Geoscience Reference
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0.2 0.4 0.6 0.8 1.0
TEMPERATURE RATION (infinity/particle surface)
Fig. 3.23
Dependence of the modifier at the reduced size 1 on the temperature ratio T 1 =T
changes to the initial and boundary conditions. The question thus arises: whether
is it necessary to have accurate expressions for the rate of elementary atmospheric
processes such as those considered here? The answer is still positive. The point is
that respective deterministic equations can be replaced by the stochastic analogues,
where the respective rates will enter the expressions for the rates of transitions
between different states. In this case, the analytical expressions for the respective
rates are absolutely irreplaceable.
In this chapter, I tried to demonstrate a simple trick (flux-matching procedure)
allowing one to operate in a very difficult situation: I mean the transition regime,
where it is necessary to solve the Boltzmann equation. Although in principle it is
possible to do numerically, the problem is how to apply these numerical results to
concrete atmospheric situations. The most striking example is the rate of particle
charging. If one needs to average over a group of boundary conditions, it would be
necessary to solve the Boltzmann equation many times.
In principle, the problem can be resolved by applying semi-empirical formulas.
But, undoubtedly, it is much better to handle the expressions derived from some
known and readily controllable principles, as has been done in this chapter.
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