Multi-component diffusion

Low-PressureAlulticomponent Mixtures These methods are outlined in Table 5-17. Stefan-MaxweU equations were discussed earlier. Smith-Taylor compared various methods for predicting multi-component diffusion rates and found that Eq. (5-204) was superior among the effective diffusivity approaches, though none is very good. They so found that hnearized and exact solutions are roughly equivalent and accurate. 

Zielinski, J.M. and Hanley, B.F. A.I.Ch.E.Jl. 45 (1999) 1. Practical friction-based approach lo modeling multi component diffusion. 

The DICTRA programme is based on a numerical solution of multi-component diffusion equations assuming that thermodynamic equilibrium is locally maintained at phase interfaces. Essentially the programme is broken down into four modules which involve (1) the solution of the diffusion equations, (2) the calculation of... 

As long as care is taken so that effective binary diffusivity obtained from experiments under the same set of conditions is applied to a given problem, the approach works well. Although the limitations mean additional work, because of its simplicity and because of the unavailability of the diffusion matrices, the effective binary diffusion approach is the most often used in geological systems. Nonetheless, it is hoped that effort will be made in the future so that multi-component diffusion can be handled more accurately. 

Cooper A.R. (1965) Model for multi-component diffusion. Phys. Chem. Glasses 6, 55-61. 

Liang Y., Richter F.M., and Watson E.B. (1996b) Diffusion in silicate melts, II multi-component diffusion in Ca0-Al203-Si02 at 1500°G and 1 GPa. Geochim. Cosmochim. Acta 60, 5021-5035. 

Chapman-Enskog theory provides the basis for the multicomponent transport properties laid out by Hirschfelder, Curtiss, and Bird [178] and by Dixon-Lewis [103]. The multi-component diffusion coefficients, thermal conductivities, and thermal diffusion coefficients are computed from the solution of a system of equations defined by the L matrix [103], seen below. It is convenient to refer to the L matrix in terms of its nine block submatrices, and in this form the system is given by... 

LPCVD reactor modeling involves many of the same issues of multi-component diffusion reactions that have been studied in the past decade in connection with heterogeneous catalysis. Complex fluid-flow phenomena strongly affect the performance of atmospheric-pressure CVD reactors. Two-dimensional and some three-dimensional flow structures in the classical horizontal and vertical CVD reactors have been explored through flow visual-... 

No, H-C., et al. (2007), Multi-component Diffusion Analysis and Assessment of GAMMA Code and Improved RELAP5 Code , Nucl. Eng. and Design, 237, 997-1008. 

The multi-component diffusivities in the gas mixture can be approximated by the modified Stefan-Maxwell equations(8,9) i.e ... 

Consider a multi-component diffusion-reaction problem. [19] [4] [20] The governing equations for molar fractions of gas and liquid reactants inside a gas-fed porous electrode of a fuel cell are ... 

Consider multi-component diffusion of gases A and B through stagnant gas C (Gianakopulos, 1972 Cutlip and Shacham, 1999).[23] The governing equations for concentration of A and B are ... 

A multicomponent Fickian diffusion flux on this form was first suggested in irreversible thermodynamics and has no origin in kinetic theory of dilute gases. Hence, basically, these multicomponent flux equations represent a purely empirical generalization of Pick s first law and define a set of empirical multi-component diffusion coefficients. 

The diffusion coefficients used to describe multi-component diffusion are mutual diffusion coefficients. In the multi-component system, mutual diffusion coefficients are defined by Equation 4-13 the matrix of diffusion coefficients depends on the concentration of individual components. The diffusion coefficients used in the earlier sections of the chapter, however, describe solute molecules diffusing in a medium at infinite dilution. The isolated molecule is called a tracer these tracer diffusion coefficients are defined by the physics of random walk processes, as described in Chapter 3. The self-diffusion coefficient, used in Equation 4-11, is a tracer diffusion coefficient in the situation where all of the molecules in the system are identical. The self-diffusion coefficient, T>aa is defined by (recall Equation 3-12) [62] ... 

Binary diffusion coefficient of solute A in water (cm /s) Multi-component diffusion coefficient (cm /s)... 

A model, frequently referred to as dusty-gas model [1-3], can be used to describe multi-component diffusion in porous media. This model is based on the Stefan-Maxwell approach for diluted gases which is an approximation of Boltzmann s equation. The pore walls are considered as consisting of giant molecules ( dust ) distributed in space. These dust molecules are treated as the n+l-th pseudo-species in a n-component gaseous mixture. The dust particles are kept fixed in space, and are treated like a gas component in the Stefan-Maxwell equations. This model analyzes the transport problem by distinguishing three separate components 1) diffusion, 2) viscous flow and 3) structure of the porous medium. 

The diagonal coefficients R m found using eq 14.24. We see that the diffusion coefficients are symmetric, Djk = Dicj. In order to obtain the Maxwell-Stefan equations for multi-component diffusion, we introduce the velocities = Using eq 14.24, we can write eq 14.22 in the form... 

The Maxwell-Stefan equations give, therefore, a convenient way to describe multi-component diffusion. ... 

Meerdink, G 1993. Drying of liquid food droplets Enzyme inactivation and multi-component diffusion. Diss., Agricultural University Wageningen, The Netherlands. 

Ammonia synthesis reaction is a complex multi-component and reversible reaction, and the kinetic equation can be expressed by power function. For simplification, the multi-component diffusion model is usually simply treated in engineering as a single-component diffusion model of key component, and the utilization ratio of internal surface is obtained by an approximate method from a simplified first-order reaction model. 

The reaction under consideration may involve a solvent and/or one or more liquid-phase products, thus making it a multi-component diffusion system. In such cases, Z>b represents the solute diffusivity in the liquid mixture including the products. To simplify the effort to make a reasonable estimate of Z>b, the relatively insignificant components may be neglected. For example, the following expression can then be used to calculate the diffusivity of a solute, gas or liquid, in 2-solvent liquid system (39) ... 

D is the multi-component diffusion coefficient of the material of gas diffusion layer given by the Bruggeman equation... 

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