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

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 p(ε;d) of volume fraction ε of the condensing material for particle diameter d in the outflow of the chamber is typically needed. In this article, analytic equations are derived p(ε;d) 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.

Computational Simulation of Secondary Organic Aerosol Formation in Laboratory Chambers

“…In this section, we highlight the governing equations for a CMFR with reference to those given for a batch reactor. Particle growth in a CMFR has been derived analytically by Seinfeld et al, Kuwata and Martin, and Martin et al…”

“…In this section, we highlight the governing equations for a CMFR with reference to those given for a batch reactor. Particle growth in a CMFR has been derived analytically by Seinfeld et al, 97 Kuwata and Martin, 98 and Martin et al 99 As noted above, in order to operate a CMFR in steady-state mode, a start-up period is required during which the entire gasparticle system comes to a steady state, and in which all the variables of the system are independent of time. The duration of the required start-up period is usually measured in terms of the number of residence times in the reactor, which is determined by the chamber volume and the influent/effluent volumetric flow rate.…”

Humidity Dependence of the Condensational Growth of α-Pinene Secondary Organic Aerosol Particles

“…11 For a given thermodynamic driving force, an upper limit of the condensation rate can be calculated. 6,12,13 The actual condensation rate can be less than the upper limit because of tempering by kinetic inhibition of mass transfer. Inhibition can occur both at the surface and within the particle, possibly including coupling to particle-phase reactions.…”

“…The thermodynamic driving force for the condensation of semivolatile and low-volatility species from the gas phase onto organic particles is governed by the difference between the gas-phase concentration and the particle-phase saturation concentration of the condensable species. , Particle-phase reactions can further increase the net mass transfer of a condensing species . For a given thermodynamic driving force, an upper limit of the condensation rate can be calculated. ,, The actual condensation rate can be less than the upper limit because of tempering by kinetic inhibition of mass transfer. Inhibition can occur both at the surface and within the particle, possibly including coupling to particle-phase reactions. − In some cases, kinetic inhibition can be so significant that the actual condensation rate and hence the growth rates are orders of magnitude less than the upper limit of the thermodynamic driving force.…”

Production and Measurement of Organic Particulate Matter in the Harvard Environmental Chamber

“…Although indoor chambers can carefully control temperature and relative humidity, the intensity and the spectrum from the artificial light are generally different from the natural sunlight, which may affect certain photochemical reactions 14 . Chambers can also be operated as batch reactors or completely mixed flow reactors (CMFR) 22 . Batch reactors are generally easier to operate and maintain but CMFR can be operated for weeks, as needed, to allow for signal integration and thereby work at low, atmospherically relevant concentrations.…”