Osmocapillary Adhesion

• Osmocapillary adhesion is a liquid-mediated bonding mechanism where a solvent-swollen polymer network sustains an interfacial liquid phase in thermodynamic equilibrium.
• It leverages the balance between osmotic pressure and capillary forces to generate suction, enabling robust adhesion even on low-energy substrates.
• Experimental studies show that surfactant-enhanced wetting and nanoscale confinement effects necessitate integrating capillary, osmotic, and structural pressures for predictive modeling.

Osmocapillary adhesion is a liquid-mediated bonding mechanism in which a solvent-containing polymer network sustains an interfacial liquid phase that remains in thermodynamic equilibrium with the bulk network and is placed under negative pressure by the coupled action of osmosis and capillarity. In the tree-frog-inspired formulation, a swollen network develops a bulk osmotic pressure $\Pi$, a concave interfacial meniscus generates a capillary pressure $p_c$, and the balance $p_c \sim \Pi$ stabilizes an interfacial liquid phase that produces suction-based adhesion (Shao et al., 6 Sep 2025). The concept differs both from conventional pressure-sensitive adhesion, which relies on direct wetting of the polymer matrix over the substrate, and from classical capillary adhesion, which depends on externally supplied liquid such as condensed humidity or secreted fluid (Shao et al., 6 Sep 2025).

1. Definition, scope, and conceptual position

Osmocapillary adhesion is defined most explicitly for gels or solvent-swollen networks whose active adhesive agent is not the polymer surface itself but an interfacial solvent phase. In that picture, the polymer network serves primarily as a solvent reservoir, a source of osmotic tension, and a compliant solid that conforms to roughness, while interfacial adhesion is governed by the wetting of the solvent phase and the suction supported by the osmotic-capillary equilibrium (Shao et al., 6 Sep 2025). This makes osmocapillarity an intrinsic material property of the swollen adhesive, rather than a mechanism requiring an externally delivered meniscus.

A useful distinction is between the source of the liquid and the variable that controls adhesion. Conventional PSAs depend on matrix-substrate wetting and are compromised by low-surface-energy substrates, moisture, oil, or grease. Classical capillary adhesion depends on an external liquid bridge or meniscus. Osmocapillary adhesion instead depends on whether the interfacial solvent can wet the substrate well enough to establish concave menisci and remain in equilibrium with the solvent-containing network (Shao et al., 6 Sep 2025).

Adhesion mode	Interfacial liquid source	Dominant interfacial variable
Conventional PSA	None required	Wetting/contact of the polymer matrix
Classical capillary adhesion	Externally supplied liquid	Meniscus geometry and capillary pressure
Osmocapillary adhesion	Liquid phase in equilibrium with bulk gel	Solvent-substrate wetting with $p_c \sim \Pi$

This positioning matters because much of the older wet-adhesion literature conflated capillary, osmotic, poroelastic, and viscous mechanisms. The more recent literature instead treats them as distinct stress-generation routes that can coexist but should not be identified with one another.

2. Capillary mechanics underlying osmocapillary adhesion

The capillary baseline is set by the mechanics of the three-phase contact line. For a liquid with $\gamma = \gamma_{\rm lv}$, Young’s equation at equilibrium is

$$\gamma \cos\theta_{\rm Y} + \gamma_{\rm sl} - \gamma_{\rm sv} = 0.$$

When the local contact angle differs from $\theta_{\rm Y}$, the pinned line experiences a lateral capillary imbalance, giving a lateral retention force per unit length

$\gamma(\cos\theta-\cos\theta_{\rm Y}),$

and, for a quasi-rectangular sliding drop, Furmidge’s law

$$f = \gamma w(\cos\theta_{\rm r}-\cos\theta_{\rm a})$$

(Madrid et al., 2022).

The same analysis yields the normal capillary anchoring force. At the triple line, the only surface-tension component normal to the substrate is $\gamma \sin\theta$, so the normal retention force is

$p_c$0

and for a circular line of radius $p_c$1 at constant $p_c$2,

$p_c$3

(Madrid et al., 2022). A central conceptual point is that this line force is not the same object as the Young-Dupré work of adhesion,

$p_c$4

which is an equilibrium energy per unit area for detaching a drop without changing its shape (Madrid et al., 2022).

That distinction is foundational for osmocapillarity. The capillary framework separates three quantities that are often conflated: the normal capillary retention force, the equilibrium Young-Dupré work, and the dissipative work of moving the contact line. For lateral triple-line motion, the mechanically defined advancing and receding works are

$p_c$5

and the sliding work is

$p_c$6

(Madrid et al., 2022). For small capillary number,

$p_c$7

steady sliding is argued to dissipate energy primarily through capillary retention rather than viscous losses (Madrid et al., 2022). In an osmocapillary setting, these results provide the capillary skeleton onto which osmotic pressure, swelling, and transport must be added.

3. Osmotic-capillary coupling and interfacial phase behavior

The defining step beyond classical capillarity is the introduction of a solvent-swollen network that exerts an osmotic pressure $p_c$8. In the reported tree-frog-inspired framework, the gel surface can undergo “osmocapillary phase separation”: a concave interfacial liquid phase coexists with the bulk gel when its capillary pressure balances the bulk osmotic pressure, schematically as

$p_c$9

(Shao et al., 6 Sep 2025). At a gel-substrate interface, that coexisting liquid behaves analogously to tree-frog mucus and generates suction of the magnitude of $p_c \sim \Pi$0 (Shao et al., 6 Sep 2025).

This mechanism changes the role of surfactants. In conventional PSAs, surfactants usually weaken adhesion by accumulating at the interface and disrupting polymer-substrate interactions. In osmocapillary adhesion, surfactants strengthen adhesion because they improve solvent-substrate wetting, lower the liquid surface tension, reduce contact angle, and, above the critical micelle concentration, solubilize oil and grease that would otherwise block interfacial wetting (Shao et al., 6 Sep 2025). The resulting adhesion is therefore governed by the wetting of the solvent phase rather than by direct bonding of the polymer network.

The platform demonstrated for this mechanism is broad. Reported systems include PAAm-water, PAAm-glycerol, PHEMA-PEG 400, and BR-dodecane, with the active architecture being a thin layer of gel or rubber adhesive on a rigid support and no required microstructures (Shao et al., 6 Sep 2025). The essential features are a polymer network capable of swelling in a favorable solvent, sufficient osmotic pressure $p_c \sim \Pi$1, a solvent phase that can wet the substrate, and, when required, a surfactant that improves wetting or removes contamination (Shao et al., 6 Sep 2025).

A further implication is that adhesion strength and adhesion energy can be tuned largely independently. In the reported interpretation, strength is controlled mainly by osmotic and interfacial factors, whereas adhesion energy depends on bulk dissipation and fracture processes (Shao et al., 6 Sep 2025). This separates osmocapillarity from both dry tack and purely capillary bridge adhesion.

4. Experimental manifestations on dry, moist, oily, and soft substrates

The most direct experimental support comes from probe-tack, peel, lap-shear, wetting, and cycling measurements on solvent-containing polymer networks (Shao et al., 6 Sep 2025). Adhesion strength in tack is defined as

$p_c \sim \Pi$2

and peel adhesion energy as

$p_c \sim \Pi$3

(Shao et al., 6 Sep 2025). For a $p_c \sim \Pi$4 v/v PAAm hydrogel, adhesion was stronger on glass than on PTFE, establishing that substrate wetting still matters. After surfactant addition, however, adhesion on low-energy surfaces increased strongly and the strengthening plateaued above the CMC; the paper reports CMC values of $p_c \sim \Pi$5 mM for Triton X-100 in water and $p_c \sim \Pi$6 mM for SDS in water (Shao et al., 6 Sep 2025).

A particularly strong mechanistic result is the collapse of data from different substrates and surfactants onto a master curve when plotted against solvent-substrate contact angle (Shao et al., 6 Sep 2025). The stated interpretation is that adhesion strength is governed by solvent wetting alone and that the polymer identity or network chemistry has negligible direct contribution to interfacial strength. This is consistent with the proposed division of labor: the solvent determines interfacial adhesion, while the network determines compliance and, if desired, bulk dissipation.

The contaminated-substrate data are especially diagnostic. On moist glass, adhesion remains substantial because environmental water can be absorbed directly into the hydrogel, although local swelling lowers $p_c \sim \Pi$7 and reduces strength. On oily and greasy glass, adhesion strengths nearly vanish without surfactant, but recover strongly when surfactant concentration is above the CMC (Shao et al., 6 Sep 2025). The kinetics reflect the underlying transport process: adhesion forms in $p_c \sim \Pi$8 s on dry and moist surfaces, but requires about $p_c \sim \Pi$9 s on oily and greasy surfaces, which is attributed to slower micelle-mediated solubilization (Shao et al., 6 Sep 2025).

The reported comparisons with commercial PSAs sharpen the distinction. Acrylic-based VHB shows about a factor of 4 drop in adhesion strength from glass to PTFE, and silicone-based APT polyimide tape shows about a factor of 2 drop, whereas osmocapillary adhesives with surfactant show much less substrate dependence and outperform commercial PSAs on low-energy substrates such as PTFE and nitrile rubber (Shao et al., 6 Sep 2025). On moist, oily, greasy, fully swollen hydrogel, and wet chicken-skin substrates, the reported osmocapillary adhesive maintained more than half of its dry-glass strength, while commercial PSAs showed $p_c \sim \Pi$0 drops on oily and greasy substrates and $p_c \sim \Pi$1 drops on moist surfaces (Shao et al., 6 Sep 2025).

Bulk dissipation alters energy but not the interfacial mechanism. Plain PAAm-water gel shows adhesion energy of about $p_c \sim \Pi$2 J/m$p_c \sim \Pi$3, whereas reducing crosslink density and synthesis polymer fraction increases adhesion energy as resilience decreases, with adhesion strength unchanged. Adding uncrosslinked PAAm chains raises adhesion energy to $p_c \sim \Pi$4 J/m$p_c \sim \Pi$5, but lowers adhesion strength and leaves residue by chain pull-out (Shao et al., 6 Sep 2025). Reusability is correspondingly good on dry glass, PTFE, oily glass, and greasy glass, with negligible change in adhesion strength over 10 cycles, while more noticeable degradation occurs on fully swollen hydrogel and moist surfaces because water uptake lowers the local osmotic pressure near the interface (Shao et al., 6 Sep 2025).

5. Nanoscale confinement, soft interfaces, and stress corrections

At nanometric separations, liquid-mediated adhesion acquires an additional pressure scale beyond classical Laplace suction. Molecular dynamics studies of liquid bridges between a spherical tip and a flat substrate, and between two parallel plates, show that continuum capillarity predicts meniscus shape and surface-tension contributions accurately to surprisingly small scales, but fails earlier for the total adhesive force because the relevant normal stress becomes anisotropic (Cheng et al., 2014, Cheng et al., 2016). In the sphere-flat case, the total capillary force is written as

$p_c \sim \Pi$6

yet the simulations show that the pressure term is systematically less attractive than the continuum prediction because the normal pressure $p_c \sim \Pi$7 is more positive than the Young-Laplace pressure (Cheng et al., 2014). In the parallel-plate geometry, the same issue appears as a confinement-induced excess

$p_c \sim \Pi$8

arising from molecular layering and pressure-tensor anisotropy (Cheng et al., 2016).

These results are not themselves osmotic in the strict thermodynamic sense: the parallel-plate study explicitly states that there are no dissolved solutes, semipermeable boundaries, Donnan effects, or explicit osmotic pressure terms (Cheng et al., 2016). Their significance for osmocapillary adhesion is that the normal stress balance in strongly confined films may require a pressure correction additional to capillary curvature. A plausible implication is that nanoscale osmocapillary theories must distinguish among capillary pressure, osmotic pressure, and structural or disjoining pressure rather than collapsing them into a single “suction” variable.

Soft interfaces add another correction. In a physically cross-linked polyacrylamide hydrogel, the directly measured surface tension is approximately $p_c \sim \Pi$9, the shear modulus is about $\gamma = \gamma_{\rm lv}$0 by resonant shear mode and $\gamma = \gamma_{\rm lv}$1 by a submerged steel-ball estimate, and the elasto-capillary length

$\gamma = \gamma_{\rm lv}$2

greatly exceeds the film thicknesses studied (Chakrabarti et al., 2014). Under adhesive tensile loading, the interface roughens with a wavelength consistent with

$\gamma = \gamma_{\rm lv}$3

modifying the pull-off stress relative to the purely elastic confined-film result (Chakrabarti et al., 2014). For osmocapillary adhesion, this means that capillary suction may coexist with capillary regularization of the soft solid itself.

An adjacent but distinct route to adhesion control is provided by hygroscopic PDMS films containing hydrophilic inclusions. Upon water uptake, these bonded films develop an elasto-osmotic surface instability with

$\gamma = \gamma_{\rm lv}$4

and a domed epoxy adherent on a $\gamma = \gamma_{\rm lv}$5 film detaches spontaneously after about $\gamma = \gamma_{\rm lv}$6 h in distilled water, with pull-off decreasing from about $\gamma = \gamma_{\rm lv}$7 N to $\gamma = \gamma_{\rm lv}$8 N (Al-sakkaf et al., 2023). That mechanism is osmotic and elastic rather than capillary, but it demonstrates that osmotic stress can govern interfacial morphology and release even when capillary bridge forces are not the principal driver.

6. Distinctions from neighboring wet-adhesion mechanisms and unresolved issues

The modern literature treats osmocapillary adhesion as one member of a broader family of liquid-mediated adhesion mechanisms rather than as a synonym for all of them. Capillary adhesion of stick insects, for example, is analyzed through a nanometric secreted liquid film and a meniscus-based force law,

$\gamma = \gamma_{\rm lv}$9

with inferred secretion surface tension between $$\gamma \cos\theta_{\rm Y} + \gamma_{\rm sl} - \gamma_{\rm sv} = 0.$$0 and $$\gamma \cos\theta_{\rm Y} + \gamma_{\rm sl} - \gamma_{\rm sv} = 0.$$1 and no osmotic term (Amador et al., 2023). By contrast, the frog toe-pad model proposes temporary underwater adhesion from viscous-poroelastic interaction alone, explicitly in the absence of capillary effects, van der Waals forces, or osmotic pressure (Tulchinsky et al., 2015). Oil-infused PDMS against glass provides another contrast case: increasing oil fraction reduces adhesion by lubricating the interface, while fully swollen PDMS shows residual capillary meniscus forces but no evidence that poroelastic relaxation increases adhesion (Jha et al., 2022).

A common misconception is therefore that any liquid-mediated adhesion involving a soft material is “osmocapillary.” The stricter usage supported by the current literature requires an interfacial liquid phase in thermodynamic equilibrium with a solvent-containing network and a suction state sustained jointly by osmotic and capillary pressures (Shao et al., 6 Sep 2025). Systems dominated only by Laplace pressure, only by viscous-poroelastic stress, or only by structural confinement pressure are neighboring mechanisms, not identical ones.

The principal unresolved issue is predictive closure. The experimental formulation of osmocapillary adhesion is strong, but the same paper states that it does not provide a detailed closed-form adhesion law linking $$\gamma \cos\theta_{\rm Y} + \gamma_{\rm sl} - \gamma_{\rm sv} = 0.$$2, curvature, contact angle, roughness, and measured force (Shao et al., 6 Sep 2025). The capillary baseline paper identifies the ingredients needed for a fuller theory: osmotic pressure differences $$\gamma \cos\theta_{\rm Y} + \gamma_{\rm sl} - \gamma_{\rm sv} = 0.$$3, swelling or poroelastic deformation, solute-dependent surface tension $$\gamma \cos\theta_{\rm Y} + \gamma_{\rm sl} - \gamma_{\rm sv} = 0.$$4, confinement-dependent geometry, a generalized normal stress balance of the form

$$\gamma \cos\theta_{\rm Y} + \gamma_{\rm sl} - \gamma_{\rm sv} = 0.$$5

and transport kinetics due to diffusion, permeation, or solvent uptake (Madrid et al., 2022). Taken together, these works suggest that osmocapillary adhesion is best understood not as a single force law but as a coupled interfacial problem in which capillary line forces, equilibrium interfacial work, osmotic pressure, confinement-induced stress, and soft-solid mechanics can all be active, with their relative importance set by wetting, chemistry, geometry, and time scale.