Concurrent growth and coarsening of spheres

A theory is developed of concurrent growth and coarsening of a dispersion of spheres that accounts for the exchange of heat by diffusion among the spheres due to their curvature differences and between the spheres and the environment due to an externally imposed heat extraction rate. The results show that in concurrent growth and coarsening the average particle radius asymptotically increases with the cube root of time, which is the same behavior as in separate growth and coarsening. The growth rate constant increases linearly with the heat extraction rate, from the LSW value in pure coarsening to a value that is 1.89 times larger in concurrent growth and coarsening with a heat extraction rate that just prevents particles from disappearing due to coarsening interactions. For larger heat extraction rates, coarsening has no effect on the particle growth rate, because the distribution becomes mono-sized.