Mean free path concept

In this section the determination of the transport properties, i.e., using the empirical method suggested by Maxwell [65], on the basis of Clausius mean free path concept is outlined. 

That is, instead of determining the transport properties from the rather theoretical Enskog solution of the Boltzmann equation, for practical applications we may often resort to the much simpler but still fairly accurate mean free path approach (e.g., [12], section 5.1 [87], chap. 20 [34], section 9.6). Actually, the form of the relations resulting from the mean free path concept are about the same as those obtained from the much more complex theories, and even the values of the prefactors are considered sufficiently accurate for many reactor modeling applications. 

The overall aim in this analysis is to determine a rough estimate of the transfer fluxes in dilute one-component gases using the elementary mean free path concept in kinetic theory. In this approach it is assumed that the only means for transport of information in the fluid is via molecular collisions. Due to the physical similarity of the flux phenomena of mass, momentum and energy, a common mathematical formalism is outlined (e.g., [104] app E [61] sect 3.4.2 [77] sect 3-4 [39] sect 2). 

Considering a dilute gas containing n molecules per unit volume inducing a macroscopic transfer flux of property tp. The symbol tp denotes any property of a single molecule that can be changed by collisions, and ( 0)m represents the average value of tp for the gas. The molecules are assumed to move in a 

At each collision it is assumed to be an equalizing transfer of properties between the two molecules, so in consequence is determined by the relative location of the last collision experienced by a molecule before it crosses the plane at 2 = 21. This particular distance is thus expected to be related to the mean free path, /. It is supposed throughout that the mean free path is small compared to the dimensions of the vessel containing the gas. 

---

One of the most usefiil applications of the mean free path concept occurs in the theory of transport processes in systems where there exist gradients of average but local density, local temperature, and/or local velocity. The existence of such gradients causes a transfer of particles, energy or momentum, respectively, from one region of the system to another. 

Mean Free Path Concept 315 The mean free path can then be determined from (2.512) and (2.511) ... 

From the above it should be evident that the mean free path concept has become one in which people are concerned about details that will allow them to make estimates to better than 20%. Where the mean free path is desired for an approximate calculation, expression (10.5) and the cross-section from (10.6) should be adequate if one can not employ the values of Table 4 (p. 483). 

---