Nitrogen mean free path

To be specific let us have in mind a picture of a porous catalyst pellet as an assembly of powder particles compacted into a rigid structure which is seamed by a system of pores, comprising the spaces between adjacent particles. Such a pore network would be expected to be thoroughly cross-linked on the scale of the powder particles. It is useful to have some quantitative idea of the sizes of various features of the catalyst structur< so let us take the powder particles to be of the order of 50p, in diameter. Then it is unlikely that the macropore effective diameters are much less than 10,000 X, while the mean free path at atmospheric pressure and ambient temperature, even for small molecules such as nitrogen, does not exceed... 

When bounding walls exist, the particles confined within them not only collide with each other, but also collide with the walls. With the decrease of wall spacing, the frequency of particle-particle collisions will decrease, while the particle-wall collision frequency will increase. This can be demonstrated by calculation of collisions of particles in two parallel plates with the DSMC method. In Fig. 5 the result of such a simulation is shown. In the simulation [18], 2,000 representative nitrogen gas molecules with 50 cells were employed. Other parameters used here were viscosity /r= 1.656 X 10 Pa-s, molecular mass m =4.65 X 10 kg, and the ambient temperature 7 ref=273 K. Instead of the hard-sphere (HS) model, the variable hard-sphere (VHS) model was adopted in the simulation, which gives a better prediction of the viscosity-temperature dependence than the HS model. For the VHS model, the mean free path becomes ... 

The mean free path X, of a molecule in air can be calculated from the sizes of the molecules involved. The most probable collision partners for a trace molecule (such as CFC-12) in air are molecular nitrogen (N2) and oxygen (02). The trace molecule i is hit whenever its center gets closer to the center of an air molecule than the critical distance, rcrit = r, + rair (Fig. 18.8). Picturing the molecules as spheres, the molecular radius r, can be estimated from the collision cross-section A listed in chemical handbooks such as the Tables of Physical and Chemical Constants (Longman, London, 1973) ... 

Table 10.1 Dependence of the typical mean free path A and time for monolayer coverage r (assuming a sticking coefficient of one) on pressure P for nitrogen at 20°C.

In general, low electron concentration and high mobility appear to depend most critically on reduction in nitrogen vacancies and a morphology in which polycrystallinity is not disadvantageous, provided crystallite interfaces are intimate and sizes are significantly larger than the mean free path determined by other scatterers. 

Example. At 27 C and 1 atm pressure, the coefficient of viscosity of nitrogen gas is 178 pP (i.e., micropoise). Calculate, (a) the mean free path X, and (b) the collision diameter o of nitrogen molecule using the Chapman equation. 

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