Mass diffusion separability

In mass diffusion, separation of isotopes occurs throu diffusion of the li t isotope of a gas mixture into a condensible vapor at higher rate than diffusion of the heavy isotope. Mass diffusion separation has been canied out in a cascade of individual mass diffusion stages and in a mass diffusion column. 

Different combinations of stable xenon isotopes have been sealed into each of the fuel elements in fission reactors as tags so that should one of the elements later develop a leak, it could be identified by analyzing the xenon isotope pattern in the reactor s cover gas (4). Historically, the sensitive helium mass spectrometer devices for leak detection were developed as a cmcial part of building the gas-diffusion plant for uranium isotope separation at Oak Ridge, Tennessee (129), and heHum leak detection equipment is stiU an essential tool ia auclear technology (see Diffusion separation methods). 

Ordinary diffusion involves molecular mixing caused by the random motion of molecules. It is much more pronounced in gases and Hquids than in soHds. The effects of diffusion in fluids are also greatly affected by convection or turbulence. These phenomena are involved in mass-transfer processes, and therefore in separation processes (see Mass transfer Separation systems synthesis). In chemical engineering, the term diffusional unit operations normally refers to the separation processes in which mass is transferred from one phase to another, often across a fluid interface, and in which diffusion is considered to be the rate-controlling mechanism. Thus, the standard unit operations such as distillation (qv), drying (qv), and the sorption processes, as well as the less conventional separation processes, are usually classified under this heading (see Absorption Adsorption Adsorption, gas separation Adsorption, liquid separation). 

Many other methods for separating isotopes have been described. A partial list includes membrane and membrane pervaporation, thermal diffusion of liquids, mass diffusion, electrolysis and electro-migration, differential precipitation, solvent extraction, biological microbial enrichment, and more. Although not discussed in... 

Non-spherical micelles of poly(ethylene)(PE)-poly(ethylene-propylene)(PEP) in decane are self-assembhng in the form of extended platelets that have a crystalline PE-core and a planar PEP brush on both sides. Due to the large size of the platelets the centre of mass diffusion is extremely slow and allows a clear separation of the density fluctuation in the brush. NSE experiments [301] have been analysed in terms of the model of de Gennes [300]. The friction coefficient and modulus of the brush were found to be similar to those of a typical gel. 

The most common separators include the Ryhage or jet diffusion separator (74), the Watson-Biemann or pore diffusion separator (75), and the membrane solution diffusion separator originally developed by Llewellyn (75). The first two separators involve direct passage of the sample into the mass spectrometer the low molecular weight helium diffuses more readily and is pumped away. The membrane separator involves diffusion of the sample through a silicone membrane while the carrier gas vents to the atmosphere carrier gas is thus not confined to helium. There is no best separator the choice depends on the nature of the compounds, the temperature range over which it will be operated, and most usually what is available in a particular laboratory. A convenient configuration for a double-beam mass spectrometer such as the AEI MS-30 is two different separators, one into each beam, which permits rapid evaluation of separator performance. 

In high temperature separation, hydrogen is separated from the hot product gas at the reaction temperature using porous membranes made of materials such as zirconia. The porous membranes separate the gases through, in general, either mass diffusion or molecular effusion [3,74,79]. In mass diffusion, the... 

The phenomenon of diffusion may be used to separate various materials, Benedict and Halle et al in Kirk Othmer (Refs 12 27) describe several devices for diffusion separations, such as mass diffusion, thermal diffusion gas diffusion apparatuses... 

The dimensionless retention parameter X of all FFF techniques, if operated on an absolute basis, is a function of the molecular characteristics of the compounds separated. These include the size of macromolecules and particles, molar mass, diffusion coefficient, thermal diffusion coefficient, electrophoretic mobility, electrical charge, and density (see Table 1, Sect. 1.4.1.) reflecting the wide variablity of the applicable forces [77]. For detailed theoretical descriptions see Sects. 1.4.1. and 2. For the majority of operation modes, X is influenced by the size of the retained macromolecules or particles, and FFF can be used to determine absolute particle sizes and their distributions. For an overview, the accessible quantities for the three main FFF techniques are given (for the analytical expressions see Table l,Sect. 1.4.1) ... 

The phenomenological coefficients are important in defining the coupled phenomena. For example, the coupled processes of heat and mass transport give rise to the Soret effect (which is the mass diffusion due to heat transfer), and the Dufour effect (which is the heat transport due to mass diffusion). We can identify the cross coefficients of the coupling between the mass diffusion (vectorial process) and chemical reaction (scalar process) in an anisotropic membrane wall. Therefore, the linear nonequilibrium thermodynamics theory provides a unifying approach to examining various processes usually studied under separate disciplines. 

In the third simulation example, we carried out an analysis of some of the aspects that characterize the case of the mass transfer of species through a membrane which is composed of two layers (the separative and the support layers) with the same thickness but with different diffusion coefficients of each entity or species. To answer this new problem the early model has been modified as follows (i) the term corresponding to the source has been eliminated (u) different conditions for bottom and top surfaces have been used for example, at the bottom surface, the dimensionless concentration of species is considered to present a unitary value while it is zero at the top surface (iii) a new initial condition is used in accordance with this case of mass transport through a two-layer membrane (iv) the values of the four thermal diffusion coefficients from the original model are replaced by the mass diffusion coefficients of each entity for both membrane layers (v) the model is extended in order to respond correctly to the high value of the geometric parameter 1/L. 

The thermal diffusion factor a is proportional to the mass difference, (mi — mo)/(mi + m2). The thermal diffusion process depends on the transport of momentum in collisions between unlike molecules. The momentum transport vanishes for Maxwellian molecules, particles which repel one another with a force which falls off as the inverse fifth power of the distance between them. If the repulsive force between the molecules falls off more rapidly than the fifth power of the distance, then the light molecule will concentrate in the high temperature region of the space, while the heavy molecule concentrates in the cold temperature region. When the force law falls off less rapidly than the fifth power of the distance, then the thermal diffusion separation occurs in the opposite sense. The theory of the thermal diffusion factor a is as yet incomplete even for classical molecules. A summary of the theory has been given by Jones and Furry 15) and by Hirschfelder, Curtiss, and Bird 14), Since the thermal diffusion factor a for isotope mixtures is small, of the order of 10", it remained for Clusius and Dickel (8) to develop an elegant countercurrent system which could multiply the elementary effect. 

In the second chapter we consider steady-state and transient heat conduction and mass diffusion in quiescent media. The fundamental differential equations for the calculation of temperature fields are derived here. We show how analytical and numerical methods are used in the solution of practical cases. Alongside the Laplace transformation and the classical method of separating the variables, we have also presented an extensive discussion of finite difference methods which are very important in practice. Many of the results found for heat conduction can be transferred to the analogous process of mass diffusion. The mathematical solution formulations are the same for both fields. 

In particular we examine situations in which diffusion occurs in two distinct regions separated by a moving boundary or interface [28, 25]. Moreover, the two regions are separated by a plane surface and diffusion takes place only in the direction perpendicular to this plane. The concentration is initially uniform in each region. The component mass diffusion may then result in a net movement of the matter in one or both regions relative to the interface. 

The stage type of mass diffusion was patented by Hertz [H4], who used this method to separate the isotopes of neon [HS, H6]. The means by which separation is effected in a mass diffusion stage are shown in Fig. 14.33, which illustrates the type of equipment used by Maier [Ml] to separate hydrogen from other gases. 

Table 14.21. Isotopes separated by cascade of mass diffusion stages...

For the mass diffusion screen, Maier used a variety of materials, such as plates perforated with 0.4-mm holes, fine-mesh wire screen, or alundum filter plates. Very fine holes, such as is needed in gaseous diffusion, are not required, although holes with diameter under 10 are preferred because control of mass flow through the screen is easier. In the uranium isotope separation design example to be given in Sec. 7.4, electroformed nickel screen with holes 6.76 tm in diameter and 30 percent free area was specified. 

Because the separation obtainable in a mass diffusion stage is even smaller than in a gaseous diffusion stage, a practical degree of separation requires either a multistage cascade, such as the 48-stage cascade used by Hertz [H3] to separate neon isotopes, or a mass diffusion column. 

Sweep diffusion is a form of mass diffusion column in which the screen separating the counterflowing light and heavy streams is not present. Cichelli et al. [C4] developed the theory of such a column and used it to separate hydrogen from natural gas and to enrich air. Table... 

Separation of Uranium Isotopes by Cascade of Mass Diffusion Stages... 

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