Principles of a Diffuser

When the back-pressure in the diffuser is optimized, a normal shock wave is set up at the lip of the diffuser and the pressure behind the shock wave is increased. No air spill-over occurs at the lip of the diffuser and the airflow velocity is as shown in Fig. D-2 (b). The pressure in the diffuser increases and the airflow velocity decreases along the flow direction. When the back-pressure is lower than the design pressure, a normal shock wave is swallowed inside of the diffuser, as shown in Fig. D-2 (c). Since the flow velocity in front of the normal shock wave in the diffuser is increased along the flow direction, the strength of the normal shock wave inside of the diffuser becomes higher than that in the case of the diffuser at the optimized back-pressure shown in Fig. D-2 (b). Thus, the pressure behind the shock wave is lowered due to the increased entropy. 

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The basic principle of a diffusion pump can be explained with a simple single-stage mercury diffusion pump (see Fig. 7.21). On the system side of the pump (at about 10 2 to 10 3 torr, or better), gas molecules wander around, limited by their mean free path and collisions with other molecules. The lowest section of this diffusion pump is an electric heater that brings the diffusion pump liquid up to its vapor pressure temperature. The vapors of the diffusion pump liquid are vented up a central chimney where, at the top, they are expelled out of vapor jets at supersonic speeds (up to 1000 ft/sec). Below these jets is a constant rain of the pumping fluid (mercury or low vapor-pressure oil) on the gases within the vacuum system. Using momentum transfer/ gas molecules are physically knocked to the bottom of the pump, where they are trapped by the vapor jets from above. Finally, they are collected in a sufficient quantity to be drawn out by the auxiliary (mechanical) pump. 

Schematic representation of the operating principle of a diffusion pump.

Figure 8.31. Principle of a Polymer Electrolyte Membrane (PEM) fuel cell. A Nation membrane sandwiched between electrodes separates hydrogen and oxygen. Hydrogen is oxidized into protons and electrons at the anode on the left. Electrons flow through the outer circuit, while protons diffuse through the...

The principle of a three-phase membrane extraction is illustrated in Figure 1.28. An organic solvent is immobilized in the pores of a porous polymeric support consisting of a flat filter disc or a hollow fiber-shaped material. This supported liquid membrane (SLM) is formed by treating the support material with an organic solvent that diffuses into its pores. The SLM separates an aqueous... 

For mixtures of substances of markedly different surface tensions also we have noted that over a considerable range of concentration the Gibbs film appears to behave as if it were unimolecular in character, but for strong solutions of these substances as well as for mixtures of liquids of similar surface activities the evidence for such a restricted film thickness is by no means so conclusive. It must indeed rather be assumed that in these cases the application of the principle of minimum surface energy to mixtures somewhat similar in internal pressure leads to the formation of a diffuse layer in which the composition varies possibly in an exponential manner with the depth. The top layer alone may be said to be formed by the operation of chemical forces. 

Values of a diffusion coefficient matrix, in principle, can be determined from multicomponent diffusion experiments. For ternary systems, the diffusivity matrix is 2 by 2, and there are four values to be determined for a matrix at each composition. For quaternary systems, there are nine unknowns to be determined. For natural silicate melts with many components, there are many unknowns to be determined from experimental data by fitting experimental diffusion profiles. When there are so many unknowns, the fitting of experimental concentration... 

The variational principle has not been widely used in diffusion kinetic problems. Nevertheless, it is such a powerful technique that it is suitable for discussing the many-body problems which have still to be tackled. Wherever approximate methods are necessary, the variational principle should be considered. The trial function(s) should be chosen with care, based on a good idea of the nature of the trial function from its behaviour in certain asymptotic limits. The only application known to the author of the variation principle to a numerical study of a diffusion kinetic problem on a molecular system is that of Delair et al. [377]. They used the variational principle to generate an implicit finite difference scheme for solving the Debye—Smoluchowski equation. Interesting comments have been made by Brykalski and Krason more in the context of heat diffusion [510]. 

All of the principles of semi-infinite potential-step experiments discussed so far apply to thin-layer work. Some modification in the quantitative response is necessary to account for the presence of a diffusion barrier. Figure 3.11 illustrates the diffusion phenomena occurring during a chronoamperometric experiment in a thin-layer cell of typical dimensions. It will be useful to compare this figure with the semi-infinite situation depicted in Figure 3.1. Notice that the supply of reactant in the bulk solution phase is effectively infinite in Fig-... 

Spry and Sawyer (1975) developed a model using the principles of configurational diffusion to describe the rates of demetallation of a Venezuelan heavy crude for a variety of CoMo/A1203 catalysts with pores up to 1000 A. This model assumes that intraparticle diffusion is rate limiting. Catalyst performance was related through an effectiveness factor to the intrinsic activity. Asphaltene metal compound diffusivity as a function of pore size was represented by... 

This consideration of the principles of diffusive sampling identifies a range of factors which may influence the performance of a diffusive sampler for monitoring VOC concentrations in indoor air. These factors will potentially be a source of error in such measurements and add to the overall uncertainty of the result given by the measurement procedure. In addition the amount of uncertainty will be influenced by other factors including amount and consistency of background contamination of sorbents, repeatability of analytical determination, formation of artifacts, stability of analyte on the sorbent, recovery of analyte during analyses and presence of interferents. 

A micromixer (100 pL) was constructed on a quartz chip with multiple small channels (5 pm wide) intersecting 45° with the main channels (27 pm wide) (see Figure 3.39). EOF flow of two solutions containing different concentrations of fluorescein was initiated to achieve mixing based on the principle of eddy diffusion after splitting in the smaller channels [493]. 

The theory of filtration is a direct application of principles of Brownian diffusion discussed previously. The objective of the theory is to provide a framework for cal-... 

High pressures can be assayed in their buildup phase by using a macroversion of such voids (Fig. 12.84). The apparatus (Minevski and Lin, 1998) shows an electrochemical cell in which the cathode is a cylinder of palladium (chosen for its large permeability coefficient for the throughput of H) that contains a void space into which H2 diffuses from the deposition of H on the surface of the cylinder. This space is connected to a pressure transducer, which works on the principle of a piezoresistor, i.e., it contains a substance that produces an electrical potential upon being compressed. The rise of pressure inside the void space is shown in Fig. 12.85. 

The principle of double diffusion in one dimension (Fig. IB) had been proposed Antigen and antiserum placed at either end of a gel column but this technique was practiced only later. Double diffusion in tubes is accomplished in a manner similar to simple diffiision, except that between the layers containing the reagents a layer containing only agar of a suitably chosen height is placed. 

The importance of diffusion in chemical kinetics was pointed out by Eyring in 1936 [77], and subjected to a wide description by Glasstone, Laidler and Eyring [78]. The applicability of the principles of the diffusion control in various reactions and the nitration among them was recently reviewed by Kidd (791. 

The principle can be carried out using gas diffusion electrodes [7]. Commercial reactors for the production of alkaline peroxide solutions have recently been realized using the principle of a monopolar trickle bed reactor [57, 69],... 

One way to partially alleviate this problem is to couple the DOSY filter with a 2-D-NMR sequence where overlapping signals are less of a problem. This results in 3-D sequences, referred to as 3-D-DOSY sequences. Since diffusion is a filter that can easily be coupled to nearly any 2-D-NMR sequence, many 3-D-DOSY sequences have been developed with relative ease. However, there are only a limited number of applications of these techniques in real chemical systems. The principle of a 3-D-DOSY in virtual separation is schematically outlined in Fig. 6.5b. Here, the result of a 3-D-DOSY-COSY sequence is presented, where COSY maps of each compound in the mixture are separated on the diffusion axis and appear on a separate plan. 

Figure 7 Principle of a Monte Carlo-based approach to mathematically model polymer degradation and drug diffusion in PLGA-based microparticles. Scheme of the iimer structure of the system (one-quarter of a spherical cross section) (A) at time t = 0 (before exposure to the release medium) and (B) during dmg release. Gray, dotted, and white pixels represent nondegraded polymer, drag and pores, respectively. Source From Ref. 48.

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