Analytical description of phase coarsening at high volume fractions

An analytical theory of volume fraction effects in diffusion-controlled phase coarsening is developed. It is based on the application of the Lifshitz–Slyozov–Wagner procedure of Ostwald ripening theory to a self-similar particle volume evolution equation which is approximated by a quadratic polynomial of the scaled particle size. A family of analytical particle size distributions with the scaled maximum particle size as a parameter is derived, which contains the size distribution of normal grain growth as a genuine limit distribution at ultra-high volume fraction without changing the t1/3-Ostwald ripening kinetics. This reflects an important characteristic feature of particle coarsening at nearly space filling, which was first noted by Ardell and which is in principle in agreement with recent observations. The obtained analytical expressions for the maximum particle size, the particle size distribution and the coarsening rate constant are easy to use for evaluating coarsening data. The results compare well with a number of experimental and simulation results at intermediate and high volume fractions of the second phase.