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REVIEW 4 major objections 5 minor 40 references

Inelastic spreading of viscoelastic drops

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Polymer elasticity does not change how far an impacting drop spreads, because the elastic energy stored during spreading is negligible compared with viscous dissipation.

desk verdict A careful experimental study with a plausible energetic criterion, but the missing supplementary derivation and dataset placeholder make the central collapse impossible to audit. read the letter →

arxiv 2608.10851 v1 pith:XMBVTPHF submitted 2026-08-11 physics.flu-dyn cond-mat.soft

Mete Abbot , Thijs Varkevisser , Manglesh Singh , Antoine Gaillard , Devranjan Samanta , Daniel Bonn This is my paper · ORCID
classification physics.flu-dyncond-mat.soft
keywords DropimpactViscoelasticdropsBogerfluidsMaximumspreadingratioElasticenergycriterionPolymeradditivesShearthinning
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 sets out to resolve why viscoelastic drops spread exactly as far as Newtonian ones even when classical dimensionless numbers ($Wi$ and $De$) predict elastic, solid-like resistance during impact. The authors' answer is that elasticity is energetically irrelevant in the spreading phase: the stored elastic energy is much smaller than the viscous dissipation for all conditions they could reach. They test this with Boger fluids (constant-viscosity, highly elastic PEO and PAAM solutions), which isolate elasticity from shear-thinning, and find the maximum spreading ratio collapses onto the Newtonian master curve up to 1000 ppm. The paper also derives a dimensionless criterion $\Gamma$ that bounds when elastic resistance could become observable, and argues that shear-thinning, not elasticity, explains the extra spreading of concentrated polymer drops. If correct, this settles the debate in favor of inertia, capillarity, and viscosity controlling maximum spreading, and shows that $Wi$ and $De$ expectations do not apply to this phase of impact.

What carries the argument

The load-bearing object is the dimensionless elastic-to-viscous damping ratio $\Gamma$ (Eq. 2), derived from an energy balance in which the impact kinetic energy is split into surface energy, viscous dissipation, and elastic storage. The elastic storage is deliberately overestimated by treating the drop as a Hookean solid in Hertzian contact, giving an elastic term scaling as $G \beta_{\max}^5$; any weaker polymer-constitutive model (Neo-Hookean, Oldroyd-B, FENE-P) would give even less resistance. The kinematic closure $D_{\max} = t_s V_s$ and the leading-order average-velocity closure $V \approx \sqrt{E}$ turn the balance into a closed expression $\beta_{\max}(\Gamma)$, with $\Gamma = \frac{8}{5\pi} \frac{G D_0}{\mu_i V_0 \sqrt{E}}$. The paper also introduces the impact Carreau number $Cu_i = \dot{\gamma}_s / \dot{\gamma}^*_{\mathrm{rheo}}$ to separate Newtonian-adherent Boger fluids from shear-thinning concentrated solutions.

What would settle it

The predicted elastic regime is currently untested: prepare a constant-viscosity elastic fluid with $\Gamma \gtrsim 1$ by the paper's own formula (for example a low-viscosity Boger fluid with $G \approx 2 \mu_i V_0 / D_0$), impact it, and measure $\beta_{\max}$. The paper predicts a measurable reduction below the Newtonian baseline in that regime; if none appears, the criterion fails.

Watch

Extended reading notes

Core claim

The central discovery is that the maximum spreading ratio $\beta_{\max} = D_{\max}/D_0$ of Boger-fluid drops (PEO and PAAM, up to 1000 ppm) is indistinguishable from the Newtonian baseline for the same impact parameters, with deviations below the typical 10% scatter. The authors formulate an energy balance with inertial, capillary, viscous, and elastic terms, and define $\Gamma$ as the ratio of elastic to viscous energy, $\Gamma = \frac{8}{5\pi} \frac{G D_0}{\mu_i V_0 \sqrt{E}}$. Evaluating $\Gamma$ with two independent relaxation-time estimates (Zimm lower bound and CaBER upper bound) gives $\Gamma \ll 1$ for every impact tested, so the elastic term is too small to shift the spreading. They conclude that Weissenberg and Deborah numbers, while large, do not predict spreading because they compare microscopic polymer relaxation to the deformation rate rather than the macroscopic energy budget. The observed enhanced spreading of concentrated shear-thinning fluids is attributed to viscosity reduction, not elastic resistance, and concentration actually lowers $G/\mu_i$ and $\Gamma$.

Load-bearing premise

Everything rests on the Newtonian baseline from the authors' companion model being accurate for the tested conditions; if that baseline is off by more than the experimental scatter, an elasticity-induced change in spreading could be hidden inside the roughly 10% noise.

Editorial extensions

If this is right

  • For Boger-fluid drops up to 1000 ppm, the maximum spreading ratio falls on the pure Newtonian master curve within experimental scatter, so adding elasticity without changing viscosity does not alter how far a drop spreads.
  • The dimensionless criterion $\Gamma$, not $Wi$ or $De$, sets the detectability of elastic resistance: only when $\Gamma \approx 1$ should a measurable (greater than 10%) reduction below the Newtonian baseline appear.
  • The material threshold for elastic resistance is approximately $G \approx 2 \mu_i V_0 / D_0$, which impact conditions do not reach because the viscous stress at impact shear rates overwhelms the polymer network's elastic modulus.
  • In concentrated polymer drops, the extra spreading comes from shear thinning, not elasticity, and polymer concentration lowers $G/\mu_i$ and therefore $\Gamma$, making elastic resistance even less relevant.

Reading between the lines

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

  • The authors do not test the predicted elastic regime, since all data sit at $\Gamma \ll 1$; a deliberate attempt to reach $\Gamma \approx 1$ (for instance a low-viscosity solvent with a high-modulus polymer) would provide the sharpest test of the criterion.
  • The same energy-budget logic could be applied to other rapid deformations where $Wi > 1$ is used to infer elasticity, such as splashing thresholds or atomization, replacing relaxation-time criteria with an elastic-to-viscous energy ratio.
  • If the Newtonian baseline's kinematic closures fail at the extremes of the tested Weber and Ohnesorge ranges, part of the claimed collapse could be masking an elasticity effect inside the noise; direct measurements of spreading time and average velocity would reveal it.
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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

4 major / 5 minor

Summary. The paper reports an experimental study of the maximum spreading ratio of viscoelastic drops, using Boger fluids (PEO and PAAM in Newtonian solvents) to decouple elasticity from shear-thinning over a wide parameter range (We = 155–763, Re = 18–11,500, Oh = 0.002–1). The authors derive a dimensionless elasto-viscocapillary energy balance, introduce the ratio Gamma of elastic to viscous energy (Eq. 2), and show that Gamma < 1 for all tested conditions, concluding that elasticity is energetically negligible during spreading and that the maximum spreading ratio is identical to the Newtonian prediction, contrary to the expectations from Wi and De. The central evidence is the collapse of experimental data onto a Newtonian master curve in Fig. 2b, together with the theoretical sensitivity analysis in Fig. 3a.

Significance. If the central claim holds, the paper resolves a long-standing paradox by showing that polymer elasticity does not resist the expansion phase of drop impact, so maximum spreading remains governed by inertia, capillarity, and viscous dissipation alone. The study has clear strengths: the use of constant-viscosity Boger fluids is the right experimental strategy to separate elasticity from shear thinning; the parameter range is broad; the Hertzian-model choice is explicitly framed as a conservative upper bound; and the Gamma criterion is a parameter-free, falsifiable prediction rather than a fit to the observed spreading data. However, the verification is currently incomplete: the derivation of Eq. (3), the rheological characterization, and the dataset are all deferred to a Supplementary Material that is not included, and the Newtonian baseline is taken from the authors' own prior model. These gaps are significant because the null result is defined as a collapse onto that baseline.

major comments (4)
  1. [Eq. (3) and Fig. 2b] The central comparison in Fig. 2b rests on Eq. (3), but the derivation of Eq. (3)—including the kinematic closure Dmax = ts Vs, the average-velocity closure V ≈ sqrt(E), and the harmonic-mean interpolation—is stated to be in the Supplementary Material, which is not included in this preprint. The data-availability link is also the placeholder "XXX". Without the derivation and the dataset, the claimed collapse onto the Newtonian master curve cannot be independently checked. Please provide the full derivation and make the data available at a permanent repository before the central claim can be assessed.
  2. [Newtonian baseline, ref. [4]] Eq. (3) with Γ = 0 recovers the Newtonian baseline βmax(Γ = 0) of ref. [4], which is the authors' own prior model; neither the derivation nor the raw dataset of that baseline is shown here. The statement that "this collapse further validates the Newtonian baseline in [4]" uses the same comparison that is supposed to establish the null result. If the baseline is inaccurate for the tested range, elasticity-induced deviations of order the quoted 10% scatter could be hidden. Please provide an independent validation of the baseline, for example Newtonian solvent data measured with the same setup, or the complete baseline dataset of ref. [4].
  3. [Boger-fluid characterization, near Eq. (2)] The decoupling from shear thinning assumes µi = µ0 for the Boger and quasi-Boger fluids at impact shear rates much greater than 1000 s^-1. The rheological evidence for constant viscosity in this range is said to be in the Supplementary Material, which is absent. If these fluids shear-thin at impact rates, enhanced spreading from thinning could offset elastic resistance and mimic the null result. Please provide high-shear rheometry for all fluids, or an explicit estimate of µi at the characteristic impact shear rate γdot_s defined in the text.
  4. [Fig. 3a and experimental scatter] The detectability argument in Fig. 3a defines the observable elastic regime as deviations exceeding approximately 10% scatter, and the text states that the ratio of experimental to theoretical spreading yields an average deviation below 10%. However, no error analysis, per-condition statistics, or table of βmax values is presented in the manuscript. Since the 10% noise floor is a load-bearing threshold for the conclusion that Γ ≪ 1 produces no observable effect, please report the actual deviations and their uncertainties.
minor comments (5)
  1. [Fig. 1 caption] The word "captublack" in the Fig. 1 caption should be "captured".
  2. [Data Availability] The data availability statement contains the placeholder "link XXX"; a working permanent repository link is needed.
  3. [Main text, first paragraph of Section 2] There are missing spaces in phrases such as "diffusionandadsorptiontimescalesaresignificantly"; please correct the line-breaking artifacts throughout.
  4. [Fig. 2b axis label] The axis label "Eq. [4]" is ambiguous; it should refer to Eq. (3) of this paper or explicitly to the reference, not to a citation number.
  5. [Fluid classification] The term "quasi-Boger fluids" is used in Fig. 2b and Fig. 3 but is not defined in the main text; please provide a definition or a criterion for this category.

Circularity Check

1 steps flagged · score 2.0 of 10

Minor self-citation burden: the Newtonian reference curve is the authors' own prior model (Eq. 3 with Γ=0, ref. [4]), but the experimental collapse provides independent support; no fitted-to-spreading parameter is involved.

  1. self citation load bearing [Section 'To evaluate deviations caused by fluid elasticity...' and Eq. (3), Fig. 2b]
    "To evaluate deviations caused by fluid elasticity, we must establish a purely Newtonian baseline. We follow a similar energy balance presented in [4]. ... As Γ→0, the equation recovers the purely Newtonian spreading ratio βmax(Γ = 0) limit [4]. ... This collapse further validates the Newtonian baseline in [4]."

    The reference curve used to establish the central claim that elastic properties do not alter maximum spreading is not an independent empirical Newtonian master curve presented in this paper; it is the Γ→0 limit of the authors' own prior model, ref. [4] (Abbot and Bonn, arXiv:2605.11797). The paper explicitly says it follows 'a similar energy balance presented in [4]' and that Eq. (3) recovers the Newtonian baseline from [4]. The key closures of that baseline (Dmax≡tsVs and V≈√E) are stated but their derivation is not shown here, being relegated to a missing Supplementary Material. The paper then uses the collapse of its own new data to 'further validate' this same self-cited baseline.

full rationale

The central null result is primarily an experimental observation: Boger-fluid and quasi-Boger-fluid drops up to 1000 ppm collapse onto the Newtonian baseline in Fig. 2b, with deviations below the quoted ~10% scatter. Because no parameter of Eq. (3) is fitted to the observed spreading values (We, Re, Oh, G, and τ are all independently measured), the collapse is genuine evidence and the paper does not commit a fitted-input-called-prediction circularity. The Γ-criterion is model-based, but it is a conservative upper bound (Hertzian β^5 scaling) and is not defined in terms of the observed βmax, so it is not self-definitional in the strict sense. The only notable circularity-adjacent burden is the reference curve itself: the Newtonian baseline βmax(Γ=0) is taken from the authors' own prior model (ref. [4]), with the kinematic closure Dmax≡tsVs and average-velocity closure V≈√E relegated to a missing Supplementary Material. The paper then uses the collapse of its own data to 'validate' that self-cited baseline. This makes the comparison dependent on an unshown, self-cited derivation, but the experimental data provide independent content, so the severity is low (score 2, not a forced circle). Missing data link and Supplementary Material are reproducibility concerns rather than circularity.

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

The ledger is small: the central experiment does not fit any parameter, but the claim rests on several modeling assumptions that are not fully demonstrated in the preprint, particularly the Newtonian baseline from ref. 4 and the Hertzian elastic upper bound. No new physical entities are introduced; Gamma is a derived dimensionless group rather than a new force or particle.

assumptions (7)
  • domain assumption The Newtonian maximum-spreading baseline beta_max(Gamma=0) from ref. 4 is accurate for the tested fluids and substrates.
    Figure 2b treats this baseline as the reference; deviations from it are attributed to elasticity or thinning. The baseline's derivation is not included in the preprint.
  • domain assumption Elastic energy storage during spreading is bounded by a linear elastic Hertzian contact model with scaling of order G beta^5.
    The text states this choice is a conservative upper bound; if actual polymer coil-stretch energy exceeded this bound, Gamma could be underestimated.
  • domain assumption Surface tension during the spreading phase equals the pure-solvent plateau value (about 72 mN/m) because polymer adsorption and diffusion timescales exceed impact timescales.
    Stated in the discussion of dynamic surface tension and supported only by supplementary dynamic bubble tensiometry, which is not present.
  • domain assumption The Boger fluids have essentially constant viscosity at impact shear rates, so mu_i = mu_0 and shear thinning is absent.
    This is the experimental isolation strategy; for quasi-Boger and concentrated solutions the assumption weakens, and the paper relies on the Carreau number Cui to separate regimes.
  • domain assumption The kinematic closure Dmax = ts Vs and the leading-order average velocity closure V approximately sqrt(E) are valid.
    Used to close the energy balance and derive Eq. 3; justification is deferred to the supplementary material.
  • domain assumption The characteristic impact shear rate is gamma_dot_s approximately (3 V0 / 2 D0) V beta_max^2, from volume conservation with h_min approximately 2 D0^3 / (3 Dmax^2).
    This estimate is used to compute Wi and Gamma; it assumes a flat film geometry with a specific minimum film thickness.
  • domain assumption Zimm relaxation times give a lower bound on tau (and therefore an upper bound on G), while CaBER relaxation times give an upper bound on tau (and therefore a lower bound on G).
    Used in Figure 3 to bracket Gamma; this is standard dilute-solution rheology but depends on the polymer being dilute and CaBER measuring the relevant mode.

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Pith. "Pith review of Inelastic spreading of viscoelastic drops." pith.science (2026). https://pith.science/paper/XMBVTPHF

@misc{pith2026260810851,
  author       = {Pith},
  title        = {Pith review of: Inelastic spreading of viscoelastic drops},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XMBVTPHF}},
  note         = {Machine review of arXiv:2608.10851}
}
abstract

When a liquid drop impacts a solid surface, rebound and splashing are known to be suppressed by additives that induce elastic effects; however, the influence of elasticity on the maximum spreading radius remains debated. The difficulty lies in isolating elastic resistance from the enhanced spreading caused by viscous shear thinning. Here, we experimentally decouple these effects by investigating Boger fluid drops (constant-viscosity solutions with high elasticity) of polyethylene oxide (PEO) and polyacrylamide (PAAM). We demonstrate that elastic properties do not alter the maximum spreading ratio, even at high concentrations up to 1000 ppm. We formulate an energy balance that accounts for the inertial, capillary, viscous, and elastic contributions, and yields a dimensionless criterion ($\Gamma$) that estimates the degree of elastic effects. We show that $\Gamma \ll 1$ for all impact conditions tested, demonstrating that elastic effects are energetically negligible during droplet spreading, opposite to what Weissenberg and Deborah numbers would predict.

Figures

Figures reproduced from arXiv: 2608.10851 by the authors.

Figure 1
Figure 1. Replication of Bergeron et al. experiments demonstrating the paradox. High-speed image captublack sequences at 4000 fps of water (top) and a highly elastic dilute polymer solution (PEO 100 ppm, bottom) impacting a parafilm coated substrate (θ = 110◦ ± 5 ◦ ) at identical conditions (V0 = 2 m/s, D0 ≈ 2.8 mm, We ≈ 155 and Oh ≈ 0.002). tension driving the retraction [16, 17]. Consequently, the critical threshold for sup… view at source ↗
Figure 2
Figure 2. Classical rheological prediction versus empirical Newtonian collapse. (a) Rheological dimen￾sionless numbers based on CaBER relaxation times predict the dominance of elasticity (Wi > 1 and De > 1). (b) Normalized Newtonian maximum spreading ratio βmax(Γ = 0)/ √ We E evaluated against the viscous damping pa￾rameter (ΛνE 2 ). Each data point represents the average of at least three independent impact events. Legend ap… view at source ↗
Figure 3
Figure 3. Evaluation of the elastic criterion Γ. (a) Sensitivity of the relative spreading ratio βmax(Γ)/βmax(0) evaluated against the energetic criterion Γ. Shaded region shows typical scatter of drop impact experiments of around 10 %. (b, c) Evaluation of the experimental Γ criterion against the characteristic impact shear rate γ˙s ≈ (3V0/2D0)V β2 max, where Γ is calculated using (b) theoretical Zimm entropic relaxation tim… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Increasing elastic modulus G (solid symbols, right axis) and its decreasing elastic modulus to zero-shear viscosity G/µ0 (open symbols, left axis) as a function of PEO-4M polymer concentration in water. c is the polymer mass concentration, and c ∗ = 0.295 kg/m3 (equiva…

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