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Work of adhesion

Pronunciation: /wɜːrk əv ədˈhiːʒən/

The work of adhesion Wa is the reversible energy per unit area needed to separate two phases along their shared interface, leaving two new surfaces behind. For a liquid on a solid it follows from the contact angle through the Young-Dupré equation, Wa = γLV (1 + cos θY).

Also called

Thermodynamic work of adhesion Reversible work of adhesion Dupré work of adhesion

Related terms

Surface free energy models Equation of State (SFE model) Fowkes method

Topics

Adhesion Surface energy Contact angle
Book a 15 minute demo Read the surface energy measurement guide

At a glance

What the work of adhesion measures, and how you get it from a contact angle.

What it is

Imagine peeling a liquid off a solid, slowly and reversibly. You destroy one interface, the solid liquid one, and create two surfaces: bare solid and free liquid. The energy balance of that step is the work of adhesion.

  • Dupré relation: Wa = γSV + γLV − γSL
  • Units: mJ/m², numerically equal to mN/m
  • Higher Wa means the liquid holds on more strongly

Why it matters

Inks, coatings and adhesives must wet a surface before they can bond to it. Wa is the thermodynamic part of that story, which is why low energy plastics need treatment before you can bond polypropylene reliably. A Fortune 500 adhesives R&D case study shows how wetting data feeds adhesive development.

Worked example

Water at 20 °C, γLV = 72.8 mN/m.

  • On PTFE, θ ≈ 110°: cos 110° = −0.342, so Wa = 72.8 × 0.658 ≈ 47.9 mJ/m²
  • On clean glass, θ ≈ 20°: cos 20° = 0.940, so Wa = 72.8 × 1.940 ≈ 141.2 mJ/m²

Water clings about three times more strongly to the glass. Our surface free energy calculator works from the same angles.

How it is measured

You do not pull the liquid off. You measure the contact angle and the liquid surface tension, then apply the Young-Dupré equation. For a solid against another material, you first find the surface energy of each with two or three liquids. The surface energy measurement guide covers that method.

Expert view

“Droplet adhesion is three-dimensional. Two side-view angles give an estimate; the whole story is how the angle and the contact line vary all the way around the drop.”

Dr. Alidad Amirfazli, Co-founder and Scientific Advisor, Droplet Lab

What the terms mean

How the work of adhesion changes with the contact angle for one liquid.

θ = 0° (Wa = 2γLV)

The liquid sticks to the solid at least as strongly as to itself. Adhesion matches or exceeds cohesion, so the liquid spreads.

0° < θ < 180° (0 < Wa < 2γLV)

Partial wetting. The lower the angle, the larger Wa. Most real liquid and solid pairs sit here.

θ → 180° (Wa → 0)

The liquid barely interacts with the solid. Real surfaces never reach zero, but superhydrophobic ones come close.

Wa rises from zero at 180° to twice the liquid surface tension at 0°. Compare it with Wc = 2γLV to see whether the liquid prefers the solid or itself.

Wa Work of adhesion, mJ/m²
Wc Work of cohesion of the liquid, 2γLV, mJ/m²
γSV, γSL, γLV Solid vapor, solid liquid and liquid vapor tensions, mN/m
θY Young (equilibrium) contact angle, degrees
d, p Dispersive and polar parts of a surface energy

Key equations

The definition, the contact angle form, and the form used with surface energy models.

Equation: Wa = γSV + γLV − γSL

Variable legend:

  • Wa: work of adhesion (mJ/m²)
  • γSV, γLV: the two surfaces created (mN/m)
  • γSL: the interface destroyed (mN/m)

Interpretation: Energy of the two new surfaces minus the energy of the interface you removed.

When to use: Use it as the definition. It holds for any two phases, including two solids or two immiscible liquids.

Assumptions:

  • Reversible separation with no plastic deformation
  • Clean surfaces in a defined vapor

Common mistakes:

  • Confusing it with the measured strength of a joint

Equation: Wa = γLV (1 + cos θY)

Variable legend:

  • Wa: work of adhesion between liquid and solid (mJ/m²)
  • γLV: surface tension of the liquid (mN/m)
  • θY: Young contact angle (°)

Interpretation: The energy needed to pull a unit area of liquid off the solid. Lower angles mean stronger adhesion.

When to use: Use it when the question is how strongly a liquid sticks to a surface rather than how it spreads.

Assumptions:

  • Same as the Young equation: smooth, rigid, uniform solid at equilibrium
  • The solid does not swell or dissolve in the liquid

Common mistakes:

  • Reporting Wa without the liquid and temperature used
  • Applying it to dynamic angles measured while the line moves

Equation: Wa = 2 √(γSd γLd) + 2 √(γSp γLp)

Variable legend:

  • γSd, γSp: dispersive and polar parts of the solid surface energy (mJ/m²)
  • γLd, γLp: dispersive and polar parts of the liquid surface tension (mN/m)

Interpretation: Splits adhesion into dispersive and polar contributions. Matching polarity between adhesive and substrate raises Wa.

When to use: Use it to predict Wa between a characterised solid and any liquid, ink or adhesive with known components.

Assumptions:

  • The geometric mean combining rule of the OWRK model holds

Common mistakes:

  • Mixing component values from different surface energy models

How to read it

What a work of adhesion value tells you, and what it does not.

Wa is only as good as the angle and surface energy that go into it. Our note on reproducible surface energy calculation from contact angles explains which inputs to trust. Standards such as ASTM D7490 for surface tension of solid coatings and substrates set out the multi liquid route, and experiment 6 on surface free energy with multiple liquids walks students through it.

From Wa to meaning

If you see It usually means Check next
Wa close to 2γLV The liquid adheres about as strongly as it coheres; it is close to spreading Whether the angle is near zero and still falling
Wa well below 2γLV Weak adhesion; the liquid prefers itself to the solid Surface treatment, contamination, or a low energy material
Wa rises after treatment then falls over days Treatment is ageing Storage time and conditions
High Wa but the joint still fails Wetting is fine; failure is elsewhere Cure, weak boundary layers, mechanical stresses

Common misconceptions

Where the work of adhesion is most often misread.

Work of adhesion equals bond strength

Wa is a reversible, thermodynamic energy. Calculated from a contact angle it can never exceed 2γLV, about 146 mJ/m² for water at 20 °C. A peel or lap shear test measures far larger energies, because the adhesive deforms and dissipates energy. Wa sets a floor for good wetting; it does not predict the failure load.

A dyne level tells you the work of adhesion

A dyne level is a single wetting threshold. Wa depends on both partners and on their polar and dispersive parts. Our article Beyond 38 dynes explains why two surfaces at the same dyne level can bond differently.

Any measured contact angle gives the right Wa

Young-Dupré uses the equilibrium angle on an ideal surface. On rough or patchy samples, advancing and receding angles differ and Wa calculated from either one shifts. Report which angle you used, and compare with reference surface free energy values for common polymers.

Higher Wa is always better

For release liners, anti fouling or easy clean surfaces, you want low Wa. The right target depends on the job. Production teams choosing a method for pre treatment and bonding checks can compare options in the best surface energy analyzer for production QC.

Related terms

Where the work of adhesion sits among other wetting and surface energy terms.

Broader term

  • Adhesion
  • Surface free energy

Related terms

  • Young equation
  • Work of cohesion
  • Spreading coefficient
  • Surface free energy models
  • Fowkes method
  • Equation of State (SFE model)

Often confused with

  • Adhesion strength (peel, lap shear)
  • Dyne level (wetting tension)

FAQ

Short answers to the questions people ask most about the work of adhesion.

How do you calculate the work of adhesion from a contact angle?

Use the Young-Dupré equation, Wa = γLV (1 + cos θ). Measure the equilibrium contact angle of the liquid on the solid and take the liquid surface tension at the same temperature. For water at 20 °C and an angle of 110°, Wa = 72.8 × (1 − 0.342) ≈ 47.9 mJ/m².

What is the difference between work of adhesion and work of cohesion?

Work of adhesion is the energy to separate two different phases at their interface. Work of cohesion is the energy to split one phase into two, which for a liquid equals 2γLV. Comparing the two tells you whether a liquid prefers the solid or itself, which is the basis of the spreading coefficient.

What units does the work of adhesion use?

Energy per unit area, usually mJ/m². Because 1 mJ/m² equals 1 mN/m, the number matches surface tension units directly. Older papers use erg/cm², which is also numerically equal. Always report the liquid, the temperature and which contact angle you used alongside the value.

References

Primary sources and further reading.

1. Dupré, A. (1869). Théorie mécanique de la chaleur. Gauthier-Villars, Paris.
2. Young, T. (1805). An essay on the cohesion of fluids. Philosophical Transactions of the Royal Society of London, 95, 65 to 87. https://doi.org/10.1098/rstl.1805.0005
3. Owens, D. K., and Wendt, R. C. (1969). Estimation of the surface free energy of polymers. Journal of Applied Polymer Science, 13(8), 1741 to 1747. https://doi.org/10.1002/app.1969.070130815
4. Israelachvili, J. N. (2011). Intermolecular and Surface Forces, 3rd edition. Academic Press.
5. Surface energy measurement guide
6. Surface free energy models
7. Fowkes method
8. Equation of State (SFE model)