Isothermal diffusivities

Structure and Properties of Metal-Ammonia Systems (Das) Studies in the Kinematics of Isothermal Diffusion. A Macrodynamical Theory of Multicomponent Fluid Diffusion (Lamm). ... 

Feng, C. and W. E. Stewart, 1973. Practical models for isothermal diffusion and flow of gases in porous solids. Ind. Eng. Chem. Fundam. 12(2) A3-A1. 

S.2.2.2 Isothermal diffusive ioss and constant radiogenic growth rate... 

Because °Ar is radiogenic, that is, it is continuously produced by the decay of °K, the situation is more complicated than the treatment above. Below we consider another simple case °Ar generation and isothermal diffusion. Suppose the production rate of °Ar is time-independent, corresponding to the slow decay assumption of Dodson (1973). This assumption is valid if the cooling timescale -tc is much shorter than the half-life of (1250 Myr), such as a Xc of less than 25 Myr. 

Carman P.C. (1968) Intrinsic mobilities and independent fluxes in multicomponent isothermal diffusion, I simple Darken systems II complex Darken systems. /. Phys. Chem. 76, 1707-1721. 

Derived from Fick s first law, the equation for unidirectional, isothermal diffusion of gas 1 (NO2) through a constant pressure mixture of gas 1 and gas 2 (air) is ... 

Let us analyze the following specific reaction [H. Schmalzried, et. al. (1990) T. Frick (1993)]. A single crystal of NiO is used as a solvent for the solid reactants CaO and Ti02, both being moderately soluble in NiO. They isothermally diffuse into NiO from opposite sides (Fig. 9-12 a). Solutes for this type of reaction do not form stable compounds with the solvent crystal, but must form at least one stable compound with each other. 

On the other hand, the value of r achieved at the end of an isothermal diffusion anneal of duration to + At is... 

As described in Section 9.2.2, grain-boundary diffusion rates in the Type-C diffusion regime can be measured by the surface-accumulation method illustrated in Fig. 9.12. Assume that the surface diffusion is much faster than the grain-boundary diffusion and that the rate at which atoms diffuse from the source surface to the accumulation surface is controlled by the diffusion rate along the transverse boundaries. If the diffusant, designated component 2, is initially present on the source surface and absent on the accumulation surface and the specimen is isothermally diffused, a quasi-steady rate of accumulation of the diffusant is observed on the accumulation surface after a short initial transient. Derive a relationship between the rate of accumulation... 

In Reprint C in Chapter 7, the behavior of a tracer pulse in a stream flowing through a packed bed and exchanging heat or matter with the particles is studied. It is shown that the diffusion in the particles makes a contribution to the apparent dispersion coefficient that is proportional to v2 fi/D. The constant of proportionality has one part that is a function of the kinematic wave speed fi, but otherwise only a factor that depends on the shape of the particle (see p. 145 and in equation (42) ignore all except the last term and even the suffixes of this e, being unsuitable as special notation, will be replaced by A. e is defined in the middle of p. 143 of Chapter 7). In this equation, we should not be surprised to find a term of the same form as the Taylor dispersion coefficient, for it is diffusion across streams of different speeds that causes the dispersion in that case just as it is the diffusion into stationary particles that causes the dispersion in this.7 What is surprising is that the isothermal diffusion and reaction equation should come up, for A is defined by... 

We designate the penetrant as component 1 and the polymer as component 2. If the mixture is incompressible and no volume change occurs on mixing of the two components and if the diffusion takes place only in one direction x, it can be shown that distribution of component i (i = 1,2) in the system during isothermal diffusion is governed by a differential equation of the form ... 

Homogeneous charge transfer can take place between chemically similar redox species of one redox couple, e.g., Fe3+ and Fe2+ ions in solution or ferrice-nium and ferrocene moieties in poly(vinylferrocene) films, the electron transfer (- electron hopping or electron exchange reaction) can be described in terms of second-order kinetics and according to the - Dahms-Ruff theory [viii-x] it may be coupled to the isothermal diffusion ... 

Dahms-Ruff theory — For fast electron exchange processes coupled to isothermal diffusion in solution, the theoretical description and its experimental verification were given by Dahms [i] and by Ruff and co-workers [ii—v]. Ruff and co-workers studied the displacement of the centers of mass particles, which is brought about by both common migrational motion and chemical exchange reaction of the type... 

In 5-TiNo,5o, the random distribution of nitrogen atoms undergoes an ordering process below about 880 °C with a concurrent tetragonal distortion of the metal lattice. The so-formed S -TiNo.s phase is only formed from 5-TiNi by lattice distortion and is not an equilibrium phase (e g. it is not formed in isothermal diffusion couples in the form of a phase band). 

Let us first consider isothermal diffusion. Einstein s diffusion law can be written... 

Maxwell-Stefan Isothermal Diffusion for Binary mixtures... 

Kelt, T. R, and Anderson, D, K., Ternary Isothermal Diffusion and the Validity of the Onsager Reciprocal Relations in Non-associating Systems, J. Phys. Chem., 72, 1268-1274 (1969). 

Kirkaldy, J. S., Isothermal Diffusion in Multicomponent Systems, Advances in Materials Research, 4, 55-100 (1970). 

The separation of small amounts of nitrogen as ammonia consists in distillation from alkaline medium [1-4]. Ammonia escapes quantitatively when a strong base is added in excess and the solution is subsequently heated. The ammonia and steam driven off are condensed and collected in dilute acid. To prevent the liquid from being superheated, porous porcelain chunks are added to the still. Ammonia has also been separated by vacuum distillation and by isothermal diffusion. 

Figure 9.9 Exceptional physical properties of liquid water (solid lines) temperature dependences (upper diagrams) of the density d (45) and isothermal compressibility Xt (adapted from Refs. (45 7)) pressure dependences (lower drawings) of the shear viscosity 7] at various temperatures (adapted from Ref. (48)) and of the isothermal diffusion coefficient Z) at 0 (adapted from Ref. (49)). Dashed lines sketch typical dependences displayed by almost all other liquids. Note that at —15 °C no value is given for 17 at/ > 300MPa, because of a phase transition towards ice V (Figure 8.5).

From a formal (macroscopic) viewpoint, the diffusion process can be described in many cases of practical interest by Fick s two laws (1-5). These laws are represented by the following equations for the isothermal diffusion of a substance in or through a V-dimensional, hyperspherioal polymer body of sufficiently large area [V=l for a slab or membrane (film), v=2 for a hollow cylinder, and V=3 for a spherical shell] (2) ... 

Although this is a very complex equation, it allows to take into consideration any function of R(t), and consequently A(t), resulting from experiments with growing drops or bubbles. In combination with an adsorption isotherm (diffusion-controlled case) or a transfer mechanism (mixed diffusion-kinetic-controlled model) it describes the adsorption process at a growing or even receding drop. Eq. (4.48) can be applied in its present form only via numerical calculations and an algorithm is given by MacLeod Radke (1994). 

Figure 4A shows the 5 O profile developed after isothermal diffusion for varying... 

The isothermal-diffusion process for fabricating carbon-carbon has been reviewed previously and is not repeated here [37]. Only recently [116-118] has the forced flow-thermal gradient proeess been applied to making carbon-earbon. The latter work is... 

In this chapter the formalism of nonequilibrium thermodynamics, is reviewed. This formalism is then applied to the theory of isothermal diffusion and electrophoresis. It is shown that this theory is important in determining the relations between the transport coefficients measured by light scattering and those measured by classical macroscopic techniques. Since much of this material is covered in other chapters, this chapter is very brief. Our presentation closely follows that of Katchalsky and Curran (1965). Other books that can be consulted are those of DeGroot and Mazur (1962) and Prigogine (1955). 

ISOTHERMAL DIFFUSION OF UNCHARGED MOLECULES IN A TWO-COMPONENT SYSTEM... 

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