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Depending on the application, spontaneous nucleation of particles can occur due to the transfer of molecules from the primary phase. For example, in crystallization from solution, the first step is the phase separation or "birth'' of new crystals. In boiling applications, the creation of the first vapor bubbles is a nucleation process referred to as nucleate boiling.
The nucleation rate is defined through a boundary condition as shown in Equation 2.2-2.