Local approach for coarsening of precipitates

Coarsening of precipitates is very often treated by the classical Lifshitz–Slyozov–Wagner (LSW) mean-field coarsening theory. The theory provides simple evolution equations for volumes of precipitates. A new model based on application of the Thermodynamic Extremal Principle extends the LSW theory by terms accounting for mutual interaction of individual precipitates during coarsening. The model is demonstrated on an example showing that only one interaction term is dominant, which leads to a set of linear equations with a non-diagonal matrix for the rates of precipitate volumes. Of course, the set of equations must be solved numerically.