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Decades ago, Derjaguin calculated formula which was able to predict the contact angle of a droplet on a solid substrate. The droplet and the solid substrate are separated by a thin liquid interlayer.

This formula was

cos(θ) = 1 + G(h0)/γ

where θ is the contact angle of the droplet on the solid substrate, h0 is the equilibrium distance between the droplet and the droplet (i.e the width of the thin liquid interlayer) and γ the surface tension of the liquid (water here).

The calculation of G(h0) leads to the following expression :

G(h0) = - A/(12.[itex]\pi[/itex].h0²)

with A the Hamaker constant of the system. This energy corresponds to the Lifshitz energy.

Here is my question : When you're calculating the Lifshitz energy between two materials (solid or liquid) you need to have between them a liquid or a gas. In this case, you just have air-water-solid substrate. I don't understand how it is possible to calculate the energy then, can somebody help me with that ? As I'm not a very good english speaker, I hope my question is clear otherwise don't hesitate to ask me to clarify any details.

For more detail one this, http://arxiv.org/pdf/1212.6583.pdf

Thanks you

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# Derjaguin formula

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