Contents

Fowkes method (SFE model)

Pronunciation: /faʊks ˈmɛθəd/

The Fowkes method is a surface free energy model that treats the attraction across an interface as the geometric mean of the dispersive components of the two phases. With a purely dispersive liquid it gives the dispersive surface energy of a solid from a single contact angle.

Also called

Fowkes theory Fowkes geometric mean method Fowkes approach

Related terms

Surface free energy (SFE) Surface energy components Surface free energy models

Topics

Surface energy Contact angle Dispersive component
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At a glance

What the Fowkes method assumes, and what it gives you.

What it is

Frederick Fowkes proposed in 1964 that surface tension is a sum of parts, one per type of molecular force. Across an interface, only like forces interact, and the dispersive part combines as a geometric mean.

  • γ = γᵈ + γᵖ (dispersive plus polar)
  • Dispersive interaction across the interface: 2√(γ1ᵈ γ2ᵈ)
  • Fowkes used it to find 21.8 mN/m as the dispersive part of water

Why it matters

The dispersive part of a surface is present on every material and controls how it wets with oils, hydrocarbons and nonpolar resins. The Fowkes idea also sits underneath OWRK, the most widely used two liquid model. Compact instruments in our guide to the best surface energy analyzer under $5,000 are often judged on which of these models they support.

Worked example

Diiodomethane (50.8 mN/m, all dispersive) on a hypothetical polymer at 20 °C, θ = 50°.

  • cos 50° = 0.6428, so 1 + cos θ = 1.6428
  • 1.6428² = 2.6988
  • γSᵈ = 50.8 × 2.6988 / 4 = 137.10 / 4 = 34.3 mJ/m²
  • Add water at 75° in a second step and the polar part comes out as 6.7 mJ/m², for 41.0 mJ/m² in total

Try it with your own angles in the surface free energy calculator.

How it is measured

You measure the sessile drop contact angle of a nonpolar liquid, usually diiodomethane, then a polar liquid such as water if you want the polar part too. The surface energy measurement guide covers liquids, timing and the full procedure.

Expert view

“Adhesion fails at the interface long before it fails in the joint; surface energy tells you whether that interface was ever ready to bond in the first place.”

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

What the terms mean

How the Fowkes method reads a dispersive liquid on different solids.

Low angle with diiodomethane

A large dispersive surface energy. The solid attracts nonpolar liquids strongly, as clean metals and many glasses do.

High angle with diiodomethane

A small dispersive surface energy, typical of fluorinated surfaces such as PTFE, where the total is only about 18 to 20 mJ/m².

Water beads but diiodomethane spreads

The surface has a healthy dispersive part but little polar character. Adding the water step quantifies that polar part.

Probe liquid values used across our model pages, 20 °C: water 72.8 = 21.8 + 51.0 mN/m; diiodomethane 50.8 = 50.8 + 0 mN/m.

γSᵈ Dispersive component of the solid surface energy, mJ/m²
γSᵖ Polar (nondispersive) component of the solid, mJ/m²
γL, γLᵈ, γLᵖ Total, dispersive and polar surface tension of the liquid, mN/m
θ Contact angle of the liquid on the solid, degrees

Key equations

The Fowkes interface rule and the two forms you will use.

Equation: γSL = γS + γL − 2 √(γSᵈ γLᵈ)

Variable legend:

  • γSL: solid liquid interfacial tension (mN/m)
  • γS, γL: total surface energy of solid and liquid (mJ/m², mN/m)
  • γSᵈ, γLᵈ: dispersive components (mJ/m², mN/m)

Interpretation: Only dispersive forces act across the interface, so the interface costs less energy the larger both dispersive parts are.

When to use: Use it when at least one phase is nonpolar, so dispersive forces are the only ones that act across the interface.

Assumptions:

  • Forces combine as a geometric mean of like components
  • Polar interactions across the interface are negligible

Common mistakes:

  • Applying it to two polar phases, where polar interactions also cross the interface

Equation: γSᵈ = γL (1 + cos θ)² / 4

Variable legend:

  • Valid when the liquid is purely dispersive (γL = γLᵈ), as diiodomethane is usually taken to be
  • θ: contact angle of that liquid (°)

Interpretation: Combine the Fowkes rule with the Young equation and the dispersive part of the solid falls out from a single angle.

When to use: Use it as the first step of a two liquid Fowkes analysis, or alone when only the dispersive part is needed.

Assumptions:

  • The liquid has no polar component
  • The contact angle is an equilibrium angle on a smooth surface

Common mistakes:

  • Using a liquid with a sizeable polar part, such as ethylene glycol, in this one liquid form

Equation: γL (1 + cos θ) = 2 √(γSᵈ γLᵈ) + 2 √(γSᵖ γLᵖ)

Variable legend:

  • Solved for γSᵖ with a polar liquid, using γSᵈ from the first step
  • Water at 75°: 45.82 − 27.34 = 18.48; 18.48² / 51.0 = 6.7 mJ/m²

Interpretation: Adds a polar term of the same geometric mean form. With these two liquids it is the same equation used by OWRK.

When to use: Use it when you need both the dispersive and the polar part of the solid.

Assumptions:

  • Polar interactions also follow a geometric mean

Common mistakes:

  • Taking water component values from one table and diiodomethane values from another

How to read it

What a Fowkes result tells you about a surface.

The dispersive part changes slowly with chemistry; the polar part responds strongly to oxidation, plasma and contamination. Reading the two separately is the main reason to use a component model. Our note on reproducible surface energy calculation from contact angles explains how to keep both comparable over time.

Reading a Fowkes result

If you see It usually means Check next
Dispersive part near the total A nonpolar surface such as a polyolefin or fluoropolymer Whether a treatment was meant to add polar groups
Polar part rises after plasma or corona Oxygen containing groups were added to the surface How fast the value falls back during storage
Dispersive part changes a lot between samples Contamination or a different surface material Cleaning, handling and the diiodomethane angle quality
Negative value under the square root Angle or liquid data are inconsistent with the model Liquid purity, drop age and the component table used

Common misconceptions

Where the Fowkes method is most often misunderstood.

Fowkes and OWRK are different answers

With diiodomethane and water, the two step Fowkes route and OWRK solve the same pair of equations and give the same result. Software often labels either one as Fowkes. What changes the answer is the liquid set and the component values, which is why studies such as experiment 6 on surface free energy with multiple liquids fix both.

The dispersive part is the whole story

A single nonpolar liquid tells you nothing about polar groups added by treatment. For coatings, as in thin film and nanocoating surface characterization, the polar part often carries the change you care about. Measure a polar liquid as well.

Related terms

Where the Fowkes method sits among surface energy models.

Broader term

  • Surface free energy (SFE)
  • Surface free energy models

Related terms

  • Surface energy components
  • OWRK method
  • Young equation
  • Work of adhesion

Often confused with

  • OWRK method
  • van Oss-Chaudhury-Good method

FAQ

Short answers to the questions people ask most about the Fowkes method.

What is the difference between the Fowkes and OWRK methods?

Fowkes introduced the geometric mean rule for the dispersive part of an interface. Owens, Wendt, Rabel and Kaelble added a polar term of the same form. With diiodomethane and water, the two step Fowkes route and OWRK give the same numbers. OWRK can also fit three or more liquids at once on one straight line.

Why is diiodomethane used for the Fowkes method?

Diiodomethane has a high surface tension, 50.8 mN/m at 20 °C, and is usually treated as purely dispersive. A high tension gives a measurable contact angle on most solids, and no polar part means one angle gives the dispersive surface energy directly. Alpha bromonaphthalene is an alternative nonpolar liquid.

Can the Fowkes method give the total surface energy?

Only with a second, polar liquid. The original method gives the dispersive part from a nonpolar liquid. Adding water and solving for the polar part, the extended Fowkes step, gives the total as the sum of the two. In the worked example that is 34.3 + 6.7 = 41.0 mJ/m².

References

Primary sources and further reading.

1. Fowkes, F. M. (1964). Attractive forces at interfaces. Industrial and Engineering Chemistry, 56(12), 40 to 52. https://doi.org/10.1021/ie50660a008
2. 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
3. Good, R. J. (1992). Contact angle, wetting, and adhesion: a critical review. Journal of Adhesion Science and Technology, 6(12), 1269 to 1302. https://doi.org/10.1163/156856192X00629
4. Surface energy measurement guide
5. Surface free energy models
6. Surface energy components
7. OWRK method