Diffusion coefficient binary

The reduced integral of collision differs according to whether the species A and B 

The polarity parameter of the binary species AB can be calculated using the following relationship  

The two constituents have a dipolar moment p which is equal to zero and consequently a non-dimensional polarity parameter 6 equal to zero as a result 8 g = 0. Equation (6) can therefore be applied to calculate 2 thus  

Calculate the diffusion coefficient of methyl chloride in sulphur dioxide at 323 K and 1 atm. 

CH3CI is called A and SO2 is called B. The following values can be found in Tables XIV.3  

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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 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). 

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] ... 

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 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 ... 

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. 

Cooper A.R. and Varshneya A.K. (1968) Diffusion in the system K20-Sr0-Si02,1 effective binary diffusion coefficients. /. Am. Ceram. Soc. 51, 103-106. 

In the specific instance of A diffusing through a catalytic pore and reacting at the end of the pore to form gaseous component B, equimolar counterdiffusion can be assumed, and an effective transition region diffusivity, D a is independent of concentration and can be calculated from the Knudsen and binary diffusion coefficients ... 

The form of Eq. (4.84) should look familiar. For large, spherical particles in a low-molecular-weight solvent, f = 671 fir, where fi is the viscosity of the pure solvent and r is the large particle radius, and Eq. (4.84) becomes Equation (4.70) a form of the Stokes-Einstein equation, which gives the binary diffusion coefficient, Dab ... 

For a two-component mixture the multicomponent diffusion coefficients D, become the ordinary binary diffusion coefficients Sh,. For these quantities 2D,-, = 2D,- and 2D = 0. For a three-component system the multicomponent diffusion coefficients are not equal to the ordinary binary diffusion coefficients. For example, it has been shown by Curtiss and Hirschfelder (C12) in their development of the kinetic theory of multicomponent gas mixtures that... 

Note that in Eq. (60) it is the multicomponent Dtj which appear, whereas in Eq. (61) the binary diffusion coefficients Sh, appear.13 For a system at constant temperature and pressure Eq. (61) may also be written... 

DiT Multicomponent thermal diffusion coefficients 3>ab Binary diffusion coefficients (37)... 

Various forms of diffusion coefficients are used to establish the proportionality between the gradients and the mass flux. Details on determination of the diffusion coefficients and thermal diffusion coefficients is found in Chapter 12. Here, however, it is appropriate to summarize a few salient aspects. In the case of ordinary diffusion (proportional to concentration gradients), the ordinary multicomponent diffusion coefficients Dkj must be determined from the binary diffusion coefficients T>,kj. The binary diffusion coefficients for each species pair, which may be determined from kinetic theory or by measurement, are essentially independent of the species composition field. Calculation of the ordinary multicomponent diffusion coefficients requires the computation of the inverse or a matrix that depends on the binary diffusion coefficients and the species mole fractions (Chapter 12). Thus, while the binary diffusion coefficients are independent of the species field, it is important to note that ordinary multicomponent diffusion coefficients depend on the concentration field. Computing a flow field therefore requires that the Dkj be evaluated locally and temporally as the solution evolves. 

In a low-density limit the binary diffusion coefficient between two gaseous species may be determined from kinetic theory as... 

Substituting all the constants yields the following expression for the binary diffusion coefficients ... 

Pressure Dependencies Equation 3.95 predicts the binary diffusion coefficient to scale as p l, which is generally true except as the pressure approaches or exceeds the critical pressure. The Takahashi formula [392], which can be used to describe the high-pressure behavior, is discussed below. The Chapman-Enskog theory also predicts that Vji, increases with temperature as T3/2. However, it is often observed experimentally the temperature exponent is somewhat larger, say closer to 1.75 [332], An empirical expression for estimating T>jk is due to Wilke and Lee [433]. The Wilke-Lee formula is [332]... 

In the foregoing discussion the diffusive mass fluxes are written in terms of the diffusion velocities, which in turn are determined from gradients of the concentration, temperature, and pressure fields. Such explicit evaluation of the diffusion velocities requires the evaluation of the multicomponent diffusion coefficients from the binary diffusion coefficients. 

Note that the Stefan-Maxwell equations involve the binary diffusion coefficients, and not the ordinary multicomponent diffusion coefficients. 

Evaluate the binary diffusion coefficient between Cd and Te2, and it plot as a function of temperature. 

The previous section discussed techniques for obtaining the molecular potential interaction parameters <7 and e based on pure species physical properties of molecule i. Interactions between unlike molecules (i.e., all i-j pairs) must also be considered in the calculation of transport properties (notably, binary diffusion coefficients). The following is a set of combining rules to estimate the i- j interaction parameters, assuming that the pure species values are known. 

Binary diffusion coefficients are given in terms of pressure and temperature as [178]... 

To expedite the evaluation of transport properties, one could fit the temperature dependent parts of the pure species viscosities, thermal conductivities, and pairs of binary diffusion coefficients. Then, rather than using the complex expressions for the properties, only comparatively simpler polynomials would be evaluated. The fitting procedure must be carried out for the particular system of gases that is present in a given problem. Therefore the fitting cannot be done once and for all but must be done once at the beginning of each new problem. 

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