Geoscience Reference

In-Depth Information

0.70

0.65

0.60

0.55

0.50

0.45

0.40

0.35

0.30

0.0

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.