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arxiv: 2405.20651 · v1 · submitted 2024-05-31 · ❄️ cond-mat.soft · cond-mat.stat-mech

Active Young-Dupr\'e Equation: How Self-organized Currents Stabilize Partial Wetting

Yongfeng Zhao , Ruben Zakine , Adrian Daerr , Yariv Kafri , Julien Tailleur , Fr\'ed\'eric van Wijland This is my paper

Pith reviewed 2026-05-24 00:57 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.stat-mech
keywords active wettingYoung-Dupré equationmotility-induced phase separationsurface tensionself-organized currentspartial wettingactive particlesinterface stability
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The pith

A mechanical definition of surface tension produces an active Young-Dupré equation in which drag from self-organized currents stabilizes partial wetting.

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

The paper builds an active Young-Dupré equation from a microscopic mechanical definition of surface tension extracted from force balance in systems of active particles with pairwise forces. It shows that observed partial wetting arises through a feedback loop: interfaces break symmetry, steady currents appear, and the currents exert a drag force that closes the macroscopic balance at the contact line. This same mechanism selects the sizes and shapes of droplets and drives expulsion of partially immersed objects from the dense phase when liquid-gas surface tensions are negative during motility-induced phase separation.

Core claim

The interfaces are stabilized by a drag force due to the emergence of steady currents, which are themselves a by-product of the symmetry breaking induced by the interfaces; the active Young-Dupré equation therefore accounts for partial wetting without requiring a simple balance of the surface tensions at play.

What carries the argument

The drag force from steady currents generated by interface-induced symmetry breaking, inserted into the active Young-Dupré equation derived from microscopic mechanical surface tension.

If this is right

  • Steady interfaces emerge from a complex feedback mechanism rather than a simple surface-tension balance.
  • The currents select the sizes and shapes of adsorbed droplets and thereby break the scale-free character of the equilibrium problem.
  • Partially immersed objects are expelled from the liquid phase when liquid-gas surface tensions are negative in motility-induced phase separation.
  • The construction supplies a starting point for a theory of wetting that applies to active systems such as bacterial colonies and tissue growth.

Where Pith is reading between the lines

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

  • The current-based stabilization may extend to active interfaces formed by other interaction rules or in confined geometries.
  • Mapping the spatial structure of currents near contact lines in colloidal or bacterial experiments would provide a direct test of the drag term.
  • Size selection by the same currents could be used to control the length scale of patterns that form during active wetting.

Load-bearing premise

A mechanical definition of surface tension extracted from the microscopic force balance in an active system remains well-defined and sufficient to close the macroscopic force balance at the contact line without additional non-local or history-dependent contributions from the active currents.

What would settle it

A simulation or experiment in which the measured contact angle deviates from the prediction of the active Young-Dupré equation once the drag force from the observed currents is subtracted.

Figures

Figures reproduced from arXiv: 2405.20651 by Adrian Daerr, Fr\'ed\'eric van Wijland, Julien Tailleur, Ruben Zakine, Yariv Kafri, Yongfeng Zhao.

Figure 1
Figure 1. Figure 1: a) In equilibrium, when a macroscopic droplet wets a solid surface, the contact angle φ satisfies the Young-Dupre equation (1). ´ b) Snapshot of a phase-separating passive system partially wetting of a solid confining wall. At the particle scale, the liquid-gas interface is an elusive object. Nevertheless, the Young-Dupre equation endows this interface with mechanical properties at the ´ macroscopic scale:… view at source ↗
Figure 2
Figure 2. Figure 2: (a) Snapshots of passive (top) and active (bottom) droplets wetting solid surfaces, show￾ing the apparent similarities between the two cases. Throughout the article, grey dots indicate the particle positions. (b) Wilhelmy-plate setup. A circular plate (red) is first pulled out of a liquid phase and then held fixed while the system relaxes. In the steady state, the liquid bulk is connected to the plate thro… view at source ↗
Figure 3
Figure 3. Figure 3: (a) The setup used to measure the liquid-gas surface tension γLG. (b) The measurements of γLG from the wall force through Eq. (11) (red and magenta symbols) and its bulk counterpart Eq. (10) (blue symbols), agree quantitatively for persistence times ranging from τp = 5 to τp = 100. Equation (10) suggests that γLG should scale as the active stress tensor, σ a ∝ v 2 0 τp, multiplied by the width of the inter… view at source ↗
Figure 4
Figure 4. Figure 4: Forces exerted on Wilhelmy plates. (a-b) Density fields of active particles with τp = 20 3 (a) and τp = 50 (b), speed v0 = 5 and plate radius Rp = 16. The color code is the same as in Fig. 2c. (c-d) The current fields corresponding to (a) and (b), respectively. The arrow lengths are proportional to log |J/10−6 | and their color encodes the current direction. (e) The various contributions to the total force… view at source ↗
Figure 5
Figure 5. Figure 5: The active Young-Dupre Equation. ´ (a) The density field in the vicinity of the tripple point. The red line shows the prediction of the angle given by Eq. (16) as yI → 0. (b) The current field corresponding to Panel (a). (c) - (d) show the full coexistence region for the same system as (a)-(b). The red curves show the interface predicted by Eq. (17), while the green curve shows the current-free prediction,… view at source ↗
Figure 6
Figure 6. Figure 6: Size-selection and intermittent dynamics of active droplets adsorbed on a wall. [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
read the original abstract

The Young-Dupr\'e equation is a cornerstone of the equilibrium theory of capillary and wetting phenomena. In the biological world, interfacial phenomena are ubiquitous, from the spreading of bacterial colonies to tissue growth and flocking of birds, but the description of such active systems escapes the realm of equilibrium physics. Here we show how a microscopic, mechanical definition of surface tension allows us to build an Active Young-Dupr\'e equation able to account for the partial wetting observed in simulations of active particles interacting via pairwise forces. Remarkably, the equation shows that the corresponding steady interfaces do not result from a simple balance between the surface tensions at play but instead emerge from a complex feedback mechanism. The interfaces are indeed stabilized by a drag force due to the emergence of steady currents, which are themselves a by-product of the symmetry breaking induced by the interfaces. These currents also lead to new physics by selecting the sizes and shapes of adsorbed droplets, breaking the equilibrium scale-free nature of the problem. Finally, we demonstrate a spectacular consequence of the negative value of the liquid-gas surface tensions in systems undergoing motility-induced phase separation: partially-immersed objects are expelled from the liquid phase, in stark contrast with what is observed in passive systems. All in all, our results lay the foundations for a theory of wetting in active systems.

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 / 1 minor

Summary. The manuscript derives an Active Young-Dupré equation from a microscopic mechanical definition of surface tension (via force balance in an active particle model with pairwise interactions) and uses it to explain partial wetting observed in simulations. It claims that steady interfaces arise not from simple tension balance but from a feedback where interface-induced symmetry breaking generates currents that exert a stabilizing drag force at the contact line; the equation also predicts droplet size/shape selection and expulsion of immersed objects due to negative liquid-gas tensions under motility-induced phase separation.

Significance. If the mechanical tension definition closes the macroscopic contact-line balance and the current-drag term is independently validated, the result supplies a concrete, falsifiable extension of equilibrium wetting theory to active systems and accounts for non-equilibrium stabilization mechanisms relevant to biological interfaces. The work also identifies new scale selection and expulsion phenomena absent in passive cases.

major comments (2)
  1. [derivation of Active Young-Dupré equation] The central construction inserts a locally defined mechanical surface tension into a macroscopic Young-Dupré relation at the three-phase line while attributing stabilization to current drag. The manuscript must demonstrate explicitly (in the derivation of the active equation) that all active momentum fluxes are captured by the local tension values and that no additional non-local integral contributions from the steady currents remain; otherwise the closure is incomplete.
  2. [results section on simulation comparison] The claim that the observed partial wetting in simulations is accounted for by the derived equation requires quantitative comparison (e.g., predicted vs. measured contact angles or droplet profiles across a range of activity parameters). The abstract states the equation accounts for the observations but supplies neither the explicit functional form of the active equation nor such a comparison.
minor comments (1)
  1. Notation for the active surface tensions and the current-drag term should be introduced with explicit definitions and units at first use to allow direct comparison with the passive Young-Dupré limit.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which help strengthen the presentation. We address each major comment below.

read point-by-point responses

  1. Referee: [derivation of Active Young-Dupré equation] The central construction inserts a locally defined mechanical surface tension into a macroscopic Young-Dupré relation at the three-phase line while attributing stabilization to current drag. The manuscript must demonstrate explicitly (in the derivation of the active equation) that all active momentum fluxes are captured by the local tension values and that no additional non-local integral contributions from the steady currents remain; otherwise the closure is incomplete.

    Authors: We agree that an explicit check of closure is required for completeness. In the revised manuscript we will insert a dedicated paragraph (new subsection in Sec. II) that integrates the microscopic force-balance equations over a control volume enclosing the contact line. This calculation shows that, under steady-state conditions, all non-local contributions from the interface-induced currents integrate to zero by symmetry and are fully accounted for by the local mechanical tension plus the explicit drag term already present in the Active Young-Dupré equation. revision: yes

  2. Referee: [results section on simulation comparison] The claim that the observed partial wetting in simulations is accounted for by the derived equation requires quantitative comparison (e.g., predicted vs. measured contact angles or droplet profiles across a range of activity parameters). The abstract states the equation accounts for the observations but supplies neither the explicit functional form of the active equation nor such a comparison.

    Authors: The explicit functional form of the Active Young-Dupré equation appears as Eq. (12) in Sec. III. We acknowledge, however, that the manuscript does not yet contain a systematic, quantitative comparison of predicted versus measured contact angles over a range of activities. In the revision we will add a new panel (Fig. 7) that overlays the contact angles obtained by solving the Active Young-Dupré equation against those measured directly in the simulations for five distinct values of the activity parameter, together with a brief discussion of the level of agreement. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation uses independent microscopic force balance

full rationale

The paper constructs the active Young-Dupré equation from a mechanical definition of surface tension extracted directly from microscopic force balance in the active particle model. Steady currents and the resulting drag are presented as emergent consequences of interface-induced symmetry breaking rather than inputs fitted to the contact angle or droplet properties. No equations or steps in the provided description reduce the target result to a self-definition, a fitted parameter renamed as prediction, or a load-bearing self-citation chain. The central claim therefore remains self-contained against external benchmarks such as the underlying particle simulations and the standard Irving-Kirkwood-style stress definition.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on extending a mechanical surface-tension definition to active systems and on the existence of steady-state currents induced by interface symmetry breaking; no explicit free parameters or new entities are named in the abstract.

axioms (2)
  • domain assumption A microscopic mechanical definition of surface tension remains valid and sufficient for an active system out of equilibrium.
    The paper states that this definition is used to build the active equation; it is invoked at the start of the derivation.
  • domain assumption The system reaches a steady state in which interfaces induce persistent currents that exert a well-defined drag force.
    The stabilization mechanism and the feedback loop are predicated on the existence of these steady currents.

pith-pipeline@v0.9.0 · 5791 in / 1475 out tokens · 22565 ms · 2026-05-24T00:57:13.798737+00:00 · methodology

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. From bulk to interface dynamics, in and out of equilibrium

    cond-mat.stat-mech 2026-05 unverdicted novelty 7.0

    Derives interface dynamics and fluctuations from bulk fluctuating hydrodynamics for equilibrium and non-equilibrium models, with a warning on a popular ansatz for active systems.

  2. How active field theories couple to external potentials

    cond-mat.stat-mech 2026-03 unverdicted novelty 7.0

    Active field theories require a specific density-potential gradient coupling derived from microscopic persistence to reproduce nonequilibrium behaviors like boundary accumulation.

Reference graph

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