RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 10, ES1005, doi:10.2205/2007ES000275, 2008

Details of the Model

[13]  The particle growth is described by the continuity equation

eq003.gif(2)

Here n=n(a,t) is the distribution of the aerosol particles over their size a so that n(a,t)da is the number concentration of the particles in the size interval [a, a+da]. a is the particle growth rate (the change of the particle size at a time)

eq004.gif(3)

where vT is the thermal velocity of a condensing molecule, V0 is the volume of one condensing molecule, and C=C(t) is the number concentration of the condensing molecules in the gas phase. This expression is valid in the free-molecule regime. If, however, we wish to consider larger particles another formula should be used. It is commonly accepted to use the Fuchs-Sutugin formula. Here we prefer another expression derived in [Lushnikov and Kulmana, 2004],

eq005.gif(4)

Here D is the molecular diffusivity of the condensing species. This formula reproduces the results obtained with the aid of the Fuchs-Sutugin formula. In contrast to the latter equation  (4) does not operate with such not well defined values like the molecular mean free path. The diffusivity enters instead.

[14]  The coagulation sink l is either a fitting parameter or can be calculated if we believe that the main cause for the particle sink is the intermode coagulation with the particles of preexisting aerosol.

eq006.gif(5)

where N(b,t) is the size distribution of the preexisting particles and K(a, b) is the coagulation efficiency

eq007.gif(6)

Here a, b are the radii of the colliding particles, eq008.gif is the thermal velocity, eq009.gif is the reduced mass, with ma, mb being the masses of colliding particles, Da,b=Da+Db is the diffusivity of the colliding pair, Da, Db are the diffusivity of each particle (should be found for the transition regime). The diffusivity D(a) is given by the formula, eq010.gif where n is the kinematic viscosity of air, rair is the air density and C is the correction factor [Phillips, 1975],

eq011.gif(7)

eq012.gif

where c1= (2-s)/s, c2=0.5 - s, with s being a factor <1 entering a slip boundary conditions (equation (9)). The Knudsen number Kn=(l/a with l being the mean free path of the carrier gas molecules. The parameter s changes within 0.79-1. Equation (7) describes the transition correction for all Knudsen numbers and gives the correct limiting values (continuous and free-molecule ones).

[15]  J(a,t)=J(t)f(a) is the source productivity of the stable embryos. The function f(a) describes the size dependence of the embryos produced by cooperative action of nucleation and intra-mode coagulation.


RJES

Citation: Lushnikov, A. A., Yu. S. Lyubovtseva, and M. Kulmala (2008), A model of nucleation bursts, Russ. J. Earth Sci., 10, ES1005, doi:10.2205/2007ES000275.

Copyright 2008 by the Russian Journal of Earth Sciences

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