Diffusion binary

Although many systems involve more than two eomponents, the diffusion of eaeh speeies ean be treated as if it were diffusing through another single spe-eies rather than through a mixture by defining an effeetive diffusivity. Methods and examples for ealeulating this effective diffusivity can be found in Hill  

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Multicomponent Diffusion. In multicomponent systems, the binary diffusion coefficient has to be replaced by an effective or mean diffusivity Although its rigorous computation from the binary coefficients is difficult, it may be estimated by one of several methods (27—29). Any degree of counterdiffusion, including the two special cases "equimolar counterdiffusion" and "no counterdiffusion" treated above, may arise in multicomponent gas absorption. The influence of bulk flow of material through the films is corrected for by the film factor concept (28). It is based on a slightly different form of equation 13 ... 

The solute 1 is dissolved in a solvent pair of 2 and 3. D are infinite dilution binary diffusivities estimated by the proper method discussed previously. The mixture viscosity can be predic ted by methods of the previous section. The average absolute error when tested on 40 systems is 25 percent. The method gives higher errors if the solute is gaseous. 

Many more correlations are available for diffusion coefficients in the liquid phase than for the gas phase. Most, however, are restiicied to binary diffusion at infinite dilution D°s of lo self-diffusivity D -. This reflects the much greater complexity of liquids on a molecular level. For example, gas-phase diffusion exhibits neghgible composition effects and deviations from thermodynamic ideahty. Conversely, liquid-phase diffusion almost always involves volumetiic and thermodynamic effects due to composition variations. For concentrations greater than a few mole percent of A and B, corrections are needed to obtain the true diffusivity. Furthermore, there are many conditions that do not fit any of the correlations presented here. Thus, careful consideration is needed to produce a reasonable estimate. Again, if diffusivity data are available at the conditions of interest, then they are strongly preferred over the predictions of any correlations. 

The generalized Stefan-Maxwell equations using binary diffusion coefficients are not easily applicable to hquids since the coefficients are so dependent on conditions. That is, in hquids, each Dy can be strongly composition dependent in binary mixtures and, moreover, the binaiy is strongly affected in a multicomponent mixture. Thus, the convenience of writing multicomponent flux equations in terms of binary coefficients is lost. Conversely, they apply to gas mixtures because each is practically independent of composition by itself and in a multicomponent mixture (see Taylor and Krishna for details). 

If a liquid system containing at least two components is not in thermodynamic equilibrium due to concentration inhomogenities, transport of matter occurs. This process is called mutual diffusion. Other synonyms are chemical diffusion, interdiffusion, transport diffusion, and, in the case of systems with two components, binary diffusion. 

According to Maxwell s law, the partial pressure gradient in a gas which is diffusing in a two-component mixture is proportional to the product of the molar concentrations of the two components multiplied by its mass transfer velocity relative to that of the second component. Show how this relationship can be adapted to apply to the absorption of a soluble gas from a multicomponent mixture in which the other gases are insoluble and obtain an effective diffusivity for the multicomponent system in terms of the binary diffusion coefficients. 

The ordinary multicomponent diffusion coefficients D j and the viscosity and thermal conductivity are computed from appropriate kinetic theory expressions. First, pure species properties are computed from the standard kinetic theory expressions. For example, the binary diffusion coefficients are given in terms of pressure and temperature as... 

The diffusion constant Dj of neutral particle j is calculated in two steps. First, the binary diffusion coefficient Dij in each of the background gas species (SiH4, Si2H6, H2) is calculated, following Perrin et al. [192]. Then Dj is approximated using Blanc s law [219] ... 

Am pseudo-binary diffusivity of species A in a multicomponent gas mixture... 

Binary diffusion, 7 39-42 Binary electricity generation plant, 72 531-532... 

A schematic illustration of the method, and of the correlation between binary phase diagram and the one-phase layers formed in a diffusion couple, is shown in Fig. 2.42 adapted from Rhines (1956). The one-phase layers are separated by parallel straight interfaces, with fixed composition gaps, in a sequence dictated by the phase diagram. The absence, in a binary diffusion couple, of two-phase layers follows directly from the phase rule. In a ternary system, on the other hand (preparing for instance a diffusion couple between a block of a binary alloy and a piece of a third... 

The variation of efficiencies is due to interaction phenomena caused by the simultaneous diffusional transport of several components. From a fundamental point of view one should therefore take these interaction phenomena explicitly into account in the description of the elementary processes (i.e. mass and heat transfer with chemical reaction). In literature this approach has been used within the non-equilibrium stage model (Sivasubramanian and Boston, 1990). Sawistowski (1983) and Sawistowski and Pilavakis (1979) have developed a model describing reactive distillation in a packed column. Their model incorporates a simple representation of the prevailing mass and heat transfer processes supplemented with a rate equation for chemical reaction, allowing chemical enhancement of mass transfer. They assumed elementary reaction kinetics, equal binary diffusion coefficients and equal molar latent heat of evaporation for each component. 

The transport of an adsorbable species from the bulk fluid flowing around an individual bead is a problem of molecular diffusion. With the fluid in motion the rate of transport to the surface of a bead or pellet of adsorbent material is generally treated as a linear driving force. Eor gas phase separations there are a variety of correlations available to describe the mass transport to the surface in terms of the particle Reynolds number, the Schmidt number, the size of the adsorbent particle and of course the binary diffusivity of the species of interest. 

The binary diffusion coefficient, D k, can be either experimentally measured or calculated using the Chapman—Enskog equation. The dependence of the diffusion coefficient on temperature and pressure is generally given by ... 

One can roughly estimate the effects of gas-phase diffusion at steady state using a simple ID diffusion model, which has been employed (in some form) by numerous workers. 343 This approach yields the following expression for the linearized steady-state chemical resistance due to binary diffusion of O2 in a stagnant film of thickness... 

Chakraborty S. and Ganguly J. (1992). Cation diffusion in aluminosilicate garnets Experimental determination in spessartine-almandine diffusion couples, evaluation of effective binary diffusion coefficients, and applications. Contrib. Mineral Petrol, 111 74-86. 

Other general cases in binary systems are referred to as interdiffusion or binary diffusion. For example, Fe-Mg diffusion between two olivine crystals of different Xpo (mole fraction of forsterite Mg2Si04) is called Fe-Mg interdiffusion. Inter-diffusivity often varies across the profile because there are major concentration changes, and diffusivity usually depends on composition. 

Interdiffusion, effective binary diffusion, and multicomponent diffusion may be referred to as chemical diffusion, meaning there are major chemical concentration gradients. Chemical diffusion is defined relative to self diffusion and tracer diffusion, for which there are no major chemical concentration gradients. 

For binary diffusion in an isotropic medium, one diffusion coefficient describes the diffusion. For binary diffusion in an anisotropic medium, the diffusion coefficient is replaced by a diffusion tensor, denoted as D. The diffusion tensor is a second-rank symmetric tensor representable by a 3 x 3 matrix ... 

When one refers to the diffusion equation, it is usually the binary diffusion equation. Although theories for multicomponent diffusion have been extensively developed, experimental studies of multicomponent diffusion are limited because of instrumental analytical error and theoretical complexity, and there are yet no reliable diffusivity matrix data for practical applications in geology. Multicomponent diffusion is hence often treated as effective binary diffusion by treating the component under consideration as one component and combining all the other components as the second component. 

The one-dimensional binary diffusion equation with constant diffusion coefficient is (Equation 3-10)... 

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