Diffusivity, mass binary

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. 

Although there has not been much theoretical work other than a quantitative study by Hynes et al [58], there are some computer simulation studies of the mass dependence of diffusion which provide valuable insight to this problem (see Refs. 96-105). Alder et al. [96, 97] have studied the mass dependence of a solute diffusion at an infinite solute dilution in binary isotopic hard-sphere mixtures. The mass effect and its influence on the concentration dependence of the self-diffusion coefficient in a binary isotopic Lennard-Jones mixture up to solute-solvent mass ratio 5 was studied by Ebbsjo et al. [98]. Later on, Bearman and Jolly [99, 100] studied the mass dependence of diffusion in binary mixtures by varying the solute-solvent mass ratio from 1 to 16, and recently Kerl and Willeke [101] have reported a study for binary and ternary isotopic mixtures. Also, by varying the size of the tagged molecule the mass dependence of diffusion for a binary Lennard-Jones mixture has been studied by Ould-Kaddour and Barrat by performing MD simulations [102]. There have also been some experimental studies of mass diffusion [106-109]. 

Several experimental techniques have been developed for the investigation of the mass transport in porous catalysts. Most of them have been employed to determine the effective diffusivities in binary gas mixtures and at isothermal conditions. In some investigations, the experimental data are treated with the more refined dusty gas model (DGM) and its modifications. The diffusion cell and gas chromatographic methods are the most widely used when investigating mass transport in porous catalysts and for the measurement of the effective diffusivities. These methods, with examples of their application in simple situations, are briefly outlined in the following discussion. A review on the methods for experimental evaluation of the effective diffusivity by Haynes [1] and a comprehensive description of the diffusion cell method by Park and Do [2] contain many useful details and additional information. 

Here is the (diffusive) mass flux of species A (mass transfer by diffusion per unit time and per unit area normal to the direction of mass transfer, in kg/s m ) and is the (diffusive) molar flux (in kmol/s m ). The mass flux of a species at a location is propoitional to the density of the mixture at that location. Note that p = Px + Pb density and C = Q + is the molar concentration of the binary mixture, and in general, they may vary throughout the mixture. Therefore, pd(pjp) dp or Cd(C /C) + dC - But in the special case of constant mixture density p or constant molar concentration C, the relations above simplify to... 

For binary mixtures the diffusive mass flux jc of species c is normally approximated by Pick s first law ... 

In addition, the net diffusive mass ffux for each phase vanishes for binary systems as s adopting Pick s law. Nevertheless, this... 

The net diffusive mass flux for each phase still vanishes for binary systems as A s using Pick s law, whereas for dilute pseudobinary systems the latter relationship is only approximate. 

The convective diffusion mass transfer equation is solved for a binary mixture of reactant A and product B. 

CONNECTION BETWEEN TRANSPORT PHENOMENA AND THERMODYNAMICS FOR DIFFUSIONAL MASS FLUXES AND DIFFUSIVITIES IN BINARY MIXTURES... 

Jj is the molar flux vector for species j with respect to the mass average velocity (kmol/m s). When the flow is laminar or perfectly ordered the term V Jj results from molecular diffusion only. It can be written more explicitly as an extension, already encountered in Chapter 3, of Pick s law for diffusion in binary systems, as... 

Krishna R. Diffusion of binary mixtures across zeohte membranes Entropy effects on permeation selectivity. Int Commun Heat Mass Transfer 2001 28 337-346. 

In this work, an incremental approach to model identification is introduced. The new method follows the steps of model development in the identification procedure. This reduces uncertainty in the estimation problems. Furthermore, it allows the efficient exploitation of model structure and thereby reduces the computational expense substantially. The proposed method is applied to examples from binary and ternary diffusive mass transfer and its performance is compared to current approaches. 

The expression for the total diffusion mass flux in a binary system for component 1 is given by Bird et al. (1960), and Ghorayeb and Firoozabadi (1999) ... 

Phase diagrams of ternary systems usually contain two-phase regions in the solid state (see e.g., [2] and Figure 10.1). The diffusion mass transfer in ternary and multicomponent systems is essentially different from the case of a binary system in quasiequilibrium as there exists the possibility of two-phase zone formation in the diffusion process. Though two-phase formation is connected with the thermodynamic disadvantage of interphase boundaries formation, there are cases when any other diffusion mode is impossible. Formation of two-phase regions may also proceed at high reaction rates at interfaces, that is, the assumption of quasiequilibrium of the interdiffusion process is imposed. Subsequently, we can apply the apparatus of hnear thermodynamics for irreversible processes [3-5]. 

Obviously, the parameter y is a measure of the kinetic situation when the rate-limiting step of the selective dissolution is the solid-phase diffusion mass transfer. It is clear that the increase in y contributes to the transition to the solid-phase diffusion control of the process the similar criterion was found in [4] for chronoampero- and chronopotentiometric diffusion problems of homogeneous binary alloys SD. 

The consistency with Pick s first law for binary systems (2.301) is examined comparing the generalized Fickian mass flux vectors (2.310), including the Maxwell-Stefan diffusivity (2.391), the Bird et al. [9] generalized Fickian diffusivity (2.311), and the binary diffusivity. For binary systems, i.e., s,r = 1,2, the Fickian mass flux vector (2.310) reduces to ... 

Find the mass transfer coefficient in this case, assuming that diffusion obeys binary equations, with diffusion coefficients that are the same for all species. 

Rate equations 28 and 30 combine the advantages of concentration-independent mass transfer coefficients, even in situations of multicomponent diffusion, and a familiar mathematical form involving concentration driving forces. The main inconvenience is the use of an effective diffusivity which may itself depend somewhat on the mixture composition and in certain cases even on the diffusion rates. This advantage can be eliminated by working with a different form of the MaxweU-Stefan equation (30—32). One thus obtains a set of rate equations of an unconventional form having concentration-independent mass transfer coefficients that are defined for each binary pair directiy based on the MaxweU-Stefan diffusivities. 

Mass Transport. An expression for the diffusive transport of the light component of a binary gas mixture in the radial direction in the gas centrifuge can be obtained directly from the general diffusion equation and an expression for the radial pressure gradient in the centrifuge. For diffusion in a binary system in the absence of temperature gradients and external forces, the general diffusion equation retains only the pressure diffusion and ordinary diffusion effects and takes the form... 

Diffusion is the molecular transport of mass without flow. The diffu-sivity (D) or diffusion coefficient is the proportionality constant between the diffusion and the concentration gradient causing diffusion. It is usually defined by Fick s first law for one-dimensional, binary component diffusion for molecular transport without turbulence shown by Eq. (2-149)... 

In binary ion-exchange, intraparticle mass transfer is described by Eq. (16-75) and is dependent on the ionic self diffusivities of the exchanging counterions. A numerical solution of the corresponding conseiwation equation for spherical particles with an infinite fluid volume is given by Helfferich and Plesset [J. Chem. Phy.s., 66, 28, 418... 

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. 

In binary solutions, for example, CuS04 in H20, the limiting current exceeds that due to convective diffusion alone by a factor of about two. The excess mass transfer is caused by migration of the reacting ion in the electric field. In both forced and free convection it is important to know the ion flux contributed by migration, which can never be suppressed completely. 

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