# Contact angle formula still holds for liquid liquid interface?

I have seen in http://books.google.fr/books/about/Molecular_theory_of_capillarity.html?id=_ydSF_XUVeEC&redir_esc=y that there is a formula for the contact angle with a solid wall of a liquid-gas interface. The formula is

$$\cos \theta=\frac{ \sigma_{liquid-solid}-\sigma_{gas-solid}}{\sigma_{gas-liquid}}$$ where $\sigma_{AB}$ are the surface tensions between $A$ and $B$.

Does this formula work also in the case where instead of gas we have another liquid?

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## 1 Answer

The formula is just a force balance. If the contact line is stationary the forces at it must balance so taking the horizontal component of the forces gives you:

$$\sigma_{gas-liquid} cos \theta + \sigma_{liquid-solid} = \sigma_{gas-solid}$$

And hence the formula you quote.

If you replace the gas with a liquid the force balance calculation is just the same, so the formula remains valid.

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Thank you. I wonder which is the best reference for results like this? I found the above formula in books.google.fr/books/about/… . Are there any better references? –  Beni Bogosel Mar 24 '12 at 10:27
Any Physical Chemistry graduate textbook should cover this material. In the UK the usual choices (at least when I was a student) are Atkins' Physical Chemistry and Moore's Physical Chemistry. I haven't read the book you mention, but it looks a bit advanced if you just want basic information. –  John Rennie Mar 24 '12 at 10:33