Mean Free Path and Related Properties

MEAN FREE PATH AND RELATED PROPERTIES OF GASES... 

Mean Free Path and Related Properties of Gases.6-57... 

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. 

Unfortunately, even though (9.5) provides valuable insights into the dependence of X.BB on the gas concentration and molecular size, it is not convenient for the estimation of the mean free path of a pure gas, because one needs to know the diameter of the molecule ob, a rather ill-defined quantity as most molecules are not spherical. To make things even worse, the mean free path of a gas cannot be measured directly. However, the mean free path can be theoretically related to measurable gas microscopic properties, such as viscosity, thermal conductivity, or molecular diffusivity. One therefore can use measurements of the above gas properties to estimate theoretically the gas mean free path. For example, the mean free path of a pure gas can be related to the gas viscosity using the kinetic theory of gases... 

Both the rarefaction and compressibility effects are a function of the Kn that determines the degree of nonequilibrium of the gas flow. For the continuum fiow regime, thermodynamic equilibrium has to be maintained which means that the mean free path must be smaller than the characteristic length (/sTn = j 1). Typically, in order to obtain a stable estimation of the macroscopic properties, the ratio, Ub > 100, should be satisfied. For gas microflows, the effects of compressibility and rarefaction are linked and tend to craiflict with each other. The Kn is also related to the Reynolds number. Re, and the Mach number, Ma, with the relation... 

In particular it allowed description of two unexpected and remarkable properties, that we consider now. For a perfect gas the mean free path is approximately related to the radius R of the gas molecules by... 

This equation relates the measurable properties of the system (viz. the area ratios of the F g and F2s peaks), and the film thickness and electron mean free paths. Denoting the measured ratios for the fluorinated films by y and the infinity values measured for simple... 

From fundamental aspects, nanosized structures exhibit quite different properties compared to their parent bidk-like materials (Norris and Bawendi 1995). Thus, the electronic density of states related to nanoparticles exhibits quantified features in similar way as the optical emission spectra might be related to those of artificial atoms (Kagan et al. 1996). The quantum confinement effect alters both electrons and phonons mean-free paths in the nanostructures. The consequence on the electronic features lies in the bandgap widening for semiconducting... 

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