Sink-limited coarsening

Source/sink-limited coarsening therefore leads to an increase in the mean particle size with the square root of time (f / ). 

Source-Limited Coarsening. During source-limited coarsening, the interfaces surrounding the particles behave as poor sources and sinks, and the coarsening rate then depends upon the rate at which the diffusion fluxes between the particles can be created or destroyed (accommodated) at the particle interfaces. In a simple model, the same assumptions can be made about the source action at the particles as those that led to Eq. 13.24. The rate of particle growth can then be written... 

If the coarsening process is limited by the rate at which atoms diffuse through the matrix from the source particles to the sink particles, it can be shown [13] that the mean particle size of the distribution will increase with time according to... 

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