Young equation proof

It is clear that the above mode of computation suffers from the defect pointed out at the start of this section, in the discussion of the force proof of the Young equation (1). If the forces are supposed to cancel each other along a vertical, rather than a horizontal, projection, then the relation obtained... 

Some important mathematical results have recently been proved by Frederick J. Almgren Jr. and Jean E. Taylor. They have been able to show that Plateau s rules for the angles of intersection of soap film surfaces and lines, discussed in Chapter 4, are a general property of the solution of the Laplace-Young equation. These proofs are beyond the scope of this book but references to the work can be found in the popular article by Almgren and Taylor entitled The Geometry of Soap Films and Soap Bubbles. 

This group of methods is based on Young s equation of wetting, i.e., Eq. (1) of the Introduction above. Two proofs of this relation are known, one dealing with forces, and the other, with energy. 

We have said that the Young Laplace equation cannot be satisfied unless V n = constant. The proof is more or less trivial. Let us suppose that u = 0. Then, according to the equation of fluid statics, (2 61),... 

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