Convenient analytical formula for cluster mean diameter and diameter dispersion after nucleation burst

We propose an alternative method of estimating the mean diameter and dispersion of clusters of particles, formed in a cooling gas, right after the nucleation stage. Using a moment model developed by Friedlander [S. K. Friedlander, Ann. N. Y. Acad. Sci. 404, 354 (1983)10.1111/j.1749-6632.1983.tb19497.x], we derive an analytic relationship for both cluster mean diameter and diameter dispersion as a function of two of the characteristic times of the system: The cooling time and the primary constituents collision time. These formulas can be used to predict diameter and dispersion variation with process parameters, such as the initial primary constituents' concentration or cooling rate. It is also possible to use them as an input to the coagulation stage, without the need to compute complex cluster generation during the nucleation burst. We compared our results with a nodal code (NGDE) and got excellent agreement.