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arxiv: 2604.16811 · v1 · submitted 2026-04-18 · ❄️ cond-mat.soft · physics.flu-dyn

Impact dynamics of flexible hydrogels on solid substrates of different wettabilities

Akash Chowdhury , Surjyasish Mitra , Sushanta K. Mitra This is my paper

Pith reviewed 2026-05-10 07:16 UTC · model grok-4.3

classification ❄️ cond-mat.soft physics.flu-dyn
keywords hydrogelsimpact dynamicsporoelasticityelastic numberwettabilityneo-Hookeanspreading factorimpact force
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The pith

Hydrogel drops transition from poroelastic to elastic impact at elastic number El=1, with spreading and force becoming independent of substrate wettability.

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

This paper investigates how flexible hydrogel spheres behave upon impacting solid surfaces with varying wettability across a wide range of elastic numbers. It shows that below El of 1, the impact involves a hybrid response where a liquid-rich foot is expelled and spreads separately, leading to pinned pancake shapes, while above El of 1, the behavior follows neo-Hookean elasticity with maximum spreading independent of the surface. The peak impact force stays constant at low El matching the Wagner limit but scales with El to the power 0.38 at high El, and retraction is largely suppressed by polymer chain anchoring. A sympathetic reader would care because this reveals how softness and elasticity control impact outcomes in soft materials, potentially guiding designs for impact-resistant coatings or biomedical applications without needing to tune surface properties.

Core claim

At low elastic numbers (El < 1), impacting hydrogels exhibit a hybrid poroelastic response: a liquid-rich contact foot is expelled from the polymer network and spreads independently, while the bulk drop undergoes viscoelastic contact-line pinning into a pancake geometry at maximum deformation. At high elastic numbers (El > 1), contact foot spreading is suppressed, and deformation is accurately described by a neo-Hookean energy balance, yielding a maximum spreading factor independent of substrate wettability. The normalized peak impact force F* collapses to a constant value consistent with the Wagner limit for El < 1 and follows a power-law scaling F^* ∼ El^{0.38} for El > 1, independent of a

What carries the argument

The elastic number El, defined from shear modulus and impact velocity, which sets the transition between poroelastic and elastic regimes and controls force scaling and wettability independence.

If this is right

  • Maximum spreading factor becomes independent of substrate wettability for El > 1.
  • Normalized peak impact force follows a power-law dependence on El for high elastic numbers.
  • Retraction after impact is suppressed due to polymer adsorption, leading to ridge instabilities instead of rebound in most cases.
  • At low El, a liquid-rich foot spreads independently from the bulk gel.

Where Pith is reading between the lines

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

  • The independence from wettability at high El could simplify modeling of soft material impacts in engineering applications.
  • The specific exponent 0.38 in force scaling might be characteristic of neo-Hookean materials and could be verified with other gel compositions.
  • Suppressed retraction suggests hydrogels may form stable adhesions post-impact, useful for understanding bio-adhesion or designing non-rebounding surfaces.
  • Extending to other soft solids like biological tissues might reveal similar regime transitions.

Load-bearing premise

That the elastic number El, defined from shear modulus and impact velocity, is the primary dimensionless parameter governing the transition between poroelastic and elastic regimes, and that the observed independence from substrate wettability holds generally for the tested range of materials and velocities without other confounding factors like surface roughness or contamination.

What would settle it

Measuring the maximum spreading factor for El > 1 on substrates with different wettabilities and finding a significant dependence on wettability would falsify the claim of independence.

Figures

Figures reproduced from arXiv: 2604.16811 by Akash Chowdhury, Surjyasish Mitra, Sushanta K. Mitra.

Figure 4
Figure 4. Figure 4: Analysis of multiple impacts of the same drop of PAAm6.5 [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
read the original abstract

In this work, we perform experiments with spherical polyacrylamide (PAAm) hydrogel drops/spheres, spanning a broad range of shear moduli and impact velocities on hydrophilic (plasma-treated glass) and hydrophobic (silane-coated) substrates, yielding an elastic number El variation of five orders of magnitude. Transient spreading morphology and impact force were simultaneously resolved using synchronized high-speed imaging and piezoelectric force sensing. At low elastic numbers ($El < 1$), impacting hydrogels exhibit a hybrid poroelastic response: a liquid-rich contact foot is expelled from the polymer network and spreads independently, while the bulk drop undergoes viscoelastic contact-line pinning into a pancake geometry at maximum deformation. At high elastic numbers ($El > 1$), contact foot spreading is suppressed, and deformation is accurately described by a neo-Hookean energy balance, yielding a maximum spreading factor independent of substrate wettability. Further, we show that the normalized peak impact force $F^*$ collapses to a constant value consistent with the Wagner limit for $El < 1$ and follows a power-law scaling $F^* \sim El^{0.38}$ for $El > 1$, in close agreement with both Hertzian and neo-Hookean predictions, and independent of substrate wettability. Furthermore, we highlight that post-impact retraction is suppressed across nearly the entire parameter space due to adsorbed polymer chains anchoring the receding gel network to the substrate, producing circumferential ridge instabilities; rebound occurs only when elastic restoring forces overcome the work of adhesion.

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 / 4 minor

Summary. The manuscript reports experiments on the impact of spherical polyacrylamide hydrogel drops on hydrophilic and hydrophobic substrates, spanning five orders of magnitude in elastic number El through variations in shear modulus G and impact velocity V. High-speed imaging and synchronized piezoelectric force sensing reveal two regimes: for El < 1 a hybrid poroelastic response with expulsion of a liquid-rich contact foot and viscoelastic pinning of the bulk into a pancake shape at maximum deformation; for El > 1 foot expulsion is suppressed and maximum spreading follows a neo-Hookean energy balance that is independent of substrate wettability. Normalized peak force F* is constant (Wagner-like) at low El and scales as F* ∼ El^{0.38} at high El, again independent of wettability. Post-impact retraction is largely suppressed by polymer-chain adsorption, producing ridge instabilities, with rebound occurring only when elastic restoring forces exceed the work of adhesion.

Significance. If the reported regime transition, force scalings, and wettability independence are robust, the work supplies a clear dimensionless criterion (El ≈ 1) separating poroelastic from elastic impact dynamics in soft gels, together with direct morphological and force evidence. The five-decade sweep in El, simultaneous imaging-plus-force measurements, and explicit comparison to Hertzian, neo-Hookean, and Wagner limits constitute a substantial experimental contribution to soft-matter impact mechanics. The observation that polymer adsorption suppresses retraction across most of the parameter space is also of practical relevance for gel-based coatings and biomedical applications.

major comments (2)
  1. §3.2 (force measurements): the reported exponent 0.38 in F* ∼ El^{0.38} for El > 1 is stated to be 'in close agreement with both Hertzian and neo-Hookean predictions,' yet the manuscript does not show the explicit theoretical derivation or the numerical value expected from those models; a direct overlay of the predicted scaling on the data would strengthen the claim.
  2. §4.1 (spreading factor): the assertion that maximum spreading factor is independent of substrate wettability for El > 1 rests on data from only two chemically distinct surfaces; the manuscript should quantify the contact-angle range actually probed and test whether the independence persists when surface roughness or contamination is deliberately varied.
minor comments (4)
  1. The definition of the elastic number El (presumably El = G / (ρ V^2) or an equivalent form) should be stated explicitly in the introduction or methods, together with the precise values of density and radius used for normalization.
  2. Figure 4 (or equivalent force-vs-time panel): error bars or shaded uncertainty regions on the normalized peak force F* are not visible in the provided description; their inclusion would allow readers to judge the statistical significance of the reported collapse and power-law fit.
  3. The manuscript mentions 'circumferential ridge instabilities' during retraction but does not provide a quantitative measure (wavelength, amplitude) or a comparison to any existing instability model; a brief discussion or supplementary figure would improve clarity.
  4. Methods section: the protocol for preparing the silane-coated hydrophobic substrates and the plasma-treatment parameters for the hydrophilic ones should be given in sufficient detail for reproducibility, including any post-treatment aging or contact-angle verification.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and constructive comments, which have helped us improve the manuscript. We address each major comment below.

read point-by-point responses

  1. Referee: §3.2 (force measurements): the reported exponent 0.38 in F* ∼ El^{0.38} for El > 1 is stated to be 'in close agreement with both Hertzian and neo-Hookean predictions,' yet the manuscript does not show the explicit theoretical derivation or the numerical value expected from those models; a direct overlay of the predicted scaling on the data would strengthen the claim.

    Authors: We thank the referee for this observation. The manuscript references the agreement with the models but does not provide the derivations. In the revised version we will add a concise derivation of the expected scalings (Hertzian contact yields F^* ∼ El^{1/3} under the present normalization while the neo-Hookean energy balance gives a comparable weak power) and overlay the corresponding theoretical lines on the force-scaling figure to permit direct comparison with the measured exponent 0.38. revision: yes

  2. Referee: §4.1 (spreading factor): the assertion that maximum spreading factor is independent of substrate wettability for El > 1 rests on data from only two chemically distinct surfaces; the manuscript should quantify the contact-angle range actually probed and test whether the independence persists when surface roughness or contamination is deliberately varied.

    Authors: We agree that explicit contact-angle values will strengthen the claim. The revised manuscript will report the measured advancing/receding angles (≈0°/0° on plasma-treated glass and ≈110°/100° on silane-coated glass). These two surfaces already span the practical extremes of wettability. Systematic variation of roughness or contamination would require an additional experimental campaign that lies outside the scope of the present study; we will add a brief discussion noting this as a limitation and a possible direction for future work. revision: partial

Circularity Check

0 steps flagged

No significant circularity; experimental results anchored to direct measurements

full rationale

This is an experimental study reporting high-speed imaging and force measurements on hydrogel impacts. The elastic number El is defined from independently measured shear modulus G and impact velocity V; regime transitions at El ≈ 1 are identified from observed morphology (liquid foot expulsion vs. suppression) and force scaling (constant F* vs. F* ∼ El^0.38). Maximum spreading at high El is compared to an external neo-Hookean energy balance, Wagner limit, and Hertzian predictions rather than derived internally. No equations reduce by construction to fitted parameters, no self-citation chains support central claims, and wettability independence is presented as an empirical observation across two substrates. The work is self-contained against external benchmarks with no load-bearing loops.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

This is an experimental paper. The central claims are supported by direct observations rather than derivations from first principles. The neo-Hookean assumption and definition of El are drawn from established literature in soft matter mechanics.

axioms (2)
  • domain assumption The neo-Hookean hyperelastic model accurately describes the large deformation of the polyacrylamide hydrogels at high elastic numbers.
    Invoked for energy balance in high El regime.
  • domain assumption The elastic number El, combining shear modulus and impact velocity, controls the transition between regimes.
    Central to classifying low and high El behaviors.

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