Population Balance for Gas Phase Synthesis

If the chemical reaction is fast, as with a high powered laser beam, the nucleation will take place instantaneously, giving an initial burst in the population resulting in the boundary condition 

FIGURE 7,10 Schematic of population, Tjir), in a plug flow reactor. 

With a single nucleation event, the population that nucleates at t = 0 has an invariant shape or self-preserving size distribution (i.e., a delta function in this case) with respect to t = x/u — r G — —r JG. As the particles move down the flame front, they increase in size according to the following equation  

This model is an idealized simplification of gas phase reactions. 

One case that is common in gas phase powder synthesis occurs when, after nucleation, the growth is controlled by the chemical reaction. In this case, the mass flux due to chemical reaction can be related to the growth rate, giving 

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