Diffusion pressure

Finally, before leaving our exploration of the dusty gas model, we must compare the large pore (or high pressure) limiting form of its flux relations with the corresponding results derived in Chapter 4 by detailed solution of the continuum equations in a long capillary. The relevant equations are (4,23) and (4,25), to be compared with the corresponding scalar forms of equations (5.23) and (5.24). Equations (4.25) and (5.24).are seen to be identical, while (4,23) and (5.23) differ only in the pressure diffusion term, which takes the form... 

Washing equipment typically includes cylinder or dmm washers, diffusion ring washers, pressure diffusers, pressure washers, and belt washers. 

Reversible Processes. Distillation is an example of a theoretically reversible separation process. In fractional distillation, heat is introduced at the bottom stiUpot to produce the column upflow in the form of vapor which is then condensed and turned back down as Hquid reflux or column downflow. This system is fed at some intermediate point, and product and waste are withdrawn at the ends. Except for losses through the column wall, etc, the heat energy spent at the bottom vaporizer can be recovered at the top condenser, but at a lower temperature. Ideally, the energy input of such a process is dependent only on the properties of feed, product, and waste. Among the diffusion separation methods discussed herein, the centrifuge process (pressure diffusion) constitutes a theoretically reversible separation process. 

Irreversible Processes. Irreversible processes are among the most expensive continuous processes. These are used only in special situations, such as when the separation factors of more efficient processes (that is, processes that are theoretically more efficient from an energy point of view) are found to be uneconomicaHy small. Except for pressure diffusion, the diffusion methods discussed herein are essentially irreversible processes. Thus,... 

In pressure diffusion, a pressure gradient is estabUshed by gravity or in a centrifugal field. The lighter components tend to concentrate in the low pressure (center) portion of the fluid. Countercurrent flow and cascading extend the separation effect. 

A second type of apparatus based on the pressure diffusion effect is the separation nozzle. Pressure gradients in a curved expanding jet produce an isotopic separation similar to that in a centrifuge. The separation effect obtained with a single jet is relatively small, and separation nozzle stages, similar to gaseous diffusion stages, must be used in a cascade to realize most of the desired separations. 

Mass Transport. An expression for the diffusive transport of the light component of a binary gas mixture in the radial direction in the gas centrifuge can be obtained directly from the general diffusion equation and an expression for the radial pressure gradient in the centrifuge. For diffusion in a binary system in the absence of temperature gradients and external forces, the general diffusion equation retains only the pressure diffusion and ordinary diffusion effects and takes the form... 

Riazi-Whitson They presented a generahzed correlation in terms of viscosity and molar density that was apphcable to both gases and liqmds. The average absolute deviation for gases was only about 8 percent, while for liquids it was 15 percent. Their expression relies on the Chapman-Enskog correlation [Eq. (5-194)] for the low-pressure diffusivity and the Stiel-Thodos correlation for low-pressure viscosity ... 

Shale stability is an important problem faced during drilling. Stability problems are attributed most often to the swelling of shales. It has been shown that several mechanisms can be involved [680,681]. These can be pore pressure diffusion, plasticity, anisotropy, capillary effects, osmosis, and physicochemical alterations. Three processes contributing to the instability of shales have to be considered [127] ... 

Table 3.45 Vapour pressure, diffusion coefficient and structure of disperse dyes [188]...

Note that 7Zu = 0 due to the continuity equation. Thus, the pressure-rate-of-strain tensor s role in a turbulent flow is to redistribute turbulent kinetic energy among the various components of the Reynolds stress tensor. The pressure-diffusion term T is defined... 

SOL. 19. 1. Prigogine, Pression, diffusion et superfluidite dans les melanges de gaz parfaits (Pressure, diffusion and superfluidity in mixtures of perfect gases), Colloquium Ultrasonore Trilingen, Cl. Sciences, Acad. Roy. Flamande, 1952, pp. 285-295. 

Part of the radiation from the reaction Zone of this flame is nonthermal, being chemiluminescent in origin. In determination of populations of species such as C2 and CH in low-pressure diffusion or premixed flames at 1-15 torr, these authors developed a simple model of a flame which reflects the characteristic requirements for start of laser action. They show that by choice of the proper experimental parameters in the model, laser action should be attainable... 

The mass flux vector is also the sum of four components j (l), the mass flux due to a concentration gradient (ordinary diffusion) jYp), the mass flux associated with a gradient in the pressure (pressure diffusion) ji(F), the mass flux associated with differences in external forces (forced diffusion) and j,-(r), the mass flux due to a temperature gradient (the thermal diffusion effect or the Soret effect). The mass flux contributions may then be summarized ... 

In these equations is the partial molal free energy (chemical potential) and Vj the partial molal volume. The Mj are the molecular weights, c is the concentration in moles per liter, p is the mass density, and z, is the mole fraction of species i. The D are the multicomponent diffusion coefficients, and the are the multicomponent thermal diffusion coefficients. The first contribution to the mass flux—that due to the concentration gradients—is seen to depend in a complicated way on the chemical potentials of all the components present. It is shown in the next section how this expression reduces to the usual expressions for the mass flux in two-component systems. The pressure diffusion contribution to the mass flux is quite small and has thus far been studied only slightly it is considered in Sec. IV,A,6. The forced diffusion term is important in ionic systems (C3, Chapter 18 K4) if gravity is the only external force, then this term vanishes identically. The thermal diffusion term is impor-... 

In the absence of pressure diffusion, forced diffusion, and thermal... 

The basic expressions for the mass fluxes and the equations of continuity for multi-component mixtures are given in Sec. II,B. For a -component mixture of ideal gases in a system in which there is no pressure diffusion, forced diffusion, or thermal diffusion, the fluxes are given by... 

This expression has been generalized by Curtiss and Hirschfelder (C12) to include thermal diffusion pressure diffusion, and forced diffusion [see reference (Hll, p. 487)]. 

In the previous section it is seen how a separation of two substances A and B may be effected by the establishment of a steady state in a system in which thermal and ordinary diffusion oppose one another. In this section we describe the analogous situation which is obtained when ordinary and pressure diffusion are in competition with each other. Use is made of this result in the separation of organic liquids or isotopes by centrifuging techniques. 

Fig. 200. Schematic view of a pneumatic press (a pressure diffuser) for dehydration of nitrocellulose with alcohol.

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