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arxiv: 1907.08067 · v1 · pith:ECUSAS22new · submitted 2019-07-18 · ❄️ cond-mat.soft

Spreading on viscoelastic solids: Are contact angles selected by Neumann's law?

M. van Gorcum , S. Karpitschka , B. Andreotti , J.H. Snoeijer This is my paper

Pith reviewed 2026-05-24 19:24 UTC · model grok-4.3

classification ❄️ cond-mat.soft
keywords soft wettingviscoelastic substrateswetting ridgeNeumann's lawcontact angleShuttleworth effectspreading dynamicscontact line motion
0
0 comments X

The pith

The wetting ridge rotates to match the dynamic liquid contact angle exactly, proving Neumann's law applies during spreading on soft solids.

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

This paper examines the spreading of liquid drops on viscoelastic soft substrates, which is slowed by strong dissipation in the solid. Direct experiments visualize the dynamic wetting ridge and measure the liquid contact angle. The ridge is found to rotate in exact agreement with the dynamic contact angle. This shows that the ridge is governed by Neumann's law even as the contact line moves. The authors develop a theory that includes the Shuttleworth effect from surface strain to explain the observations.

Core claim

The wetting ridge exhibits a rotation that follows exactly the dynamic liquid contact angle, proving that the wetting ridge is still governed by Neumann's law despite contact line motion. The theory incorporating surface strain confirms the Neumann balance through boundary conditions and dissipation analysis.

What carries the argument

The rotation of the dynamic wetting ridge, which enforces the Neumann balance of surface tensions at the three-phase contact line.

If this is right

  • The Neumann law can be used to describe the geometry of moving wetting ridges on soft solids.
  • Surface tension of the substrate varies with strain during spreading.
  • The new theory provides a framework for predicting contact line dynamics including viscoelastic effects and the Shuttleworth effect.
  • Dissipation in the solid does not invalidate the Neumann condition at the contact line.

Where Pith is reading between the lines

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

  • If the ridge rotation is general, it could simplify models of soft wetting in applications like coatings or biomedical devices.
  • Similar effects might be testable in other systems with moving three-phase lines on deformable surfaces.
  • Accounting for variable surface tension could resolve discrepancies in previous soft wetting experiments.

Load-bearing premise

The measured rotation of the wetting ridge results solely from the Neumann force balance at the contact line and is not an artifact of other viscoelastic deformations or surface effects.

What would settle it

High-resolution imaging showing that the ridge rotation angle differs from the independently measured dynamic contact angle in a regime where strain effects are controlled would falsify the central claim.

Figures

Figures reproduced from arXiv: 1907.08067 by B. Andreotti, J.H. Snoeijer, M. van Gorcum, S. Karpitschka.

Figure 1
Figure 1. Figure 1: FIG. 1. (ab) Soft wetting at equilibrium. (a) Zoom of the wetting ridge near the contact line on the scale of the elastocapillary [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) A rectangular cuvette filled with transparent gel with a cylindrical cavity is observed perpendicular to the sidewall [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Space-time diagrams for slow dynamics. (a) Wetting ridge moving at a constant velocity, for [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Experimental ridge shapes, for gradually increasing contact line speeds (0, 6 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Space-time diagrams for rapid dynamics, leading to stick-slip motion. (a) Wetting ridge moving at high velocity, with [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Equality of the dynamic contact angle of the liquid and the ridge rotation angle. The main panel reports data on the [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Solid opening angle [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Curvilinear coordinate [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Typical static and dynamic solutions with Shuttleworth effect, on an infinitely thick substrate. Red curves are [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Dependence of the liquid angle ∆ [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Dependence of the solid angle ∆ [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Measured PDMS gel rheology. The diamonds show the storage modulus, the circles show the loss modulus. The fit [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗
read the original abstract

The spreading of liquid drops on soft substrates is extremely slow, owing to strong viscoelastic dissipation inside the solid. A detailed understanding of the spreading dynamics has remained elusive, partly owing to the difficulty in quantifying the strong viscoelastic deformations below the contact line that determine the shape of moving wetting ridges. Here we present direct experimental visualisations of the dynamic wetting ridge, complemented with measurements of the liquid contact angle. It is observed that the wetting ridge exhibits a rotation that follows exactly the dynamic liquid contact angle -- as was previously hypothesized [Karpitschka \emph{et al.} Nature Communications \textbf{6}, 7891 (2015)]. This experimentally proves that, despite the contact line motion, the wetting ridge is still governed by Neumann's law. Furthermore, our experiments suggest that moving contact lines lead to a variable surface tension of the substrate. We therefore set up a new theory that incorporates the influence of surface strain, for the first time including the so-called Shuttleworth effect into the dynamical theory for soft wetting. It includes a detailed analysis of the boundary conditions at the contact line, complemented by a dissipation analysis, which shows, again, the validity of Neumann's balance.

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 reports direct experimental visualizations of dynamic wetting ridges during liquid drop spreading on viscoelastic solids. It observes that the ridge rotates exactly in accordance with the dynamic liquid contact angle, which is taken as proof that Neumann's law continues to govern the ridge geometry despite contact-line motion. A new theoretical framework is introduced that incorporates the Shuttleworth effect (strain-dependent substrate surface tension) into the dynamical description, together with an analysis of contact-line boundary conditions and viscoelastic dissipation that is said to confirm the Neumann balance.

Significance. If the central experimental observation is robust, the work supplies direct evidence resolving a long-standing question in soft wetting about whether local three-phase force balance survives at moving contact lines. The explicit inclusion of the Shuttleworth effect in a dynamical model, combined with the dissipation analysis, represents a concrete advance over prior hypotheses. These elements would strengthen predictive modeling of slow spreading on soft substrates.

major comments (2)
  1. [Experimental results] Experimental visualizations and contact-angle measurements: the manuscript states that the ridge rotation 'follows exactly' the dynamic liquid contact angle, yet no quantitative error bars, statistical measures of agreement, or controls for alternative mechanisms (strain-dependent surface tension or distributed viscoelastic relaxation) are reported. This leaves open whether the observed rotation isolates the local Neumann vector balance or could arise from the distributed effects already included in the theory.
  2. [Theory] Theory section on boundary conditions and Shuttleworth effect: the model introduces strain-dependent surface tension, which modifies the effective tensions entering the Neumann balance. The text does not derive or show explicitly how the modified tensions still produce a rotation that matches the liquid angle solely through the standard three-vector closure rather than through the additional strain or dissipation terms; without this step the claim that Neumann's law is validated remains circular with the model's own constitutive assumptions.
minor comments (2)
  1. Notation for surface strains and tensions is introduced without a dedicated table or consistent symbol list, making it difficult to track which quantities are strain-dependent versus constant across the boundary-condition analysis.
  2. [Dissipation analysis] The dissipation analysis is summarized but lacks an explicit comparison (e.g., an equation or plot) between the full model and a reduced model that omits the local Neumann condition, which would help readers assess its independent contribution.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and positive evaluation of the significance of our work. We address each of the major comments below.

read point-by-point responses

  1. Referee: [Experimental results] Experimental visualizations and contact-angle measurements: the manuscript states that the ridge rotation 'follows exactly' the dynamic liquid contact angle, yet no quantitative error bars, statistical measures of agreement, or controls for alternative mechanisms (strain-dependent surface tension or distributed viscoelastic relaxation) are reported. This leaves open whether the observed rotation isolates the local Neumann vector balance or could arise from the distributed effects already included in the theory.

    Authors: We agree that the experimental section would benefit from quantitative measures. In the revised manuscript, we will include error bars derived from multiple independent measurements of the ridge rotation and contact angles to quantify the agreement. Concerning controls for alternative mechanisms, the theory section already incorporates the strain-dependent surface tension via the Shuttleworth effect and analyzes the dissipation, showing that the local balance is necessary for the exact matching observed. Distributed effects alone would not lead to the precise rotation with the liquid angle without the Neumann condition. We will add a brief discussion clarifying this distinction. revision: yes

  2. Referee: [Theory] Theory section on boundary conditions and Shuttleworth effect: the model introduces strain-dependent surface tension, which modifies the effective tensions entering the Neumann balance. The text does not derive or show explicitly how the modified tensions still produce a rotation that matches the liquid angle solely through the standard three-vector closure rather than through the additional strain or dissipation terms; without this step the claim that Neumann's law is validated remains circular with the model's own constitutive assumptions.

    Authors: We acknowledge that an explicit derivation of this point would improve clarity. Although the manuscript includes the boundary conditions and dissipation analysis leading to the validity of Neumann's balance, we will revise the theory section to provide a step-by-step derivation demonstrating how the strain-modified tensions enforce the three-vector closure independently of the dissipation terms. This will address any potential concern of circularity by separating the geometric balance from the dynamical contributions. revision: yes

Circularity Check

1 steps flagged

Experimental ridge rotation observation provides independent data; minor self-citation to co-author hypothesis does not reduce central claim

specific steps
  1. self citation load bearing [Abstract]
    "It is observed that the wetting ridge exhibits a rotation that follows exactly the dynamic liquid contact angle -- as was previously hypothesized [Karpitschka et al. Nature Communications 6, 7891 (2015)]. This experimentally proves that, despite the contact line motion, the wetting ridge is still governed by Neumann's law."

    The claim that the observed rotation 'proves' Neumann's law at the moving contact line is justified by matching a behavior hypothesized in prior work by an overlapping author; while the experiment supplies new data, the load-bearing interpretive step that equates the geometric match specifically to the standard three-tension Neumann balance (rather than distributed strain or viscoelastic effects) imports its justification from the self-citation.

full rationale

The paper's strongest claim rests on direct experimental visualizations showing that wetting ridge rotation matches the dynamic liquid contact angle. This match is interpreted as proving Neumann's law governs the ridge despite motion, referencing a prior hypothesis by co-author Karpitschka. However, the new data and the introduced theory (incorporating Shuttleworth effect and viscoelastic dissipation) do not reduce the reported observation or boundary-condition analysis to a fitted parameter or self-defined input by construction. The self-citation is present but not load-bearing for the experimental result itself, which remains falsifiable against external benchmarks. No equations or derivations in the provided text exhibit self-definitional closure or renaming of known results.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the assumption that the imaged ridge shape is set by local force balance at the contact line and that surface tension can be treated as strain-dependent; no free parameters or invented entities are stated in the abstract.

axioms (1)
  • domain assumption Neumann's law applies at the moving contact line on a viscoelastic solid
    Invoked to interpret the observed ridge rotation as proof of the balance.

pith-pipeline@v0.9.0 · 5750 in / 1129 out tokens · 18489 ms · 2026-05-24T19:24:45.199990+00:00 · methodology

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