Mutual diffusivity

In a gas phase. Gaseous diffusion processes can generate both elemental and isotopic fractionation in natural gases. Marty (1984) reviews the processes that can affect noble gases after Present (1958) and distinguishes among a) free-molecule diffusion mutual diffusion and thermal diffusion. 

By comparing colloid dynamics, probe dynamics (sedimentation, electrophoresis, probe diffusion), and chain dynamics (single-chain diffusion, mutual diffusion, solution viscosity, and viscoelasticity), information on the importance of topological constraints becomes accessible. Any properties found equally for colloid and chain dynamics cannot be created by topological constraints, because colloidal... 

The list of experimentally accessible properties of colloid solutions is the same as the list of accessible properties of polymer solutions. There are measurements of single-particle diffusion, mutual diffusion and associated relaxation spectra, rotational diffusion (though determined by optical means, not dielectric relaxation), viscosity, and viscoelastic properties (though the number of viscoelastic studies of colloidal fluids is quite limited). One certainly could study sedimentation in or electrophoresis through nondilute colloidal fluids, but such measurements do not appear to have been made. Colloidal particles are rigid, so internal motions within a particle are not hkely to be significant the surface area of colloids, even in a concentrated suspension, is quite small relative to the surface area of an equal weight of dissolved random-coil chains, so it seems unlikely that colloidal particles have the major effect on solvent dynamics that is obtained by dissolved polymer molecules. 

For a binary mixture of two components A and B in the gas phase, the mutual diffusion coefficient such as defined in 4.3.2.3, does not depend on composition. It can be calculated by the Fuller (1966) method ... 

Z) g = mutual coefficient of diffusion AB = mutual coefficient of diffusion calculated by Fuller s method... 

This study detects the defect of the void and the exfoliation in the solid phase diffusion bonding interface of ductile cast iron and stainless steel with a nickel insert metal using ultrrasonic testing method, and examine the influence of mutual interference of the reflectional wave both the defect and the interface. 

Balcom B J, Fischer A E, Carpenter T A and Flail L D 1993 Diffusion in aqueous gels—mutual diffusion-... 

Note the use of a script for the binary pair mutual diffusion coefficient, as distinct from the Roman D already used to represent Knudsen diffusion coefficients. This convention will be adhered to throughout. 

Diffusion Theory. The diffusion theory of adhesion is mosdy appHed to polymers. It assumes mutual solubiUty of the adherend and adhesive to form a tme iaterphase. The solubiUty parameter, the square root of the cohesive eaergy deasity of a material, provides a measure of the iatermolecular iateractioas occurring within the material. ThermodyaamicaHy, solutioas of two materials are most likely to occur whea the solubiUty parameter of oae material is equal to that of the other. Thus, the observatioa that "like dissolves like." Ia other words, the adhesioa betweea two polymeric materials, oae an adherend, the other an adhesive, is maximized when the solubiUty parameters of the two are matched ie, the best practical adhesion is obtained when there is mutual solubiUty between adhesive and adherend. The diffusion theory is not appHcable to substantially dissimilar materials, such as polymers on metals, and is normally not appHcable to adhesion between substantially dissimilar polymers. 

For good adhesion, the adhesive and the adherend should, if possible, display mutual solubiHty to the extent that both diffuse into one another, providing an interphasal zone. 

A key feature of encapsulation processes (Figs. 4a and 5) is that the reagents for the interfacial polymerisation reaction responsible for shell formation are present in two mutually immiscible Hquids. They must diffuse to the interface in order to react. Once reaction is initiated, the capsule shell that forms becomes a barrier to diffusion and ultimately begins to limit the rate of the interfacial polymerisation reaction. This, in turn, influences morphology and uniformity of thickness of the capsule shell. Kinetic analyses of the process have been pubHshed (12). A drawback to the technology for some apphcations is that aggressive or highly reactive molecules must be dissolved in the core material in order to produce microcapsules. Such molecules can react with sensitive core materials. 

In other designs, a diffused siUcon sensor is mounted in a meter body that is designed to permit caUbration, convenient installation in pressure systems and electrical circuits, protection against overload, protection from weather, isolation from corrosive or conductive process fluids, and in some cases to meet standards requirements, eg, of Factory Mutual. A typical process pressure meter body is shown in Figure 10. Pressure measurement from 0—746 Pa (0—3 in. H2O) to 0—69 MPa (0—10,000 psi) is available for process temperatures in the range —40 to 125°C. Differential pressure- and absolute pressure-measuring meter bodies are also available. As transmitters, the output of these devices is typically 4—20 m A dc with 25-V-dc supply voltage. 

Mutual Diffusivity, Mass Diffusivity, Interdiffusion Coefficient. 5-46... 

Mutual Diffusivity, Mass Diffusivity, Interdiffusion Coefficient Diffusivity is denoted by D g and is defined by Tick s first law as the ratio of the flux to the concentration gradient, as in Eq. (5-181). It is analogous to the thermal diffusivity in Fourier s law and to the kinematic viscosity in Newton s law. These analogies are flawed because both heat and momentum are conveniently defined with respec t to fixed coordinates, irrespective of the direction of transfer or its magnitude, while mass diffusivity most commonly requires information about bulk motion of the medium in which diffusion occurs. For hquids, it is common to refer to the hmit of infinite dilution of A in B using the symbol, D°g. 

In the special case that A and B are similar in molecular weight, polarity, and so on, the self-diffusion coefficients of pure A and B will be approximately equal to the mutual diffusivity, D g. Second, when A and B are the less mobile and more mobile components, respectively, their self-diffusion coefficients can be used as rough lower and upper bounds of the mutual diffusion coefficient. That is, < D g < Dg g. Third, it is a common means for evaluating diffusion for gases at high pressure. Self-diffusion in liquids has been studied by many [Easteal AIChE]. 30, 641 (1984), Ertl and Dullien, AIChE J. 19, 1215 (1973), and Vadovic and Colver, AIChE J. 18, 1264 (1972)]. 

Tracer Diffusivity Tracer diffusivity, denoted by D g is related to both mutual and self-diffusivity. It is evaluated in the presence of a second component B, again using a tagged isotope of the first component. In the dilute range, tagging A merely provides a convenient method for indirect composition analysis. As concentration varies, tracer diffusivities approach mutual diffusivities at the dilute limit, and they approach selr-diffusivities at the pure component limit. That is, at the limit of dilute A in B, D g D°g and... 

Caldwell-Babb Darken observed that sohd-state diffusion in metallurgical applications followed a simple relation. His equation related the tracer diffusivities and mole fractious to the mutual diffusivity ... 

Caldwell and Babb used virtually the same equation to evaluate the mutual diffusivity for concentrated mixtures of common liquids. 

Liquid Diffusion The movement of liquids by diffusion in soUds is restricted to the equihbrium moisture content below the point of atmospheric saturation and to systems in which moisture and solid are mutually soluble. The first class apphes to the last stages in the diying of clays, starches, flour, textiles, paper, and wood the second class includes the diying of soaps, glues, gelatins, and pastes. 

Monomer molecules, which have a low but finite solubility in water, diffuse through the water and drift into the soap micelles and swell them. The initiator decomposes into free radicals which also find their way into the micelles and activate polymerisation of a chain within the micelle. Chain growth proceeds until a second radical enters the micelle and starts the growth of a second chain. From kinetic considerations it can be shown that two growing radicals can survive in the same micelle for a few thousandths of a second only before mutual termination occurs. The micelles then remain inactive until a third radical enters the micelle, initiating growth of another chain which continues until a fourth radical comes into the micelle. It is thus seen that statistically the micelle is active for half the time, and as a corollary, at any one time half the micelles contain growing chains. 

Another subsidiary field of study was the effect of high concentrations of a diffusing solute, such as interstitial carbon in iron, in slowing diffusivity (in the case of carbon in fee austenite) because of mutual repulsion of neighbouring dissolved carbon atoms. By extension, high carbon concentrations can affect the mobility of substitutional solutes (Babu and Bhadeshia 1995). These last two phenomena, quenched-in vacancies and concentration effects, show how a parepisteme can carry smaller parepistemes on its back. 

In Section 4.2.2 the central role of atomic diffusion in many aspects of materials science was underlined. This is equally true for polymers, but the nature of diffusion is quite different in these materials, because polymer chains get mutually entangled and one chain cannot cross another. An important aspect of viscoelastic behavior of polymer melts is memory such a material can be deformed by hundreds of per cent and still recover its original shape almost completely if the stress is removed after a short time (Ferry 1980). This underlies the use of shrink-fit cling-film in supermarkets. On the other hand, because of diffusion, if the original stress is maintained for a long time, the memory of the original shape fades. 

Initial intimacy of contact between the adhesive and adherend must of course precede the formation of a diffusion interphase, but in contrast to contact adhesion, the issue which is dominant is not the maximization of the work of adhesion but instead must be some appropriate measure of the phase compatibility, in the sense of mutual solubility. 

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