Theory of Ostwald ripening: Competitive growth and its dependence on volume fraction

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Abstract
The theory of Ostwald ripening is extended to include the dependence on the volume fraction of the minority phase. The size distribution function for droplets of the minority phase and the power laws of the time dependences are derived for the late stages of phase separation. The asymptotic distribution function is found to be independent of initial conditions but does depend on the equilibrium volume fraction associated with a given quench. We show that the average radius grows as t1/3 and the density of droplets decays as t−1. The growth law and the amplitudes for these temporal power laws derivate from their value in the limit of zero volume fraction as the square root of the volume fraction. The effect of competition among droplets causes the distribution to broaden and to increase the coarsening rate.

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