Continuity Equation

Let be the PSD of a precipitate phase, the number of particles per unit volume, the mean radius and the particle volume fraction, is expressed as

[Eq. 1]         

[Eq. 2]         

[Eq. 3]         

The time evolution of follows the continuity as in Langer and Schwartz [1980Lan].

[Eq. 4]         

Where is the growth rate of a particle of size , and is the distributed nucleation rate, which is defined by

[Eq. 5]         

where is the nucleation rate.

Reference

[1980Lan] J. S. Langer, A. J. Schwartz, Kinetics of nucleation in near-critical fluids. Phys. Rev. A. 21, 948–958 (1980).