Molecular flow conditions

Molecular Flow Under molecular flow conditions, conductance is independent of pressure. It is proportional to with the pro-... 

Equation (1.7) is the general equation for any individual component of the system under molecular flow conditions and with it one can calculate the overall pumping time for a system, if the conductances of the individual components of the system are known. The effective pumping speed at any point along the vacuum line is given by ... 

In the case of an orifice, Pr = 1. For other types of pipes and ducts Pr < 1. A significant part of assessing molecular flow in ducts involves the estimation of Pr. An initial assumption is that molecules arrive at the entrance plane of a duct with an isotropic velocity distribution. Conductance under molecular flow conditions is independent of the pressure but obviously the throughput is proportional to the Ap as stated by the definition of C (e.g Equation (2.6)). 

Manufacturers of vacuum components often state conductance values (for N2 or air, under molecular flow conditions) for such products. If a conductance value, either calculated or measured, is known for gas A, its value for gas B (at the same temperature) is readily calculated. For example, under molecular flow conditions ... 

Fig. 19. Apparatus for the study of atom reactions under molecular flow conditions. (Courtesy Wood [72].)...

The model of ideal linear gas chromatography (Equation 1) [12] also describes the transport of a chemical species in the temperature gradient of a vacuum tube. At molecular flow conditions the linear velocity of the carrier gas, which is identical to the transport velocity of the adsorbate in the gas phase, has to be substituted by the fraction of the column length over the average retention time of the species in the column ... 

Fig 2. Trigonometry of an adsorbate jump at molecular flow conditions in a cylindrical tube... 

Fig. 16. (a) SFG spectra of CO adsorbed on the polycrystalline Pt foil recorded at different substrate temperatures at a CO pressure of 10 mbar. SFG intensity is plotted versus the frequency of the tunable IR laser. Experimental data points are represented by crosses, the solid lines represent results of least-squares fits. Details of the fitting procedure are described in the text. The depicted SFG spectra are on the same vertical scale, (b) TPD spectra of CO obtained under molecular flow conditions recorded after the corresponding SFG measurements shown in (a). Desorption was started at different substrate temperatures at the same CO pressure of 10 mbar. All TPD spectra are also on the same vertical scale. 

Farber et al. (JL) also performed weight loss experiments under molecular flow conditions by allowing hydrogen to flow over... 

Although very useful, the above solution to heat transfer under slip flow and molecular flow conditions, is rather tedious leaving a definite incentive for simplification. Extension of this treatment to other geometrical shapes and elimination of the trial-and-error solution might be the next objective. 

At the low pressures required for these experiments (< 10 7 torr), the molecular mean free path is very large compared with the dimensions of the vessel and molecular flow conditions operate. The rate of pumping is thus directly proportional to the pressure and is written as RP = FP, where F is the system pumping speed (conveniently expressed in units molecules torr-1s-1). At steady state, dP/dt — 0 assuming no desorption, so that PD = 0, we have... 

Although several mathematical treatments model the gas flow in filters under free molecular flow conditions, their detailed discussion is beyond the scope of this chapter. In order for a filter to perform in the free molecular regime the ambient pressure would need to be much less than atmospheric or the fibers would need to be on the order of 10 nm. However, these models... 

For thin channel, that is, A>h, free molecular flow condition can be assumed. Here, the intermolecular collisions are negligible in comparison to the interaction of molecules with the surface. Let us assume the molecule wall interaction to be specular (o- = 0) and explain the thermal creep phenomena observed experimentally. 

When the mean free path for collision is long, the molecules move independently of each other and the flow is called molecular flow. In molecular flow conditions, backstreaming may be appreciable. All oil-sealed and oil vapor vacuum pumps show some degree of backstreaming that contributes to surface contamination in the deposition system. Knudsen flow is the transition region between viscous flow and molecular flow regimes. 

In the case in which molecular flow conditions are satisfied, one can easily calculate the conductance. For example, for a straight cylindrical tube of length L and diameter D... 

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