Phase-Field Models of Nonequilibrium Interfacial Patterns.
Alain Karma (Northeastern University, Universitté Paris VI & Paris VII, Chaire Condorcet ENS)

Jeudi 15 janvier 2004

Coarse-grained continuum descriptions of bulk matter have been used to model phase transitions and interfacial phenomena and include the van der Waals theory of the liquid-gas transition (1893), the Landau-Ginzburg theory of superconductivity (1950), and the Cahn-Hilliard description (1958) of spinodal decomposition in materials science. More recently, these continuum approaches have been extended to model a wide range of interfacial pattern formation problems, first in the context of solidification, and subsequently in several other contexts that include stress-driven and hydrodynamic interfacial instabilities, microstructural evolution in polycrystalline materials, surface evolution during epitaxial growth, dislocation dynamics, corrosion, and fracture.

These "phase-field" models are generally formulated by first writing down a physically sensible free-energy density. The gradient dynamics that minimizes this energy can be readily simulated on computers of today and analyzed in some limits. The flexibility to add arbitrarily many terms to the free-energy makes the phase-field approach extremely powerful to model simultaneously a wide range of physical processes (such as surface or bulk diffusion, flow, stress, etc). Symmetries and conservation laws, however, only help to guide but do not uniquely specify the choice of the phenomenological free-energy functional. This, in turn, makes it often challenging to construct phase-field models and to relate their results to experiments.

This talk will present a survey of the the phase-field approach and describe recent progress made in coping with this challenge. Examples of applications will include new topics like fracture and nanoporosity formation during electrochemical dissolution as well as more mature examples, such as solidification, where quantitative comparisons with experiments have been made.