Aerosol nucleation and growth during laminar tube flow. II: quenching effects and wall condensation

Abstract

Homogeneous nucleation during the flow of a vapour–gas mixture along a tube with cooled wall is considered in cases where nucleation is “self-quenching”, that is, vapour depletion by the condensational growth of previously nucleated particles is sufficient to reduce the vapour saturation to a level where nucleation is negligible. Approximate results are derived by matching the rate of rise of the nucleation rate, ignoring vapour depletion, to its rate of fall due to condensational growth alone. The nucleation rate when these two rates are equal is identified as its peak value J p, and 2 J p divided by the rate gives the number of particles nucleated. Agreement between this approximation and accurate numerical results for dibutyl phthalate vapour in Nitrogen is very good for the cases considered. For moderate inlet–wall temperature differences, particle production is roughly constant over much of the tube cross-section but falls near the wall. However, for large temperature differences, a peak in particle production occurs near the wall, due to the very rapid rate of change in conditions there. As the nucleation increases, the fraction of inflowing vapour condensing on the wall decreases and an approximate analytic formula for this fraction is presented. This formula is very accurate provided more than about 20% of the vapour condenses on the wall. For lower wall condensation fractions, the formula under predicts the aerosol mass, however these results ignore the effect of particle deposition. The influence of seed aerosol on quenching nucleation is considered and found to depend on whether significant particle production occurs near the wall. An estimate of deposition by thermophoresis suggests that it is negligible for moderate wall–inlet temperature differences, but important for high temperature differences where there is significant particle production and growth near the wall.