Collision number, significance

As mentioned earlier, the termolecular reactions, shown in Table 2.5f, are either NO reactions or atom recombinations involving a third-body collision. The activation energies in these reactions are all essentially zero and, indeed, one would not expect to observe termolecular reactions with significant activation energies. Since the collision numbers are very low compared with bimolecular values, the... 

In order to perform such an analysis, equation (14.25) for (which was identified with 6 (2000)) is used as a subcorrelation. Similarly, a representation for the rotational collision number was derived based on experimental information and the Brau-Jonkman formula (Brau Jonkman 1970). Furthermore, it has been assumed that vibrational collision numbers for nitrogen are very large (order of magnitude of 10 ) and will not influence significantly the subcorrelation for 6 (0001). 

Suppose you have a cylinder that contains a certain volume of gas at a certain pressure. When you decrease the volume, the same number of gas particles is now contained in a much smaller space, and the number of collisions increases significantly. Therefore, the pressure is greater. 

We should bear in mind that Arrhenius pre-exponential factors (A = FZ, where P is the steric factor and Z is collision number) are almost equal for all isotopically labeled compounds. Namely, the change of the number of neutrons in nuclei does not significantly influence the value of PZ, because the charge of the species does not change. Investigating different reaction models it was found that A /Aj) was always between 0.7 and 1.2 (for the temperature range 20-2000 K) the absolute minimum was O.S. Thus, we can write ... 

In deriving this relation it has been assumed that the distribution function does not change significantly in a distance b, so that the distribution function describing the number of v2 particles is evaluated at the same point in space as that for the vx particles. Since the number of vx particles is f(r,v1,t)drdv1, the number of collisions between particles of velocity vx and v2 in At is... 

Factorization of the impact operator (5.1) greatly reduces the computational effort required in any variant of IOS [197]. When the inequality (5.43) holds, this factorization is acceptable but only for purely non-adiabatic relaxation as is J-diffusion. Though N2-Ar collisions are mostly non-adiabatic, it would still be better to account for adiabatic-ity, which becomes more significant the higher the rotational quantum number j. 

As described above, the magnitude of Knudsen number, Kn, or inverse Knudsen number, D, is of great significance for gas lubrication. From the definition of Kn in Eq (2), the local Knudsen number depends on the local mean free path of gas molecules,, and the local characteristic length, L, which is usually taken as the local gap width, h, in analysis of gas lubrication problems. From basic kinetic theory we know that the mean free path represents the average travel distance of a particle between two successive collisions, and if the gas is assumed to be consisted of hard sphere particles, the mean free path can be expressed as... 

The first possibility is that the attractive potential associated with the solid surface leads to an increased gaseous molecular number density and molecular velocity. The resulting increase in both gas-gas and gas-wall collision frequencies increases the T1. The second possibility is that although the measurements were obtained at a temperature significantly above the critical temperature of the bulk CF4 gas, it is possible that gas molecules are adsorbed onto the surface of the silica. The surface relaxation is expected to be very slow compared with spin-rotation interactions in the gas phase. We can therefore account for the effect of adsorption by assuming that relaxation effectively stops while the gas molecules adhere to the wall, which will then act to increase the relaxation time by the fraction of molecules on the surface. Both models are in accord with a measurable increase in density above that of the bulk gas. 

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