Knudsen gas

Knudsen GA, Jacobs LM, Kuester RK, Sipe IG (2007) Absorption, distribution, metabolism and excretion of intravenously and orally administered tetrabromobisphenol A (2,3-dibromopropyl ether) in male Fischer-344 rats. Toxicology 237 158-167... 

In connection with multiphase diffusion another poorly understood topic should be mentioned—namely, the diffusion through porous media. This topic is of importance in connection with the drying of solids, the diffusion in catalyst pellets, and the recovery of petroleum. It is quite common to use Fick s laws to describe diffusion through porous media fJ14). However, the mass transfer is possibly taking place partly by gaseous diffusion and partially by liquid-phase diffusion along the surface of the capillary tubes if the pores are sufficiently small, Knudsen gas flow may prevail (W7, Bl). 

To distinguish between the viscous and Knudsen gas-phase flows (Section 5.8.2), the ratio between the mean free path, X, and the characteristic length of the flow geometry, L, is defined as... 

In a good vacuum where the pressure is of the order of IO3 atm, a simple calculation shows that X is very large compared with the dimensions of the container. Thus, in a good vacuum the gas molecules collide far more frequently with the walls of the container than with one another. Under such conditions, the gas is called a Knudsen gas. 

Numerical Model for the Effect of a Spatial Temperature Gradient on Chemical Reactions in a Knudsen Gas... 

Ultrafiltration (UF) and microfiltration (MF) membranes can be made on less sophisticated supports. The simplest MF tubular membrane consists of an extruded porous tube (layer 1) as a support coated on the inside or outside with a macroporous layer (layer 2) which serves as the functional filtration layer. The support system shown in Fig. 6.3 is in fact a sophisticated UF or Knudsen gas separation membrane. For less demanding applications a 2-layer support could also be used. 

Gas diffusion in a porous structure is of particular interest to this book as many porous fibre preforms are densified by CVI. The diffusion of gases in porous media can be classified into three regimes according to the ratio of the free mean path to the pore diameter within the structure. As shown in Figure 2.15, they are Fick gas diffusion, transition gas diffusion and Knudsen gas diffusion. 

For the sake of simplicity, we discuss below thermo-osmosis of a Knudsen gas. 

In order to understand the meaning of the different transport coefficients arising in the liquid vapour phase change we consider a liquid surface at temperature T with an adjacent vapour phase at temperature T (Fig.l). The vapour pressure is assumed to be so low that gas collisions can be neglected (Knudsen gas). The entropy flux can be expressed in terms of the flux of internal energy and the mass flux J by the following equation... 

We obtain the following transport matrix for the mass and heat exchange in of a liquid surface of temperature T with a Knudsen gas of temperature T the linear region where 1(T - T )/ T l 1 ... 

Figure 7.6-1. Types of diffusion of gases in small capillary tubes (a) Knudsen gas diffusion, (b) molecular or Pick s gas diffusion, (c) transition gas diffusion.

We have repeatedly used the term hydrodynamic, and we now give it a more precise definition. By a hydrodynamic process we mean one for which the local thermodynamic variables, temperature, chemical potential (or density), and velocity, are determined by the past history of their boundary values. The normal solution to the Boltzmann equation, as well as its generalization obtained in the previous Sections, then clearly corresponds to a hydrodynamic process. The significance of the term hydro-dynamic may be clarified by the consideration of some processes of non-hydrodynamic type. A process of relaxation in momentum space in a spatially uniform gas is clearly non-hydrod5mamic, since the local thermod5mamic variables are not at all pertinent to its description. Another example is provided by processes in a Knudsen gas. Here there is an essential dependence on the particular form of the boundary forces. An insensitivity to the nature of the boundary forces is implied in the definition of a hydrod5mamic process, for which it is immaterial whether a thermal reservoir is constructed of, say, copper or aluminum, and... 

Secondly, the existence of critical thicknesses and temperatures, at which Knudsen gas flow runs through thin solid films (according to electron microscopy data), formed from oligomers. 

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