coarsening

Coarsening is the time evolution of a heterogeneous system toward configurations with larger characteristic length scales and a reduced interfacial area or free energy. It is observed in phase-separating alloys and polymers, emulsions and foams, suspensions, and other multiphase systems, as well as in precipitation or aging of nanoparticles. The process reflects a tendency to minimize interfacial energy by reorganizing constituents on a larger scale.

The driving mechanism is the reduction of interfacial energy. In many systems, small domains dissolve while larger ones grow through diffusion of material (Ostwald ripening); droplets may also migrate and coalesce if mobility permits. The driving force is curvature-dependent chemical potential, often described by the Gibbs–Thomson relation. Coarsening can be governed by diffusion in the continuous phase, by attachment and detachment at interfaces, or by hydrodynamic transport in fluids.

Theoretical frameworks include the Lifshitz–Slyozov–Wagner (LSW) theory for Ostwald ripening in dilute dispersions, which predicts self-similar size distributions and a characteristic length scale that grows with time roughly as t1/3 under diffusion-controlled transport. In spinodal decomposition and other phase-separating scenarios with conserved or non-conserved order parameters, coarsening can also exhibit power-law growth, with exponents depending on transport mechanisms and dimensionality.

Applications and control strategies are central to materials science. Coarsening affects strength, hardness, optical and magnetic properties, and stability of emulsions and foams. It is intentionally managed through heat treatment, alloy composition, surfactants, and additives that slow diffusion or pin interfaces to achieve desired material performance.