An Analytic Equation for the Volume Fraction of Condensationally Grown Mixed Particles and Applications to Secondary Organic Material Produced in Continuously Mixed Flow Reactors

Abstract

<div><p>Secondary condensation of organic material onto primary seed particles is one pathway of particle growth in the atmosphere, and many properties of the resulting mixed particles depend on organic volume fraction. Environmental chambers can be used to simulate the production of these types of particles, and the optical, hygroscopic, and other properties of the mixed particles can be studied. In the interpretation of the measured properties, the probability density function <i>p</i>(<i>ϵ</i>;<i>d</i>) of volume fraction <i>ϵ</i> of the condensing material for particle diameter <i>d</i> in the outflow of the chamber is typically needed. In this article, analytic equations are derived <i>p</i>(<i>ϵ</i>;<i>d</i>) for condensational growth in a continuously mixed flow reactor. The equation predictions are compared to measurements for the condensation of secondary organic material on quasi-monodisperse sulfate seed particles. Equations are presented herein for discrete, Gaussian, and triangular distribution functions for the seed particle number–diameter distributions, including generalization to any linearly segmented distributions. The analytic equations are useful both for the interpretation of laboratory data from environmental chambers, such as the construction of probability density functions for use in interpretation of hygroscopic growth data, cloud–condensation–nuclei data, or other laboratory data sets dependent on organic volume fraction, as well as for understanding atmospheric processes at times that condensational growth processes prevail.</p><p>Copyright 2014 American Association for Aerosol Research</p></div