Diffusion-Controlled Evaporation of an Aerosol Droplet

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Diffusion-controlled evaporation of aerosol droplets in an ambient gas is important in various engineering and scientific fields, such as premixing air and fuel, ink-jet printing, spraying of pesticides, biochemical assays, and atmospheric pollution. For isothermal, quasi-steady evaporation, Maxwell [1], showed that the time rate of change of the droplet radius is given by



where is the binary diffusion coefficient for the vapor molecules of species in a surrounding continuous phase , is the vapor pressure of species , is the molecular weight of species , and is its density. The quantities and are the temperature of the surrounding phase and the universal gas constant, respectively. Under isothermal conditions the surface area of the evaporating drop is given by

, where .

The binary diffusion coefficients can be predicted from the kinetic theory of gases using the Chapman–Enskog theory with a Lennard–Jones (6-12) potential [2]. The vapor pressure of species at temperature can be related to a reference temperature by applying the Clausius–Clapeyron equation:


where is the heat of vaporization of species .

In this Demonstration you can select an aerosol compound from a family of commonly used plasticizers that have low vapor pressures: DOP (dioctyl phthalate), DBP (dibutyl phthalate), and DBS (dibutyl sebacate). The necessary thermodynamic properties for the plasticizers are taken from [3]. You can also select species for the surrounding gas phase. Using the sliders, you can specify the temperature , the pressure of the surrounding gas phase, the initial aerosol droplet radius , and the evaporation time . Then using the pull-down menu you can view: (1) a plot of versus ; (2) an image of the drop (relative to its initial size) at a specified evaporation time ; and (3) the droplet properties displayed in tabular form at time . Note: in the droplet properties table denotes the evaporation time such that . To accommodate the wide range of values for different diffusion experiments, the evaporation time slider is reset to when any of the other controls are changed.


Contributed by: Brian G. Higgins and Housam Binous (February 2013)
Open content licensed under CC BY-NC-SA




[1] J. C. Maxwell, The Scientific Papers of James Clerk Maxwell, Vol. II, (W. D. Niven, ed.), Cambridge, England: Cambridge University Press, 1890 p. 625. archive.org/details/scientificpapers02maxwuoft.

[2] R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, 2nd ed., New York: John Wiley & Sons, 2002.

[3] A. K. Ray, E. J. Davis, and P. Ravindran, "Determination of Ultra-Low Vapor Pressures by Submicron Droplet Evaporation," Journal of Chemical Physics 71(2), 1979 pp. 582–587. doi:10.1063/1.438408.

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