On the thermodynamic theory of fluid interfaces: Infinite intervals, equilibrium solutions, and minimizers

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We outline a thermodynamic theory for one-dimensional fluid interfaces and compare our findings with the classical results of the variational van der Waals-Cahn-Hilliard approach. After establishing necessary and sufficient conditions for their equivalence, we list all types of possible solutions giving the structure of the density profile in an infinite interval. Then we examine the stability of these solutions, strictly within a variational thermodynamic context and prove that transitions are minimizers, but reversals and oscillations are not. To the best of our knowledge, this is the first proof available for this old problem. It substantiates previous intuitive statements and makes rigorous certain mathematical assertions existing in the physical literature. © 1986.

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Journal of Colloid And Interface Science