Asymptotic evaluation of probability density functions for mean aerosol particle formation rates by homogeneous nucleation in turbulent gas jets

Mean aerosol particle formation rates resulting from homogeneous nucleation in turbulent gas jets are evaluated using a probability density function (pdf) for temperature and vapor concentration fluctuations in the gas phase. Nucleation rates are assumed to depend sensitively on the gas-phase conditions, allowing asymptotic analysis to be used for evaluating mean particle formation rates. The asymptotic analysis shows that to leading order, the overall shape of the pdf does not matter significantly when calculating mean particle formation rates. Instead, mean particle formation rates are essentially linearly proportional to the value of the pdf where an exponential term in the expression for particle nucleation rates is maximized. Homogeneous nucleation rates of particles in turbulent gas jets may thus potentially be controlled by suitable modifications of the value of the pdf only in the region of the pdf where particle nucleation rates are maximized. Asymptotic analyzes for mean particle formation rates compare favorably with results obtained using numerical integration.