Schematic of metastable zone

Particle growth refers to an increase in particle size due to separation of material from solution. The growth rate is often mass transfer controlled and is given by  

The literatme on crystallization kinetics [95, 96, 97] have discussed several mathematical expressions depending upon the process complexity for each of the mentioned mechanisms. For example, growth can be size-independent or size-dependent, it can have a constant value, or it may be a function of thermodynamic parameter like solubility. Thus, the selection of proper kinetics specific to the batch crystallization process is a very essential part in process modeling. 

One of the first models for crystal growth is McCabe AL law and is given by the following size independent rate. 

Nucleation involves formation of solid particles from solution. Nucleation is characterized by both primary and secondary nucleation rates. The primary nucleation occurs in the solution spontaneously without any solids (seeds) present but secondary nucleation starts in the presence of solid interface. The rates are generally 

The primary nucleation in general is a function of supersaturation and can be given by the following function 

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