Coupled diffusion and phase transition: Phase fields, constraints, and the Cahn–Hilliard equation

Abstract We develop a constrained theory for constituent migration in bodies with microstructure described by scalar phase field. The distinguishing features of the stem from systematic treatment and characterization reactions needed to maintain internal constraint given coincidence mass fraction also boundary conditions situations which interface between body its environment is structureless cannot support transport. In addition yielding new derivation Cahn–Hilliard equation, affords an interpretation that equation as limiting variant Allen–Cahn type diffusion system arising unconstrained obtained considering field independent quantities. corroborate three-dimensional numerical simulations recently proposed benchmark problem.