Mutual diffusion, definition

Whereas mutual diffusion characterizes a system with a single diffusion coefficient, self-diffusion gives different diffusion coefficients for all the particles in the system. Self-diffusion thereby provides a more detailed description of the single chemical species. This is the molecular point of view [7], which makes the selfdiffusion more significant than that of the mutual diffusion. In contrast, in practice, mutual diffusion, which involves the transport of matter in many physical and chemical processes, is far more important than self-diffusion. Moreover mutual diffusion is cooperative by nature, and its theoretical description is complicated by nonequilibrium statistical mechanics. Not surprisingly, the theoretical basis of mutual diffusion is more complex than that of self-diffusion [8]. In addition, by definition, the measurements of mutual diffusion require mixtures of liquids, while self-diffusion measurements are determinable in pure liquids. 

If Eq. (2.3-6) is chomn as the definition, then it immediately follows by use of Eq. (2.3-5) that = Dba thal is, there is a single mutual diffusion coefficient in a binary system. If Eq. (2.3-6a) is chosen, Dj,A DXb, but there would be a relationship between them so that there still is only a single chaincteristic diffusivity fora binary system. The choice of Eq. (2.3-6) is preferred because of its simplicity although it certainly is not intrinsically better then Eq- (2.3-6a). 

Bridging effects. A definite interaction is involved in this process that may include mutual diffusion or "alloying" between the substance of the particle and the surface. Liquid/solid bridging may be involved at the interface that invokes capillary forces. 

The diffusivity (D) defined in this way is not necessarily independent of concentration. It should be noted that for diffusion in a binary fluid phase the flux (/) is defined relative to the plane of no net volumetric flow and the coefficient D is called the mutual diffusivity. The same expression can be used to characterize migration within a porous (or microporous) sohd, but in that case the flux is defined relative to the fixed frame of reference provided by the pore walls. The diffusivity is then more correctly termed the transport diffusivity. Note that the existence of a gradient of concentration (or chemical potential) is implicit in this definition. 

In the absence of bulk flow one is led by arguments using a d)mamic version of the random phase approximation to an alternative expression to equation (4.4.11), in which it is the slow chains that dominate the kinetics (Brochard et al. 1983). This is sometimes referred to as the slow theory . There have been suggestions (Akcasu et al. 1992) that mutual diffusion should approach the slow-theory limit as the temperature is reduced towards the glass transition temperature of one of the components. A definitive solution to this problem awaits more work, both theoretical and experimental. 

The driving force of a membrane for gas separation is the pressure difference across the membrane. The yield of the separated gas can be expressed in terms of membrane permeance, which can be characterised by the amount of permeated gas that passes through a certain membrane area in a given time at a definite pressure difference. The values of permeability are often quoted in Barter (1 Barter=10 cm s cm cm Hg = 3.35 x 10 mol m m s Pa STP, standard temperature and pressure). Gas permeation phenomena can be described by a simple solution diffusion model, which involves (l) sorption or dissolution of the permeating gas in the membrane at the higher pressure side, (2) diffusion through the membrane and (3) desorption or dissolution at the lower pressure side. Thus, the permeability coefficient P can be determined by the product of the solubility coefficient S and the mutual diffusion coefficient D [eqn (5.1)] ... 

The definitions of the mass, molar, and volume average bulk velocities are given in Table 1 along with selected mass and molar flux expressions related to each of the specified reference velocities for a binary system of components A and B. The mutual diffusion coefficient Dab is the diffusivity of component A and B in the mixture as defined below. The mutual diffusion coefficients appearing in Table 1 are identical in all of the expressions and Dab = DBA-... 

Table I presents six basic equations in a general way. Those on the left apply to transfer within a phase A, and those on the right to transfer across a phase boundary AB. The top row expresses the mutual definition of force F, proportionality constant K, and potential . The second row expresses the phenomenological proportionality between flux J and force F. The bottom row states the conservation constraints. The left equation says merely that in a given volume the difference between the accumulation rate and the emanation rate must be attributed to a source S. As stated, these equations apply to any conserved quantity which is diffusing, either within a phase under the influence of a potential gradient or across a phase under the influence of a potential difference.

The linear stability of these new supercritical branches is then tested (Ai = Ai s + One finds that if 90 < 9nd, as is usually the case in isotropic reaction-diffusion problems (heterogeneous catalysis may provide counterexamples), the stripes are stable and the squares unstable. The reverse condition leads to the opposite conclusion. Therefore stripes and squares are mutually exclusive [33]. However no definitive conclusion regarding the stability of the winning state should be drawn as its stability must still be tested with respect to perturbations involving higher values of M. As always their stability should also be checked regarding wavenumber changes (Section 4). 

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