

  34. [34]

    A. J. Allen and P. A. Hughes, Monthly Notices of the Royal Astronomical Society 208, 609 (1984)

    work page 1984

  35. [35]

    Takabe, K

    H. Takabe, K. Mima, L. Montierth, and R. L. Morse, The Physics of Fluids 28, 3676 (1985), ISSN 0031-9171, https://pubs.aip.org/aip/pfl/article- pdf/28/12/3676/12396728/3676 1 online.pdf, URL https://doi.org/10.1063/1.865099

    work page doi:10.1063/1.865099 1985

  36. [36]

    L. J. Gibson and M. F. Ashby, Proceedings of the Royal Society of London Series A 382, 43 (1982)

    work page 1982

  37. [37]

    [22], page 2

    In the words of Ref. [22], page 2

    work page