Quasistatic Process of a Two-dimensional Problem

For quasi-static process, if one ignores the gravity, the pressure on each side of an interface is a constant at any time. This implies that the curvature of the interface is constant (from the Young-Laplace equation). Thus, the interface is a circular arc. From (4.16), it is easy to show that the contact point X is related to 6 as. 

From (4.3), the normaUzed total interface energy can be computed as  

We now study the behavior of the quasi-static motion of the interface. The quasi-static states are obtained by computing the local minimizer 6 of 

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