A self-consistent approach to phase separation: Free-energy shaped Cahn–Hilliard dynamics

For the Cahn–Hilliard equation, the dynamics of the order parameter distribution with the values at plus and minus infinity corresponding to the binodal of the system is considered. A new family of exact solutions of this problem is analytically constructed. Solutions are expressed in terms of the Lambert W  -function and generalized hypergeometric functions. It is shown that the dynamics of the interface width obey the power law with an exponent of 1/41/4. The interface energy normalized to its equilibrium value is found to be equal to the arithmetic mean of the interface width normalized to its equilibrium value and its reciprocal.