Volume Reaction-Controlled Growth

Finally, we consider the case in which the rate of growth is controlled by the conversion of dissolved A to a second species B. This case corresponds to the dissolution of A in a liquid particle and its subsequent reaction and conversion to a product B. The sequence can be depicted as 

If the concentration of dissolved A is Cv and the rate of conversion to B is first order, with rate constant the rate of gain of particle mass due to volume reaction is 7t At steady state this rate must equal the rate of diffusion of molecules of A to the particle. Thus 

When the rate-determining step is the volume reaction, the second term in the denominator of (12.132) dominates the first term and (12.132) reduces to 

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The main objective of this section is to theoretically compare aerosol size spectra evolving by the mechanisms of diffusion-, surface reaction-, and volume reaction-controlled growth. The results will provide a basis for the interpretation of atmospheric and laboratory aerosol size spectra with respect to the original growth mechanisms. 

The crystallisation reaction is surface-controlled rather than volume diffusion-controlled. The rate constant was found to be independent of the stirring speed and the apparent activation energy for growth was deter-... 

The following can be assumed to simplify this problem (1) local equilibrium exists at the interface between the crystal and the liquid, i.e. diffusion-controlled growth takes place (2) the sohdification occurs in a steady state (3) dilute-solution approximation is permitted for diffusion of Pr (4) Ba and Cu ions are Raoultians (5) the difference between unit volume of crystal and that of the Ba—Cu-0 solvent is negligible, therefore the supersaturation estimated for the mole fraction causes crystallization of the same volume fraction and the growth rate of the crystal can be calculated from the supersaturation in the solution given by the mole fraction (6) the interface of the solidifying crystal is planar (7) the peritectic reaction takes place isothermally (8) thermo-physical properties are constant. 

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