Mechanics of Gases

The transport mechanism of gases through supported ionic liquid membranes has also been studied by several workers [24,28,36]. The basic governing principle in solution-diffusion-based mass transport process applicable to gas separation in ionic liquids is embodied in the Eq. 11.4 ... 

A number of excellent books and reviews have been published on the subject of polymeric gas separating membranes, which are recommended to the interested reader [266-272]. It is the purpose of this chapter to supply the reader with a basic background that is important for the understanding of the transport mechanism of gases through polymers, to introduce those polymers that are currently of commercial importance and finally to give an outlook on interesting developments in this field. 

The factor (qr/q )s is given on the basis of statistical mechanics of gases and liquids as follows (Fujikawa and Maerefat [6]) ... 

The shock-tube has been applied to determine the c.p. and the c.c. of methanol, water, and carbontetrachloride vapour. The values of c.p. and c.c. are 0.04 and 0.14, respectively, for methanol vapour, 0.10 and 0.35 for water vapour, and 0.20 and 0.71 for carbontetrachloride vapour, which are all significantly less than the values for the complete capture of the molecules. These values have been explained by the transition state theory on the basis of statistical mechanics of gases and liquids. The theory has clearly suggested that the c.p. and the c.c. are relating to the rotational degrees of freedom of molecules in both gas and liquid state. 

Excluded volume n. The volume surrounding and including a given object, which is excluded to another object. This terminology comes from the statistical mechanics of gases, where this function arises in the leading order concentration expression (virial coefficient) for the pressure in the case of gas particles that repeal each other with a hard-core volume exclusion. 

The model of the ideal gas ignores intermolecular interactions. Given some intermolecular interactions, statistical mechanics must be employed to obtain the equation of state of the real fluid. For fluids of high density, approximations are necessary, but these naturally evolve from the formal, general statistical mechanical framework. For polymers in bulk, the present theories are of the kinetic theory variety since they do not, in principle, relate all macroscopic properties to the constituent molecular properties. In approaching a statistical mechanical theory of polymers in bulk, we can first ask if we can learn from these successes in the statistical mechanics of gases. One way to accomplish this is to consider a bulk polymer situation whicli simulates as closely as possible ideal gas situations. This model illustrates the following ... 

Electrolyte diffusion into hydrophobic plastics is similar to the diffusion mechanisms of gases and vapor. Therefore, electrolytes with high vapor pressure (e.g., hydrochloric acid) exhibit water absorption and diffusion values similar to water. By contrast, very low values are found in electrolytes with low vapor pressure (e.g., chlorides or phosphates) because of the hydrophobic character of the plastic [896]. 

In statistical mechanics (e.g. the theory of specific heats of gases) a degree of freedom means an independent mode of absorbing energy by movement of atoms. Thus a mon-... 

A diffusion mechanism is also used in dialysis as a means of separating colloids from crystalloids. The rate of diffusion of molecules in gels is practically the same as in water, indicating the continuous nature of the aqueous phase. The diffusion of gases into a stream of vapour is of considerable importance in diffusion pumps. 

Substances at high dilution, e.g. a gas at low pressure or a solute in dilute solution, show simple behaviour. The ideal-gas law and Henry s law for dilute solutions antedate the development of the fonualism of classical themiodynamics. Earlier sections in this article have shown how these experimental laws lead to simple dieniiodynamic equations, but these results are added to therniodynaniics they are not part of the fonualism. Simple molecular theories, even if they are not always recognized as statistical mechanics, e.g. the kinetic theory of gases , make the experimental results seem trivially obvious. 

We will almost always treat the case of a dilute gas, and almost always consider the approximation that the gas particles obey classical, Flarniltonian mechanics. The effects of quantirm properties and/or of higher densities will be briefly commented upon. A number of books have been devoted to the kinetic theory of gases. Flere we note that some... 

Dorfman J R and van Bei]eren H 1977 The kinetic theory of gases Statisticai Mechanics, Part B Time-Dependent Processes ed B J Berne (New York Plenum)... 

TPD Temperature programmed desorption After pre-adsorption of gases on a surface, the desorption and/or reaction products are measured while the temperature Increases linearly with time. Coverages, kinetic parameters, reaction mechanism... 

Fig. 36. Mechanisms for permeation of gases through porous and dense gas-separation membranes.

An embrittling effect, the mechanism of which is stiU debated, is possible with a hydrogen content of more than ca 3 ppm. The content of hydrogen and other gases can, however, be reduced by vacuum dagassing. 

Fig. 6. Size distribution of an urban aerosol showing the three modes containing much of the aerosol mass. The fine mode contains particles produced by condensation of low volatility gases. The mid-range, or accumulation mode, results from coagulation of smaller aerosols and condensation of gases on preexisting particles. Coarse particulates, the largest aerosols, are usually generated mechanically.

The accumulation of matter on the surface of the catalyst restricts gas passage into the catalyst by a mechanism known as pore mouth plugging (see Fig. 10b). It takes only a smaU amount of material on the surface of the catalyst to restrict the free passage of gases into and out of the active porous... 

Practical separation techniques for hquid particles in gases are discussed. Since gas-borne particulates include both hquid and sohd particles, many devices used for dry-dust collection (discussed in Sec. 17 under Gas-Sohds Separation ) can be adapted to liquid-particle separation. Also, the basic subject of particle mechanics is covered in Sec. 6. Separation of liquid particulates is frequently desirable in chemical processes such as in countercurrent-stage contacting because hquid entrainment with the gas partially reduces true countercurrency. Separation before entering another process step may be needed to prevent corrosion, to prevent yield loss, or to prevent equipment damage or malfunc tion. Separation before the atmospheric release of gases may be necessaiy to prevent environmental problems and for regula-toiy compliance. 

Few mechanisms of liquid/liquid reactions have been established, although some related work such as on droplet sizes and power input has been done. Small contents of surface-ac tive and other impurities in reactants of commercial quality can distort a reac tor s predicted performance. Diffusivities in liquids are comparatively low, a factor of 10 less than in gases, so it is probable in most industrial examples that they are diffusion controllech One consequence is that L/L reactions may not be as temperature sensitive as ordinary chemical reactions, although the effec t of temperature rise on viscosity and droplet size can result in substantial rate increases. L/L reac tions will exhibit behavior of homogeneous reactions only when they are very slow, nonionic reactions being the most likely ones. On the whole, in the present state of the art, the design of L/L reactors must depend on scale-up from laboratoiy or pilot plant work. 

Just as at low pH, concentration mechanisms substantially increase attack. The two principal mechanisms of concentration are evaporation and condensation. Evaporation increases solute concentrations of compounds with vapor pressures lower than water (such as caustic compounds). Condensation increases concentration of aggressive gases such as ammonia. 

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