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REVIEW 3 major objections 6 minor 62 references

Balloon regime: Drop elasticity leads to complete rebound

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper claims a new Balloon regime in which viscoelastic drops rebound completely on superhydrophobic surfaces at Weber numbers up to 408.

desk verdict A novel and visually arresting experimental rebound regime for viscoelastic drops on superhydrophobic surfaces, with an honest but non-predictive simulation that doesn't undercut the core observation. read the letter →

arxiv 2502.10081 v1 pith:7WIJJU3M submitted 2025-02-14 cond-mat.soft physics.flu-dyn

D. Díaz , A.G. Balasubramanian , K. Amini , X. Li , F. Lundell , S. Bagheri , O. Tammisola This is my paper · ORCID
classification cond-mat.softphysics.flu-dyn
keywords dropimpactviscoelasticdropletssuperhydrophobicsurfaceballoonregimeCassie-Wenzeltransitionpolymerelasticityligamentbreakupcompleterebound
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

At impact speeds where ordinary water drops shatter into satellite droplets, dilute polyacrylamide drops on a superhydrophobic surface instead grow a vertical filament that inflates into a balloon-like head and detaches whole, rebounding completely. The paper claims this is a new regime—the Balloon regime—caused by impact pressure forcing liquid into the surface's nanoscale roughness (a Cassie-Wenzel transition), which sharply lowers the receding contact angle to about 60 degrees and anchors the filament. High liquid elasticity then keeps the thinning filament from breaking up, so the entire drop departs in one piece rather than leaving a ligament and secondary droplets. The authors show that ligament growth is governed mainly by inertia and gravity, that the effect disappears on a smooth hydrophobic surface, and that it becomes more pronounced at higher polymer concentrations. If correct, the result points to a way of repelling complex viscoelastic liquids at high impact speeds without splashing, with implications for inkjet printing, pesticide deposition, and self-cleaning surfaces.

What carries the argument

The central object is the Balloon regime: a ligament-driven rebound whose origin the paper traces to the Cassie-Wenzel transition. The load-bearing mechanism has three coupled ingredients: (i) at impact, the Hammer pressure $P_H = \rho C v_0/5$ overcomes the capillary pressure of the surface's air pockets, forcing liquid into the nanostructure spacing $\sim 0.1\,\mu$m; (ii) the resulting partial wetting makes the dynamic contact angle plunge to about $60^\circ$ during receding, pinning the contact line and letting a vertical ligament grow; (iii) high polymer elasticity, modeled with the L-PTT constitutive relation (and cross-checked with FENE-P), makes the polymer chains stretch along the filament, suppressing its breakup and allowing the ligament to detach as a whole. The filament length itself is set by inertia versus gravity, described by the ballistic centroid trajectory $Y_c(t) = Y_0 + v_{y0}t - \tfrac{1}{2}gt^2$, with the total dissipative force estimated to be at least an order of magnitude smaller than the gravitational force on the drop.

What would settle it

Measure the extensional rheology of the polymer solutions—for example, the relaxation time and strain-hardening behavior from capillary breakup extensional rheometry—and compare with the L-PTT parameters used in the simulations. Then test a solution with comparable shear viscosity but no extensional elasticity, or with elasticity but no impalement (a smooth substrate): if such a drop still rebounds completely on the rough surface, or if a highly elastic drop still splashes when impalement is absent, the claim that elasticity is what prevents ligament breakup would be falsified.

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Extended reading notes

Core claim

On a spray-coated superhydrophobic silica surface, polyacrylamide drops with concentrations from 0.025 to 1 wt% and Weber numbers up to 408 rebound completely through what the authors call the Balloon regime: as the contact line recedes, a vertical ligament emerges from the impact spot, a head droplet forms at its tip and inflates into a balloon-like shape for 0.5–1 wt%, and the ligament detaches as a whole, leaving no satellite droplets. Water drops under identical conditions splash. The authors attribute the ligament root to impact-driven impalement into the surface's nanoscale protrusions: the impact Hammer pressure $P_H = \rho C v_0/5$ exceeds the capillary pressure of the air pockets, consistent with the measured $\sim 0.1\,\mu$m spacing of the surface. Supporting evidence includes the dynamic contact angle falling from about $140^\circ$ to $60^\circ$ during the ligament phase, the absence of ligaments on a smooth Teflon surface, and interface-resolved simulations that reproduce the wetting length and show polymer chains stretching strongly along the thinning filament. The authors conclude that inertia and gravity set the ligament length—a ballistic fit to the drop centroid height gives a dissipative force at least an order of magnitude below gravity—while elasticity, concentrated in the stretched filament, is what prevents breakup and enables complete detachment.

Load-bearing premise

The numerical evidence rests on a tuned viscoelastic simulation whose parameters do not match the measured steady-shear viscosity (the paper uses $\beta = 2\times10^{-4}$, $\mu_p = 90$ Pa·s, and $\lambda = 6.25$ s) and on imposing the experimentally measured dynamic contact angle, which drops to about $60^\circ$ during receding, so if that simulation misrepresents the extensional stress in the thinning ligament, the conclusion that elasticity prevents breakup and enables complete rebound is not established.

Editorial extensions

If this is right

  • At Weber numbers above 136, where water drops splash into multiple satellite droplets, polymer drops rebound as a single body, so polymer additives can restore complete rebound on superhydrophobic surfaces at high impact speeds.
  • Ligament length increases with Weber number ($L_{\max} \sim We$), meaning the impact pressure and inertia control how far the filament stretches before detachment.
  • Ligament formation is surface-controlled: it is suppressed on a smooth hydrophobic surface (rms roughness ~5 nm) and promoted on a spray-coated surface with ~0.1 µm protrusion spacing, offering a design knob for drop repellency.
  • The balloon-like head appears only at polymer concentrations of 0.5–1 wt%, so the regime can be tuned by polymer concentration as well as by Weber number.
  • The drop of the dynamic contact angle to about 60° during receding serves as an experimental signature that the surface has transitioned from the Cassie-Baxter to the Wenzel state before the ligament develops.

Reading between the lines

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

  • If the proposed mechanism is correct, the onset of the Balloon regime should obey a simple threshold comparing the impact Hammer pressure to the capillary pressure of the surface microstructures; this could be tested by varying surface spacing and impact speed independently.
  • The balloon inflation likely reflects a capillary draining of the filament into the head drop, so the time scale of balloon growth might scale with the polymer relaxation time and could be probed with high-speed imaging across concentrations.
  • The finding suggests that strain-hardening in extension, rather than shear viscosity alone, is the rheological property that suppresses breakup; comparing drops of equal zero-shear viscosity but different extensional behavior on the same surface would separate these contributions.
  • For applications, this regime implies that satellites from high-speed jetting can be eliminated by combining a small amount of polymer with a suitably rough superhydrophobic surface, at the cost of turning the impact into a delayed, filament-mediated deposition.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper reports an experimental and numerical study of the impact of viscoelastic polyacrylamide (PAA) droplets on superhydrophobic Glaco surfaces. For Weber numbers between 136 and 408, water droplets splash, whereas PAA droplets form a vertical ligament during the receding phase that inflates into a balloon-like head and detaches completely; the authors call this the Balloon regime. They attribute the ligament formation to liquid impalement into the surface microstructure (Cassie–Wenzel transition), supported by experiments on smooth Teflon and on Glaco with a hydrophilic spot, and by measurements of the dynamic contact angle. Axisymmetric L-PTT simulations with an imposed experimental contact angle show polymer stress concentrations in the thinning ligament, and a ballistic model shows the ligament length is governed mainly by inertia and gravity. The central claim is that high elasticity prevents ligament breakup and thereby enables complete rebound.

Significance. The discovery of a drop-impact regime with complete rebound and no satellite droplets at Weber numbers up to 408 is visually convincing and could be important for applications such as spray coating, anti-icing, and pesticide deposition. The Teflon control and the hydrophilic-spot experiment are elegant and clearly demonstrate that surface roughness and wettability control ligament formation. The paper also provides a simple ballistic description for the droplet centroid trajectory. However, the causal role of elasticity is not established by the experiments alone, and the simulation evidence is limited by unmatched rheological parameters and an imposed contact-angle model; these issues are detailed in the major comments.

major comments (3)
  1. [Supplemental Sec. E2, Figs. S6–S7; main-text abstract] The claim that 'high elasticity prevents the ligament break up, enabling complete rebounds' is grounded in the polymer-stress trace from the L-PTT simulation, but the simulation uses β=2×10^-4, μ_p=90 Pa·s, and λ=6.25 s, which the authors state do not match the measured steady-shear viscosity, while the rheologically fitted parameters (β=5×10^-5, μ_p=19.23 Pa·s, λ=65.5 s) are not used for numerical stability. The reported sensitivity of the FENE-P model to L_max (breakup before detachment for other values) further indicates that the suppression of breakup is not robust across the constitutive-model parameter space. Because the experiments do not include a non-elastic viscous control with comparable zero-shear viscosity and shear-thinning, the data do not isolate elasticity as the cause of complete rebound. Please validate the constitutive parameters against transient extensional rheology, add a non-elastic shear-thinning control, or explicitly limit the elasticity claim to a hypothesis supported by illustrative simulations.
  2. [Supplemental Eq. (S7) and Sec. E5; main text, 'We imposed the dynamic contact angles...'] The dynamic contact angle in the simulation is fitted to the experimental measurements, including the decrease to a receding plateau of about 30° (experimental plateau ~60°) that is itself interpreted as evidence of impalement. The simulated wetting length therefore cannot independently confirm the impalement mechanism; the good qualitative agreement partly reproduces the imposed input. The conclusion that the contact-angle decrease is 'in good agreement with direct numeral simulations' is circular as stated. The simulation should be presented as a consistency check, or the authors should use a predictive contact-angle model that derives the receding angle from the impalement state.
  3. [Main text, 'To verify the role of Hammer pressure and Cassie-Wenzel transition'] The impalement mechanism is inferred from three indirect observations: the Hammer-pressure estimate r~0.1 μm, the drop in dynamic contact angle, and the suppression of ligament formation on smooth Teflon. The estimate relies on a single representative spacing r and a sound-speed-based pressure, and the Teflon experiment changes both roughness and chemistry relative to Glaco. The hydrophilic-spot experiment introduces a discrete defect rather than a distributed Cassie–Wenzel transition. Direct imaging of the liquid–solid contact (for example, bottom-view total-internal-reflection microscopy) or a systematic roughness variation with fixed surface chemistry would substantially strengthen the attribution of ligament formation to impalement; at minimum, the manuscript should state that impalement is inferred rather than directly observed.
minor comments (6)
  1. [Main text, ballistic model paragraph] The calculation of ΔE_p used for the dissipative force estimate is not shown; please provide the expression and the integration interval, and state how Y_0 and v_y0 are extracted from the experiments.
  2. [Main text, detachment pressure estimate] Please define V_ret explicitly (is it the centroid velocity of the head droplet or the ligament tip one frame after detachment?) and report the uncertainty in P_det.
  3. [Main text, Fig. 4a discussion] The statement 'L_max is proportional to fluid inertia (L_max ∼ We)' should be supported by a fit or by the data in Fig. 4a; if the relation is approximate, say so.
  4. [Supplemental Sec. A4] Please provide an estimate of the measurement uncertainty of the dynamic contact angles (e.g., repeatability over several drops).
  5. [Supplemental Sec. E5] The caveat that the numerical methodology 'is not employed as a predictive tool' is important for the paper's central claim and should appear in the main text near the simulation discussion, not only in the Supplemental Material.
  6. [References and notation] The main text refers to Supplemental 'Secs. I–IV' whereas the supplemental document uses 'Appendix A–E'; please align the labeling. Also, 'lower than Ph' should be 'lower than P_H' for consistency.

Circularity Check

1 steps flagged · score 6.0 of 10

Dynamic-contact-angle validation reduces to input: simulation imposes measured angles, so 'good agreement' is by construction; elasticity conclusion rests on a non-predictive, rheologically mismatched model.

  1. fitted input called prediction [Main text, discussion of Figs. 2b/3; Supplemental Material Sec. E5, Eq. S7 and Fig. S9]
    "We imposed the dynamic contact angles from experiments to our interface-resolved numerical simulations (Fig. 3, See Supplemental Material, Sec. IV [21] for details on the numerical setup) for a qualitative comparison. The wetting length, Lw and interface profiles display a good qualitative agreement for PAA 1 wt. % at We=272. [...] This is evidenced by a significant decrease in the dynamic contact angle during the receding phase, which is in good agreement with direct numeral simulations."

    Equation S7 prescribes theta(UCL) by fitting the experimental contact-angle data shown in Fig. S9; the drop to roughly 60 degrees during receding is part of the fitted input. The main-text comparison of Lw and interface profiles against those same experiments, and the conclusion that the contact-angle decrease is 'in good agreement with direct numeral simulations,' therefore verifies the simulation against its own boundary condition. The supplement's admission that the methodology 'is not employed as a predictive tool' makes this a consistency check, not an independent confirmation of the impalement/Cassie-Wenzel mechanism.

full rationale

The central experimental observation—PAA drops on Glaco rebound completely at Weber numbers up to 408 with a balloon-like ligament and no satellite splash—is self-contained high-speed imaging data and is not circular. The ballistic centroid model is a curve fit, but it is used only to estimate dissipation and does not define the rebound mechanism. However, the numerical support for the causal story is partially circular: the dynamic contact angle, including the receding-phase decrease cited as evidence of impalement, is imposed from experiment as a boundary condition (Eq. S7), so the simulated wetting-length agreement is partly reproduction of input. Moreover, the simulation is explicitly non-predictive, and the L-PTT parameters used do not match the measured steady-shear viscosity, as the authors state in Sec. E2 of the Supplement. Thus the claim that 'high elasticity prevents the ligament break up' is not independently established by the simulation; it is a tuned-model outcome. This warrants a partial circularity score of 6, though the experimental phenomenology itself remains non-circular.

Assumptions & free parameters 8 free parameters · 7 assumptions · 0 invented entities

The central experimental observation is independent of tuning, but the mechanistic explanation depends on several fitted simulation parameters and domain assumptions. The free parameters are dominated by the L-PTT/FENE-P fluid parameters and the imposed dynamic contact angle model. The key domain assumption is that impalement can be inferred from contact angle behavior and pressure scaling rather than being observed directly. No new physical entities are introduced.

free parameters (8)
  • Solvent-to-total viscosity ratio beta = 2e-4
    Set for numerical stability; deviates from the optimum steady-shear fit beta = 5e-5 and from experiments.
  • Polymer viscosity mu_p = 90 Pa.s
    Revised from 19.23 Pa.s; chosen together with lambda to roughly mimic 1% PAA while not matching the measured steady-shear viscosity.
  • Relaxation time lambda = 6.25 s
    Taken from frequency-sweep crossover for 1% PAA, whereas the steady-shear L-PTT fit gave 65.5 s; the value used in simulations is therefore a modeling choice.
  • L-PTT extensibility parameter epsilon = 0.14
    Assigned without independent measurement; controls shear-thinning versus extensional hardening in the model.
  • FENE-P extensibility limit Lmax^2 = 3600
    Set by hand in FENE-P trial simulations; not used in the final L-PTT runs but listed as a chosen parameter.
  • Dynamic contact angle plateau values theta_adv and theta_rec = 135 and 30 degrees
    Fitted to experimental contact angle versus contact-line-speed data and imposed in the numerical model.
  • Dynamic contact angle transition parameters = slope 20, offset 0.05 m/s
    Fitted to the experimental UCL-theta curve used in equation S7.
  • Navier slip length = 0.04 R0
    Chosen to regularize the moving contact line; no independent measurement provided.
assumptions (7)
  • standard math Navier-Stokes equations with a one-fluid, volume-of-fluid formulation and height-function curvature are adequate for this impact problem.
    Used throughout the simulation methodology; standard in interface-resolved CFD.
  • domain assumption The PAA solution can be represented by single-mode L-PTT or FENE-P constitutive equations.
    The authors fit these models to rheology data, but the revised parameters deviate from the measured viscosity, so the constitutive representation is approximate.
  • domain assumption Impalement onset is governed by the condition PH = PC, with PH = rho*C*v0/5 and PC from the capillary pressure formula.
    Used to estimate the microstructure spacing r at the observed onset Weber number; based on literature scalings, not directly measured here.
  • domain assumption The dynamic contact angle drop during receding is a proxy for the Cassie to Wenzel transition and liquid impalement.
    The authors infer impalement from contact angle measurements and the Teflon control, without direct imaging of liquid inside the surface texture.
  • ad hoc to paper Initial polymer stress in the simulation is zero.
    The authors acknowledge that stresses would develop if the drop were simulated from its release height; this simplification may alter early ligament dynamics.
  • domain assumption The drop centroid follows a ballistic trajectory Yc(t) = Y0 + vy0*t - 0.5*g*t^2 with negligible dissipation.
    Used to conclude that ligament length is controlled by inertia and gravity; the residual difference is interpreted as a small dissipative force.
  • domain assumption The flow is axisymmetric in the numerical simulation.
    The Basilisk simulation is two-dimensional axisymmetric, while the experimental surface is a random 3D nanostructure; this is a standard simplification but unverified here.

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Cite this review

Pith. "Pith review of Balloon regime: Drop elasticity leads to complete rebound." pith.science (2026). https://pith.science/paper/7WIJJU3M

@misc{pith2026250210081,
  author       = {Pith},
  title        = {Pith review of: Balloon regime: Drop elasticity leads to complete rebound},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7WIJJU3M}},
  note         = {Machine review of arXiv:2502.10081}
}
read the original abstract

When a viscoelastic shear-thinning drop of high elasticity hits a superhydrophobic surface, a growing tail-like filament vertically emerges from the impact spot as the contact line recedes. Notably, the ligament transitions into a balloon-like shape before detaching (Balloon regime) completely from the surface. Here, we attribute the ligament formation to the liquid impalement upon impact into the surface protrusion spacing. Our findings reveal that ligament formation can be controlled by tuning the roughness and surface wettability. We show that ligament stretching mainly depends on inertia and gravity, whereas the high elasticity prevents the ligament break up, enabling complete rebounds.

Figures

Figures reproduced from arXiv: 2502.10081 by the authors.

Figure 1
Figure 1. FIG. 1: ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3: ( [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4: Height of the droplet centroid in time for PAA [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

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Works this paper leans on

62 extracted references · 62 canonical work pages

  1. [1]

    Y. S. Joung and C. R. Buie, Nat. Commun. 6, 6083 (2015)

    work page 2015

  2. [2]

    Gilet and L

    T. Gilet and L. Bourouiba, J. R. Soc. Interface 12, 20141092 (2015)

    work page 2015

  3. [3]

    Bourouiba, Ann

    L. Bourouiba, Ann. Rev. Fluid Mech. 53, 473 (2021)

    work page 2021

  4. [4]

    C. D. Modak, A. Kumar, A. Tripathy, and P. Sen, Nat. Commun. 11, 4327 (2020)

    work page 2020

  5. [5]

    Lohse, Ann

    D. Lohse, Ann. Rev. Fluid Mech. 54, 349 (2022)

    work page 2022

  6. [6]

    H. Wu, N. Mendel, D. van den Ende, G. Zhou, and F. Mugele, Phys. Rev. Lett. 125, 078301 (2020)

    work page 2020

  7. [7]

    Shiri and J

    S. Shiri and J. C. Bird, Proc. Natl. Acad. Sci. USA 114, 6930 (2017)

    work page 2017

  8. [8]

    A. L. Yarin, Annu. Rev. Fluid Mech. 38, 159 (2006)

    work page 2006

Show all 62 references
  1. [9]

    Mohammad Karim, J

    A. Mohammad Karim, J. Appl. Phys. 133 (2023)

    2023

  2. [10]

    Fujisawa, T

    N. Fujisawa, T. Yamagata, K. Hayashi, and T. Takano, Nucl. Eng. Des. 250, 101 (2012)

    2012

  3. [11]

    Poloprudsk` y, A

    J. Poloprudsk` y, A. Chlupov´ a, I.ˇSul´ ak, T. Kruml, and S. Hloch, Materials 14, 5212 (2021)

    2021

  4. [12]

    Nastic, M

    A. Nastic, M. Vijay, A. Tieu, and B. Jodoin, Phys. Fluids 35 (2023)

    2023

  5. [13]

    Milionis, C

    A. Milionis, C. S. Sharma, R. Hopf, M. Uggowitzer, I. S. Bayer, and D. Poulikakos, Adv. Mater. Interfaces 6, 1801202 (2019)

    2019

  6. [14]

    T. Zhu, Y. Cheng, J. Huang, J. Xiong, M. Ge, J. Mao, Z. Liu, X. Dong, Z. Chen, and Y. Lai, J. Chem. Eng. 399, 125746 (2020)

    2020

  7. [15]

    Zhang, Z

    Y. Zhang, Z. Zhang, J. Yang, Y. Yue, and H. Zhang, Nanomaterials 12, 44 (2021)

    2021

  8. [16]

    H. Xu, A. Clarke, J. Rothstein, and R. Poole, App. Phys. Lett. 108 (2016)

    2016

  9. [17]

    L. Chen, Y. Wang, X. Peng, Q. Zhu, and K. Zhang, Macromolecules 51, 7817 (2018)

    2018

  10. [18]

    Bergeron, D

    V. Bergeron, D. Bonn, J. Y. Martin, and L. Vovelle, Na- ture 405, 772 (2000)

    2000

  11. [19]

    Bartolo, A

    D. Bartolo, A. Boudaoud, G. Narcy, and D. Bonn, Phys. Rev. Lett. 99, 174502 (2007). 0

    2007

  12. [20]

    P. Dhar, S. R. Mishra, and D. Samanta, Phys. Rev. Flu- ids 4, 103303 (2019)

    2019

  13. [21]

    [43–53], for a description of experimental and nu- merical methods

    See Supplemental Material at http://link.aps.org/ supplemental/10.xx/PhysRevLett.yy, which includes Refs. [43–53], for a description of experimental and nu- merical methods. Also, see Supplemental Movie 1

  14. [22]

    A. B. D. Cassie and S. Baxter, Trans. Faraday Soc. 40, 546 (1944)

    1944

  15. [23]

    R. N. Wenzel, Resistance of solid surfaces to wetting by water, Ind. Eng. Chem. Res. 28, 988 (1936)

    1936

  16. [24]

    Bartolo, F

    D. Bartolo, F. Bouamrirene, E. Verneuil, A. Buguin, P. Silberzan, and S. Moulinet, Europhys. Lett. 74, 299 (2006)

    2006

  17. [25]

    Reyssat, A

    M. Reyssat, A. P´ epin, F. Marty, Y. Chen, and D. Qu´ er´ e, Europhys. Lett. 74, 306 (2006)

    2006

  18. [26]

    T. Deng, K. K. Varanasi, M. Hsu, N. Bhate, C. Keimel, J. Stein, and M. Blohm, Appl. Phys. Lett. 94 (2009)

    2009

  19. [27]

    Del Grosso and C

    V. Del Grosso and C. Mader, Speed of sound in pure water, J. Acoust. Soc. Am. 52, 1442 (1972)

    1972

  20. [28]

    B. Zhao, X. Wang, K. Zhang, L. Chen, and X. Deng, Langmuir 33, 144 (2017)

    2017

  21. [29]

    K. R. Langley, E. Q. Li, I. U. Vakarelski, and S. T. Thoroddsen, Soft Matter 14, 7586 (2018)

    2018

  22. [30]

    X. Li, P. Bista, A. Z. Stetten, H. Bonart, M. T. Sch¨ ur, S. Hardt, F. Bodziony, H. Marschall, A. Saal, X. Deng, et al., Nat. Phys. 18, 713 (2022)

    2022

  23. [31]

    Shumaly, F

    S. Shumaly, F. Darvish, X. Li, A. Saal, C. Hinduja, W. Steffen, O. Kukharenko, H.-J. Butt, and R. Berger, Langmuir 39, 1111 (2023)

    2023

  24. [32]

    Zhang, V

    B. Zhang, V. Sanjay, S. Shi, Y. Zhao, C. Lv, X. Feng, and D. Lohse, Phys. Rev. Lett. 129, 104501 (2022)

    2022

  25. [33]

    P. Bhat, S. Appathurai, M. Harris, M. Pasquali, G. McKinley, and O. Basaran, Nat. Phys. 6, 625 (2010)

    2010

  26. [34]

    H. J. Cho, D. J. Preston, Y. Zhu, and E. N. Wang, Nat. Rev. Mater. 2, 1 (2016)

    2016

  27. [35]

    M. Liu, S. Wang, and L. Jiang, Nat. Rev. Mater. 2, 1 (2017)

    2017

  28. [36]

    C. Hao, Y. Liu, X. Chen, J. Li, M. Zhang, Y. Zhao, and Z. Wang, Small 12, 1825 (2016)

    2016

  29. [37]

    S. Ren, S. Wang, Z. Dong, J. Chen, and L. Li, Colloids Surf. A 626, 127056 (2021)

    2021

  30. [38]

    N. Z. Mehdizadeh, S. Chandra, and J. Mostaghimi, J. Fluid Mech. 510, 353 (2004)

    2004

  31. [39]

    Shah and M

    P. Shah and M. M. Driscoll, Soft Matter (2024)

    2024

  32. [40]

    M. H. Biroun, L. Haworth, H. Abdolnezhad, A. Khos- ravi, P. Agrawal, G. McHale, H. Torun, C. Semprebon, M. Jabbari, and Y.-Q. Fu, Langmuir 39, 5793 (2023)

    2023

  33. [41]

    S. M. An and S. Y. Lee, Exp. Therm. Fluid Sci. 37 (2012)

    2012

  34. [42]

    U. Sen, C. Datt, T. Segers, H. Wijshoff, J. H. Snoei- jer, M. Versluis, and D. Lohse, J. Fluid Mech. 929, A25 (2021)

    2021

  35. [43]

    Bradski, Dr

    G. Bradski, Dr. Dobb’s Journal: Software Tools for the Professional Programmer 25, 120 (2000)

    2000

  36. [44]

    W. H. Press and S. A. Teukolsky, Comput. Phys. 4, 669 (1990)

    1990

  37. [45]

    Popinet, J

    S. Popinet, J. Comput. Phys. 228, 5838 (2009)

    2009

  38. [46]

    Popinet and Collaborators, Basilisk C (Available at: http://basilisk.fr (Last accessed: 16 December, 2024), 2013–2024)

    S. Popinet and Collaborators, Basilisk C (Available at: http://basilisk.fr (Last accessed: 16 December, 2024), 2013–2024)

    2024

  39. [47]

    Popinet, Numerical models of surface tension, Ann

    S. Popinet, Numerical models of surface tension, Ann. Rev. Fluid Mech. 50, 49 (2018)

    2018

  40. [48]

    J. U. Brackbill, D. B. Kothe, and C. Zemach, J. Comp. Phys. 100, 335 (1992)

    1992

  41. [49]

    Comminal, J

    R. Comminal, J. Spangenberg, and J. H. Hattel, J. Non- Newtonian Fluid Mech. 223, 37 (2015)

    2015

  42. [50]

    Fattal and R

    R. Fattal and R. Kupferman, J. Non-Newtonian Fluid Mech. 123, 281 (2004)

    2004

  43. [51]

    M. A. Alves, F. T. Pinho, and P. J. Oliveira, J. Non- Newtonian Fluid Mech. 101, 55 (2001)

    2001

  44. [52]

    Snoeijer, A

    J. Snoeijer, A. Pandey, M. Herrada, and J. Eggers, Proc. R. Soc. (London) A 476, 20200419 (2020)

    2020

  45. [53]

    Yokoi, D

    K. Yokoi, D. Vadillo, J. Hinch, and I. Hutchings, Phys. Fluids 21 (2009). 1 SUPPLEMENT AL MA TERIAL FOR BALLOON REGIME: DROP ELASTICITY LEADS TO COMPLETE REBOUND Appendix A: Materials and experimental methods

    2009

  46. [54]

    Afterwards, substrates were sprayed three times with silica nanoparticles suspended in Isopropanol (Glaco Mirror Coat “Zero” from Soft99 Co)

    Surface preparation and contact angle measurements For the surface preparation, glass slides (1 × 75 × 40 mm 3) were first Oxygen plasma activated (5 min, 70 W). Afterwards, substrates were sprayed three times with silica nanoparticles suspended in Isopropanol (Glaco Mirror Co...

  47. [55]

    The impact process is recorded simultaneously from the side and bottom view by two high- speed cameras (Dantec dynamics, Denmark, 2500-4900 fps)

    Experimental setup Drops are dispensed by a stainless needle attached to a syringe pump (New Era Pump Systems, Inc., USA) at a pump rate of 0.8 µL/s. The impact process is recorded simultaneously from the side and bottom view by two high- speed cameras (Dantec dynamics, Denmar...

  48. [56]

    Rheology flow curves Polyacrylamide (PAA) in concentrations of 250, 1000, 2500, 5000, and 10000 ppm (0.025%, 0.1%, 0.25%, 0.5% and 1%wt.) in deionized water is used. Rheometry of the fluid samples is performed with an Anton Paar MCR 702e Space (Anton Paar, Austria), using a 50...

  49. [57]

    The 4S-SROF toolkit effectively utilizes the OpenCV library [43] to manipulate the images, such as separate the drop from its background

    Image Processing of dynamic contact angles for droplet impact For automated measurements using image processing, we adapted the 4S-SROF toolkit to match our require- ments [31]. The 4S-SROF toolkit effectively utilizes the OpenCV library [43] to manipulate the images, such as ...

  50. [58]

    The interface-resolved simulations are performed using Basilisk C [45, 46]

    Constitutive model To identify the polymeric stress effects, we perform an axi-symmetric numerical simulation of viscoelastic droplet impinging on a wetting substrate. The interface-resolved simulations are performed using Basilisk C [45, 46]. The volume of each phase of the f...

  51. [59]

    Viscoelastic liquid rheology Our aim is to replicate the experimental observation of drop impact of PAA solution and hence we consider L-PTT constitutive relationship (based on network theory for polymer dynamics) to adequate model the elastic characteristic of the material. F...

  52. [60]

    For both liquid and gas, free-slip and no-penetration boundary con- ditions are applied at the domain boundaries, while a zero-gradient condition is used for pressure

    Simulation domain and boundary conditions We consider a square domain measuring 8 R0 on each side, representing only one slice of the drop impact process considering the axisymmetric flow assumption. For both liquid and gas, free-slip and no-penetration boundary con- ditions a...

  53. [61]

    Initial condition The droplet is initialized very close to the wall (as shown in figure S8) with the impact velocity of U0 = √2gH , where H is the release height of droplet in experiments and g is the acceleration due to gravity. In this numerical investigation, we report the ...

  54. [62]

    Dynamic contact angle model The dynamics of the droplet on the surface is highly dependent on the formulation of dynamic contact angle, which is related to the wettability of the surface [53]. In this work, we aim to simulate the viscoelastic drop impact dynamics on a super-hy...

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.