Diffusion in a Binary System

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... 

Uphill diffusion in a binary system is rare and occurs only when the phase undergoes spinodal decomposition. In multicomponent systems, uphill diffusion occurs often, even when the phase is stable. The cause for uphill diffusion in multicomponent systems is different from that in binary systems and will be discussed later. 

Diffusion in a binary system may also be determined by measurement of the intradiffusion coefficient (sometimes referred to as the self-diffusion coefficient), D. In the case of intradiffusion, no net flux of the bulk diffusant occurs the molecules undergo an exchange process. Measurements are usually carried out by using trace amounts of labelled components in a system free of any gradients in the chemical potential. The molecular movement of the solute is governed by frictional interactions between labelled solute and solvent, and labelled solute and unlabelled solute. 

In comparison with the qualitative description of diffusion in a binary system as embodied by Eqs. (11), (12) or (14), the thermodynamic factors are now represented by the quantities a, b, c, and d and the dynamic factors by the phenomenological coefficients which are complex functions of the binary frictional coefficients. Experimental measurements of Dy in a ternary system, made on the basis of the knowledge of the concentration gradients of each component and by use of Eqs. (21) and (22), have been reviewed 35). Another method, which has been used recently36), requires the evaluation of py from thermodynamic measurements such as osmotic pressure and evaluation of all fy from diffusion measurements and substitution of these terms into Eqs. (23)—(26). 

After this formal discussion of chemical diffusion, let us now turn to some more practical aspects. In order to compare the formal theory with experiment, we have to carefully define the reference frame for the diffusion process, which is not trivial in the case of binary or multicomponent diffusion. To become acquainted with the philosophy of this problem, we deal briefly with defining a suitable reference frame in a binary system. Since only one (independent) transport coefficient is needed to describe chemical diffusion in a binary system, then according to Eqn. (4.57) we have in a one-dimensional system... 

Figure 3.2 Diffusion couple for measuring solute self-diffusion in a binary system.

The ZLC method offers advantages of speed and simplicity and requires only a very small adsorbent sample thus making it useful for characterization of new materials. The basic experiment using an inert carrier (usually He) measures the limiting transport difiiisivity (Do) at low concentration. A variant of the technique using isotopically labeled tracers (TZLC) yields the tracer diffiisivity and counter diffusion in a binary system may also be studied by this method. To obtain reliable results a number of preliminary experiments are needed, e.g. varying sample quality, nature of the purge gas, the flow rate and, if possible, particle size to confirm intracrystalline diffusion control. 

Stability with respect to Diffusion in a Binary System. 

For diffusion in a binary system, the energy barrier for lattice hopping is given by Equation (4.7) for an atom, j, with a given configuration of A and B metal and electrolyte neighbors. 

Reactive Diffusion in a Binary System at an Imposed Electric Current at Nonequilibrium Vacancies... 

The simple mean free path approach is not adequate for describing mutual diffusion in a binary system at constant temperature. Only in one case is the theory self-consistent—when the molecules are mechanically indistinguishable (self-diffusion). By integrating (2.31) we obtain the total flux of one component, /a = J Since the only position-dependent quantity is nj (z), the analysis used in the derivation of Poiseuille s law yields... 

In simple molecular diffusion in a binary system under iso-baric condition. 

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