Role of a Free Energy Action Principle in Predicting Microstructure Formation

Abstract

AbstractIt is demonstrated that some twenty representative free boundary diffusion-reaction and hydrodynamic patterning systems fall within the compass of the isothermal variational principle where the Lagrangian density is the free energy density g, and η is an appropriate order parameter. To illustrate the universality of the formulation we survey in some detail its degree of equivalence to twenty-one currently adopted or promoted procedures for resolving pattern degeneracies, and critically reappraise theoretical descriptions of grain growth, ordinary diffusion, spinodal decomposition and Ostwald Ripening and their predictive success. The importance of a hierarchy of kinetic scaling laws is discussed. The physics of fluctuations is essential to understanding.