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OWRK (Owens-Wendt-Rabel-Kaelble) method

Pronunciation: /ˈoʊ dʌbəljuː ɑːr keɪ/

The OWRK method is a surface free energy model that splits the surface energy of a solid into a dispersive and a polar component. It combines each pair of like components with a geometric mean and solves for both from the contact angles of two or more liquids.

Also called

Owens-Wendt method OWRK Owens-Wendt-Rabel-Kaelble method Geometric mean method

Related terms

Surface energy components Surface free energy models Equation of State (SFE model)

Topics

Surface energy Contact angle Polar component
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At a glance

What the OWRK method does and what you need to use it.

What it is

Owens and Wendt published the method in 1969; Rabel and Kaelble developed equivalent forms around the same time, hence the four names. It extends the Fowkes idea with a polar term.

  • γS = γSᵈ + γSᵖ
  • Two unknowns, so at least two liquids
  • Usual pair: water and diiodomethane

Worked example

Hypothetical polymer at 20 °C, linear form y = √γSᵖ x + √γSᵈ:

  • Diiodomethane, 50°: y = 50.8 × 1.6428 / (2 × √50.8) = 83.45 / 14.25 = 5.854, x = 0
  • Water, 75°: y = 72.8 × 1.2588 / (2 × √21.8) = 91.64 / 9.338 = 9.814, x = √(51.0/21.8) = 1.530
  • Slope = (9.814 − 5.854) / 1.530 = 2.588, so γSᵖ = 6.7; intercept 5.854, so γSᵈ = 34.3
  • γS = 41.0 mJ/m²

Key equations

The OWRK equation and its straight line form.

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

Variable legend:

  • γSᵈ, γSᵖ: dispersive and polar parts of the solid (mJ/m²)
  • γL, γLᵈ, γLᵖ: total, dispersive and polar parts of the liquid (mN/m)
  • Water 72.8 = 21.8 + 51.0; diiodomethane 50.8 = 50.8 + 0 (20 °C)

Interpretation: Dispersive pairs with dispersive and polar with polar. The same equation as the extended Fowkes method.

When to use: Use it for polymers, coatings and treated surfaces where a dispersive and polar split is enough.

Assumptions:

  • Geometric mean combining rule
  • Equilibrium angles on a smooth, uniform, nonreactive solid

Common mistakes:

  • Two liquids of similar polarity, which makes the fit unstable

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

Variable legend:

  • Plot y against x = √(γLᵖ/γLᵈ) for each liquid
  • Slope squared: γSᵖ; intercept squared: γSᵈ

Interpretation: With three or more liquids the points should fall on one straight line. Scatter shows the model or the angles are off.

When to use: Use it whenever more than two liquids are measured.

Assumptions:

  • Same as the OWRK equation

Common mistakes:

  • Reading a poor fit as a precise result

How to read it

OWRK compared with the other common models.

OWRK is the most widely reported model for polymers and coatings, but it is one choice among several. Some instruments report surface energy with the Equation of State approach instead, which gives a single total and no polar split. Our note on reproducible surface energy calculation from contact angles explains why the model must be named with every value.

OWRK next to other models

Model Liquids needed What you get
OWRK Two or more Dispersive and polar parts and their total
van Oss-Chaudhury-Good Three Lifshitz-van der Waals, acid and base parameters
Equation of State One per value One total, no components

Common misconceptions

Where OWRK results are most often misread.

Related terms

Where OWRK sits among surface energy models.

Broader term

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

Related terms

  • Surface energy components
  • Fowkes method
  • Young equation

Often confused with

  • Equation of State (SFE model)
  • van Oss-Chaudhury-Good method

FAQ

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

What liquids are used for the OWRK method?

Water and diiodomethane are the standard pair because water is strongly polar and diiodomethane is purely dispersive. Ethylene glycol, formamide or glycerol can be added as extra points. Use one published table for all liquid component values, and check that no liquid swells or dissolves your sample.

Is OWRK the same as the Fowkes method?

Closely related. Fowkes introduced the geometric mean for the dispersive part; OWRK adds a polar term of the same form. With water and diiodomethane, the two step extended Fowkes calculation and OWRK give identical results. OWRK is more often used with three or more liquids on a straight line fit.

Do all instruments report surface energy with OWRK?

No. Many report OWRK by default, but others use the Equation of State, which gives one total from each liquid, or offer several models. The numbers are not interchangeable. When comparing results from different instruments or labs, check which model and liquid values each one used.

References

Primary sources and further reading.

1. 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
2. Fowkes, F. M. (1964). Attractive forces at interfaces. Industrial and Engineering Chemistry, 56(12), 40 to 52. https://doi.org/10.1021/ie50660a008
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. Equation of State (SFE model)