RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 10, ES1005, doi:10.2205/2007ES000275, 2008
[13] The particle growth is described by the continuity equation
![]() | (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)
![]() | (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],
![]() | (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.
![]() | (5) |
where N(b,t) is the size distribution of the preexisting particles and K(a, b) is the coagulation efficiency
![]() | (6) |
Here
a, b are the radii of the colliding particles,
is the thermal velocity,
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,
where
n is the kinematic viscosity of air,
rair is the air density and
C is the correction factor
[Phillips, 1975],
![]() | (7) |
![]() |
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.
Citation: 2008), A model of nucleation bursts, Russ. J. Earth Sci., 10, ES1005, doi:10.2205/2007ES000275.
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