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aspects of the problem were considered earlier by Wagner ( 1982 ). Respective
theoretical interpretations were presented in several works (Clement et al. 1996 ;
Widmann and Davis 1997 ; Qu and Davis 2001 ; Li and Davis 1995 ). The models
of uptake process were also proposed by Smith et al. ( 2003 ) and Tsang and Rao
( 1988 ).
Data of experimental measurements of mass accommodation efficiencies were
reportedbyLietal.( 2001 ) and Winkler et al. ( 2004 , 2006 ). In two recent papers
(Poschl et al. 2007 ; Ammann and Poschl 2007 ), the authors summarized the state of
art in this problem and tried to unify existing very diverse terminology applied by
different authors working in this direction.
As shown in the review article (Clement 2007 ) and by P¨oschletal.( 2007 ), since
the very end of the last century the discrepancies in approaches to the kinetics of
uptake have almost disappeared. Commonly accepted schemes now assume the
sequential transports of the gaseous reactant through the gas phase, then through the
interface, and then in the bulk of the particle, including possible chemical reactions
inside accompanying the transport process.
This section considers only a part of the uptake process: reactant transport
through the gas phase. Transport in the gas phase is normally assumed to be
described by semi-empirical theories that connect the total flux of the reactant with
its concentration far away from the particle.
The main idea is to replace the semi-empirical approaches by a theory that applies
the Boltzmann kinetic equation with Maxwell's boundary conditions (Cercignani
1975 ) corresponding to noncomplete sticking of the reactant molecule to the particle
surface and to derive analytically the expression for the efficiency of trapping the
reactant molecules. It is possible to do for not very great cost. The final formula
is even simpler than those proposed by the semi-empirical approaches. The theory
itself is also simple and transparent.
Let a particle of the radius a initially containing N B molecules of a substance B
be embedded in the atmosphere containing a reactant A. The reactant A is assumed
to be able to dissolve in the host particle material and to react with B. The particle
will begin to consume A molecules and will do this until the pressure of vapor A
over the particle surface is enough to block the diffusion process. Our task is to find
the consumption rate of the reactant A as a function of time. Next, we focus on
sufficiently small particles whose sizes are comparable to or less than the mean free
path of the reactant molecules in the carrier gas. The mass transfer to such particles
is known to depend strongly on the dynamics of the interaction between incident
molecules and the particle surface. In particular, the value of the probability S p for
a molecule to stick to the particle surface is suspected to strongly affect the uptake
The first simplest theories of mass transfer from gas to particles applied the
continuous models (the particle radius a much exceeds the condensing molecule
mean free path l ). Such models were not able to describe very small particles with
sizes less than l . It was quite natural therefore to try to attack the problem starting
with the free molecule limit, that is, to consider a collisionless motion of condensing
molecules. Respective expressions for the condensational efficiencies had been
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