Flow regime collision-dominated

CVD reactors operate at sufficiently high pressures and large characteristic dimensions (e.g., wafer spacing) such that Kn (Knudsen number) << 1, and a continuum description is appropriate. Exceptions are the recent vacuum CVD processes for Si (22, 23) and compound semiconductors (156, 157, 169) that work in the transition to the free molecular flow regime, that is, Kn > 1. Figure 7 gives an example of SiH4 trajectories in nearly free molecular flow (Kn 10) in a very low pressure CVD system for silicon epitaxy that is similar to that described by Meyerson et al. (22, 23 Meyerson and Jensen, manuscript in preparation). Wall collisions dominate, and be-... 

The reader may be surprised not to And a Reynolds number defined speciflcally for the disperse phase. This is because the disperse-phase viscosity is well defined only for Knp 1 (i.e. the collision-dominated or hydrodynamic regime). In this limit, Vp oc oc Knp/Map so that the disperse-phase Reynolds number would be proportional to Map/Krip when Map < 1. However, in many gas-particle flows the disperse-phase Knudsen number will not be small, even for ap 0.1, because the granular temperature (and hence the collision frequency) will be strongly reduced by drag and inelastic collisions. In comparison, molecular gases at standard temperature and pressure have KUp 1 even though the volume fraction occupied by the molecules is on the order of 0.001. This fact can be... 

In the transition regime, the rarefaction effects dominate and the intermolecular collisions need to be taken into account. For the free-molecular flow, intermolecular collisions can be considered negligible when compared to the probability of the molecule colliding with the wall surface. As the flow enters the transition flow regime and continues into the free-molecular flow regime, the Kn becomes significant enough that the molecular approach has to be utilized. Thus, the Boltzmann equation... 

It is evident from the above discussion that there must be a wide range of conditions under which both Knudsen and molecular diffusion are significant. Indeed, in a given adsorbent it is quite possible for molecular diffusion to be dominant in the larger pores while Knudsen flow is dominant in the smaller pores. Because of the dependence of mean free path on pressure, for any given adsorbent and adsorbate there will be a transition from molecular diffusion at high pressure to Knudsen flow at low pressures. In the intermediate regime both wall collisions and intermolecular collisions contribute to the diffusional... 

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