where t is time, z is altitude, and $i is the total vertical diffusive flux. The net production term Ci from collisionally driven reactions is determined from the expression
j i where vlj is the reactant stoichiometric coefficient of species l involved in each collisional reaction j with forward reaction rate kj (T,p). We recall that the general elementary reaction can be written as
where Xi is species l taking part in reaction j, vj is the product stoichiometric coefficient and ^lj is the net stoichiometric coefficient for species l, given by
so that ^ij < 0 if species l is a reactant species and ^lj > 0 if it is a product species. As an example, in the bimolecular collisional reaction
The net photolysis production term Pi of species i is determined from the expression
k for each photolysis reaction k with rate jk and
so that ^ik < 0 if species i is a photolyzed species and ^ik > 0 if it is a photolysis product species. As an example, in the photolysis reaction
7.3 Brownian and turbulent diffusion
Let us define l as the mean free path between collisions between like molecules undergoing random thermal motion (Brownian). If v is the mean velocity of the molecules then the frequency of collision is f = v/l (s-1). For an isotropic velocity distribution one third of the molecules will move in the X-direction and of these half will go forward. Thus, the number of collisions in the forward direction will be vn/6l, where n is the particle density in molecules cm-3. For molecules moving along the X-axis towards the origin x = 0, the probability of reaching the origin after colliding at x without further collisions is e-x/l. Thus, the change in the net flux $ in the positive x-direction about x = 0 is d(f>=—n(x)e-x/ldx, (7.10)
6l on integrating, we get the flux at the origin r0 f œ
Now, for atmospheres the mean free path is very small compared to distances over which the density is changing (see next section), thus we can consider small gradients in the number density about x = 0 and so through a Taylor expansion we obtain dn n(x) =n0 + i - +..., (7.12)
dx 0 so that
and so we can write
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