Gases theoretical basis

The results of computations of T o for an isolated fiber are dhistrated in Figs. 17-62 and 17-63. The target efficiency T t of an individual fiber in a filter differs from T o for two main reasons (Pich, op. cit.) (1) the average gas velocity is higher in the filter, and (2) the velocity field around the individual fibers is influenced by the proximity of neighboring fibers. The interference effect is difficult to determine on a purely theoretical basis and is usually evaluated experimentally. Chen (op. cit.) expressed the effecd with an empirical equation ... 

In this sub-section it is intended first to outline the theoretical basis of these diagrams by considering a simple metal-/4-gas-5 binary system followed by a quantitative treatment of a hypothetical metal A/(at. wt. 50) and oxygen binary system. Finally the application of these diagrams will be... 

The study of the reactions of the simple free radicals begun by Bodenstein and Lind in 1906 on the kinetics of gas phase reactions showed that the reactions of H2 with CI2 and Bt2 were complex processes/ and a radical chain mechanism for these reactions (equations 14-18) was proposed in 1919 by Christiansen, Herzfeld, and Polanyi/ The theoretical basis for understanding these reactions in terms of free radicals was presented by G.N. Lewis in 1916, with the theory of the electron pair bond, and free radicals, or odd molecules / Further studies on chain reactions including the extension to explosions in gaseous systems were made by Hinshelwood and by Semenovwho shared the Nobel Prize in 1956. 

One of the reasons for the wide acceptance of gas-liquid chromatography is that there exists such a variety of liquid phases with different properties. Because of this large number of liquid phases there has been a great amount of work to clarify the interaction between liquid phase and the solute molecules. There is hope that some theoretical basis can be found for choosing a liquid phase to accomplish a particular separation and lately there has been an effort to decrease the number of liquid phases which are used. We now wish to discuss in general terms the role of the liquid phase and describe some of the criteria needed to discuss its role in a chromatographic separation. 

Mass chromatography is a new form of gas chromatography that uses two gas density detectors operated in parallel and provides (a) mass of components within 1-2% relative without determination of response factors, (b) molecular weight of components within 0.25-1% in the mass range 2—400, and (c) a powerful identification tool by the combined use of retention time and molecular weight data. The theoretical basis of the technique and its scope as a molecular weight analyzer, a qualitative identification tool, and a quantitative analyzer in the polymer field are discussed. 

This chapter describes the fundamental principles of heat and mass transfer in gas-solid flows. For most gas-solid flow situations, the temperature inside the solid particle can be approximated to be uniform. The theoretical basis and relevant restrictions of this approximation are briefly presented. The conductive heat transfer due to an elastic collision is introduced. A simple convective heat transfer model, based on the pseudocontinuum assumption for the gas-solid mixture, as well as the limitations of the model applications are discussed. The chapter also describes heat transfer due to radiation of the particulate phase. Specifically, thermal radiation from a single particle, radiation from a particle cloud with multiple scattering effects, and the basic governing equation for general multiparticle radiations are discussed. The discussion of gas phase radiation is, however, excluded because of its complexity, as it is affected by the type of gas components, concentrations, and gas temperatures. Interested readers may refer to Ozisik (1973) for the absorption (or emission) of radiation by gases. The last part of this chapter presents the fundamental principles of mass transfer in gas-solid flows. 

The theoretical basis for sputtering has been known for a long time but more recently commercial methods have been developed along lines similar to those in vacuum evaporation just described. Essentially, a discharge of argon gas plasma is established between an anode and cathode electrode in this instance, the source material is the cathode, and the work piece the anode. Gas ions charged positively are attracted to the cathode, where they collide with it and remove atoms of the source material—which in turn travel to the anode and form a coating of sputtered material on the work piece. 

Theoretical Basis for a Continuous Large-Capacity Gas Chromatographic Apparatus, J. C. Giddings, Anal. Chem., 34, 37 (1962). 

The theoretical basis of CASTEP is the density functional theory (DFT) in the local density approximation (LDA) or gradient-corrected LDA version, as developed by Perdew and Wang (GGA).6-7 The DFT description of electron gas interactions is known to be sufficiently accurate in most cases, and it remains the only practical way of analyzing periodic systems. LDA is known to underestimate bond lengths in molecules and cell parameters in crystals, while GGA is typically more accurate to these optimized geometries. In the present calculations, we selected GGA, which is the default setting in CASTEP. 

For the sake of simplicity, the theoretical basis of equation (58) will be considered only for homogeneous reactions in ideal gas mixtures, although the principal concepts presented require only small modifications to be applied to other homogeneous reactions and to heterogeneous processes. 

This method has been approved as a ASTM procedure [120-122] and used in the commercial computer controlled Coulter Porometer (Coulter Electronic Ltd) for pore sizes much larger than 0.44 pm. However the theoretical basis used for the evaluation of the accumulated data neglects the specificity of gas flow in pores and incorrectly considers the flowing gas as an incompressible fluid. The assumption of gas flow dependency only on AP distorts the resulting... 

After introducing the theoretical basis of gas-liquid contacting, the remainder of this entry focuses on gas-liquid contact through gas bubbles dispersed within a continuous liquid, i.e., the most common mode of gas-liquid contact within the chemical industry. Finally, the gas-liquid contactor design procedure is presented, followed by an example involving an industrial-scale STR. Further discussion of bubble columns, packed beds, thin films, and venturi scrubbers is found in related entries in this encyclopedia. 

Point (a) is best optimised by experiment, although several attempts have been made to provide a theoretical basis for determining the optimum concentration of a species of known molar decadic absorption coefficient for resonance Raman studies. The deleterious effects on the signal-noise ratio of the Raman spectram attributable to point (b) can be obviated by spinning the sample at ca. 1600 rev min as a solid, liquid or gas. Several articles contain details of many of these devices, the common object of which is to ensure relative motion between the sample and the focused laser beam (64). Surface scanning devices are also in use, and these enable the laser beam, while remaining focused on the surface of the sample, to scan over its surface in either a circular or linear fashion to achieve the same object. Such a procedure is particularly effective when the sample is held at liquid nitrogen temperatures. A device which allows this mode of operation is shown in Fig. 10 in this case the laser beam... 

In depth discussions of the TCD can be found in most texts on gas chromatography [1-4]. Lawson and Miller [5] have written a review of the TCD, and give multiple references to discussions regarding the TCD. A comparison of the various modes of operation has been made by Wells and Simon [6] which compares the constant voltage, constant current, and constant mean temperature modes of operation on both an empirical and a theoretical basis. 

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