Condensation rate of trace vapor on Knudsen aerosols from the solution of the Boltzmann equation

Sitarski, Marek; Nowakowski, B.

doi:10.1016/0021-9797(79)90187-5

Cited by 52 publications

(19 citation statements)

References 13 publications

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“…β M is the transition regime correction for mass transfer which has been considered by several workers; e.g. Fukuta and Walter (1970); Sitarski and Nowakowski (1979); Dahneke (1983);Loyalka (1983). Here, we apply the formula derived by Fuchs and Sutugin (1970) …”

Section: Discussionmentioning

confidence: 99%

Commentary on cloud modelling and the mass accommodation coefficient of water

et al. 2005

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Abstract. The mass accommodation coefficient of water is a quantity for which different experimental techniques have yielded conflicting values in the range 0.04-1. From the viewpoint of cloud modelling, this is an unfortunate situation, since the value of the mass accommodation coefficient affects the model results, e.g. the number concentration of activated cloud droplets. In this commentary we note that in cloud modelling, the primary quantity of interest is the droplet growth rate rather than the mass accommodation coefficient, and that experimental investigations of droplet growth rates provide more direct verification of cloud models than do measurements of the mass accommodation coefficient. Furthermore, we argue that the droplet growth rates calculated in cloud model studies are consistent with experimental results obtained so far only if a mass accommodation coefficient of unity is applied.

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Section: Discussionmentioning

confidence: 99%

Commentary on cloud modelling and the mass accommodation coefficient of water

et al. 2005

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“…As an alternative, Fuchs and Sutugin (1970) later interpolated Sahni's (1966) solution to the Boltzmann equation for neutron absorption by a black body, giving an expression for β for all ratios of the colliding entities' persistence distance to particle radius. Collision kernel expressions for particle collisions with small entities have also been proposed by Loyalka (1973Loyalka ( , 1982, Seaver (1984), and Sitarski and Nowakowski (1979). Experimental measurements (Davis and Ray 1978;Ray et al 1979;Li and Davis 1996; of evaporation, the reverse process) show reasonable agreement with these expressions in the transition regime, with particularly good agreement with the Fuchs-Sutugin expression; thus, it is the most widely used expression to describe particle-vapor molecule collisions (Kuang et al 2009).…”

Section: Introductionmentioning

confidence: 87%

“…While both Equations (2) and (3) apply exactly in the continuum and free molecular limits, respectively, aerosol particles in atmospheric pressure environments typically have radii ranging from tens to hundreds of nanometers. In this "transition regime" (Brock 1966;Sitarski and Nowakowski 1979), the continuum and free molecular collision models break down. Motivated by this issue, a variety of approaches have been used to determine transition regime collision kernels, with work on this topic dating back over 65 years.…”

Section: Introductionmentioning

confidence: 99%

Determination of the Transition Regime Collision Kernel from Mean First Passage Times

Gopalakrishnan

Hogan

2011

Aerosol Science and Technology

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Particle-vapor molecule (condensation) and particle-particle (coagulation) collision kernels are critically important parameters for the description of particle size distribution evolution in aerosols. We use mean first passage time calculations to find a dimensionless form of the collision kernel that applies in the limit where the ratio of the masses of colliding entities (aerosol particles or vapor molecules) to gas molecule mass, Z, approaches infinity, and the colliding entities are dilute in concentration. In these calculations, the motion of colliding entities is monitored with Langevin dynamics, and the collision kernel is inferred from the time required for collision. The presented analysis reveals that the dimensionless collisional kernel (H) is a function solely of the diffusive Knudsen number (Kn D , the square root of the product of kT and the reduced mass divided by the product of the reduced friction factor and collision radius), and a number of commonly used expressions for the collision kernel also collapse to the functional form H(Kn D ), irrespective of whether they were derived for Z → ∞ or Z → 0 conditions. The examined collision kernel expressions are further found to agree within 10% of our calculations as well as with each other across the entire Kn D range. This result suggests that a single collision kernel can be used to describe all transition regime collision rates, i.e., both condensation and coagulation rates, with reasonable accuracy, and establishes that Langevin-equationbased mean first passage time calculations can serve as a simple approach to examine transition regime collision phenomena.

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“…The same method of linearization has been applied in the kinetic theory of condensation by Sitarski and Nowakowski (1979). Accordingly, the above Eqs.…”

Section: The Thirteen-moment Equationsmentioning

confidence: 99%

“…Analysis of transport of vapor molecules to/from the absorbing droplet surface. In this part, the isothermal condensation theory by Sitarski and Nowakowski (1979) is utilized. II.…”

Section: Introductionmentioning

confidence: 99%

Brownian Coagulation of Knudsen Particles on Evaporating/Condensing Aerosol Droplet; Modeling of Capture of Soot Particles by Marine Fog

Sitarski

2012

Aerosol Air Qual. Res.

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The theoretical model presented in this work allows quantitative prediction of the rate of Brownian coagulation of pollutant particles on a condensing aerosol droplet. The coupling of the processes of condensation and Brownian coagulation is established through the hydrodynamic-diffusiophoretic force acting upon the Brownian particles in the vicinity of the droplet. The new analytical approach is based on the Grad's moment method of solution to the Fokker Planck equation. The aerosol system is assumed to be isothermal and close to the thermodynamic equilibrium (i.e., the condensation and coagulation fluxes are small). The numerical predictions of the diffusiophoretic enhancement of Brownian coagulation rates are provided for NaCl-water droplets capturing small (primary) soot particles. The results of calculations show substantial enhancement (10 to 200 times) of the capture of soot particles by the condensing marine droplets for typical conditions that occur on the north-eastern coast of the U.S.A.

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Condensation rate of trace vapor on Knudsen aerosols from the solution of the Boltzmann equation

Cited by 52 publications

References 13 publications

Commentary on cloud modelling and the mass accommodation coefficient of water

Commentary on cloud modelling and the mass accommodation coefficient of water

Determination of the Transition Regime Collision Kernel from Mean First Passage Times

Brownian Coagulation of Knudsen Particles on Evaporating/Condensing Aerosol Droplet; Modeling of Capture of Soot Particles by Marine Fog

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