Cross-diffusion

If cross-diffusion due to the chemical reaction is neglected, the diffusive currents are proportional to the gradients of concentrations... 

Polymer transport in ternary systems including an analysis of the cross diffusion coefficients and component distribution within the systems. 

DSi are the principal or main diffusion coefficients and Dy the interaction or cross-diffusion coefficients. These diffusion coefficients can be expressed by phenomenological coefficients and chemical potentials as follows ... 

This will be elaborated in detail in the following section. However, it is of interest that the existence of concentration-dependent (implying a far-from-equilibrium condition) cross-diffusion terms creates a non-linear mechanism between elements of the system, i.e. the flux of one polymer depends not only on its own concentration gradient but also on that of the other polymer component. This is consistent with two of the criteria required for dissipative structure formation. Furthermore, once a density inversion is initiated, by diffusion, it will be acted upon by gravity (as the system is open ) to produce a structured flow. The continued growth, stability and maintenance of the structures once formed may depend on the lateral diffusion processes between neighbouring structures. 

Chloramphenicol. The broad-spectrum antibiotic chloramphenicol is completely absorbed after oral ingestion. It undergoes even distribution in the body and readily crosses diffusion barriers such as the blood-Luellmann, Color Atlas of Pharmacology 2005 Thieme All rights reserved. Usage subject to terms and conditions of license. 

It is pertinent to consider separately the enhancement effect of salt on two steps the initiation step (onset of the flow) and the structured flow. The transport rates are related to the properties of the final structured flow and are contributed from the effects on both steps. The effect on the initiation step is clearly noticed since the critical PVP concentrations for the occurrence of the structured flow depended on the kind of salt. Effects of a salt on the cross diffusion constants of the two polymer components will be examined on both excluded volume and frictional effect. The effect on the excluded volume interaction between the two polymer components is expected to be small. This expectation is partly supported by the result that coil dimension of PVP was not influenced by the addition of a salt at 2 M in the cases of three salts LiCl, NaCl and CsCI, while these salts showed quite diverse effects on the trrmsport rates of PVP. Since viscosities vary with the kind and the concentration of salt, frictional coefficients are influenced by the presence of a salt. In this respect cross diffusion constants may be affected by salt through a change in viscosity of the medium. 

As to the osmotic model, Comper and Preston have questioned its validity as a probable mechanism leading to density inversion. According to their argument, the main diffusion constant of PVP should equal to the cross diffusion constant of dextran if the osmotic model is valid. This expected relation was not found experimentally. 

At the beginning of the 1980s, the interest in DMFC arose and methanol was used as fuel for high-temperature fuel cells [12]. Nowadays, PEM fuel cells with Nafion as electrolyte appear to be well suited for the direct oxidation of methanol. There are, however, some major problems in adapting a PEMFC to operate with methanol. The catalytic material of the anode has to be improved in order to avoid the loss of activity because of the formation of by-products. As in the case of a PEMFC using hydrogen from a reformer as fuel, a method to improve the anodic material is the use of Pt-Ru or Pt-Ru-Sn mixtures [8]. A particular problem of the DMFC is cross-diffusion of methanol through the electrolyte. 

Organic Mercury. Distribution of organic mercury compounds in humans and animals is similar to that of metallic mercury. Methylmercury distributes readily to all tissues, including the brain and fetus, after absorption from the gastrointestinal tract. The uniform tissue distribution is due to methylmercury s ability to cross diffusion barriers and penetrate all membranes without difficulty (Aberg et al. 1969 Miettinen 1973). Thus, tissue concentrations tend to remain constant relative to blood levels. About 90% of the methylmercury in blood is found in the red blood cells (Kershaw et al. 1980). The mean mercury concentrations in red blood cells were 27.5 ng/g and 20.4 ng/g in males and females, respectively, exposed to mercury, primarily from mercury-contaminated fish (Sakamoto et al. 1991). Because of this uniform distribution in tissues, blood levels are a good indicator of tissue concentrations independent of dose (Nordberg 1976). 

Fig. 3.6 The top (a) and the side (b) views of the cross-diffusion geometry used for the preparation of the molecular gradients. The glass filters are used as a preconcentration zone for the thiols. The geometry of the cell, including Teflon barriers, allows only diffusion in one direction. Several reservoirs for the organic solvent (swelling fluid) were added to guarantee a permanent wetting of the gel. The cell was covered with a lid to avoid evaporation...

Possible influences of nonequilibrium cross-diffusion effects on the mixing process were investigated by means of direct numerical simulations (DNS) of mass fraction fluctuations in stationary isotropic turbulence for binary mixtures under supercritical conditions (26,27). The authors have shown that after some time, the initially perfectly mixed species become segregated owing to the presence of temperature and pressure fluctuations and the resulting Soret mass cross-diffusion fluxes Jj and /f, induced by temperature and pressure gradients. Based on DNS results (26,27), we propose a phenomenological model that predicts the rate of production of the concentration variance as... 

Results of calculations (Figure 9) show that the concentration variance increases with increases in both the power input for mixinge and the molecular weight ratio of the species. The cross-diffusion effects can affect the process of particle production only in the case of fast mixers (e.g., nozzle mixers), characterized by extremely large values of the rate of energy dissipation. It should be noted particle nucleation is very sensitive to supersaturation (Section 5) and... 

Here, Z) is the diffusion coefficient for the A species and we have dropped cross-diffusion effects. Similar equations can be written for the other species. 

A result with the same structure as the macroscopic law follows when terms to order are retained, cross-diffusion and cross-diffusion-reaction terms are neglected, and a Markov approximation 2 (z = 0)5(/), is... 

Since the second term is 0(/ifq) we have, to lowest order in solute densities with neglect of cross-diffusion-reaction terms as in (5.11),... 

For the barrier reactions for which this simple model is suitable, the probability of reaction upon collision is 0(exp( —)), with barrier height. Slow reactions therefore have small a. The order of magnitude of 5(r,2 - ab) i2 [ i2 can be estimated from the arguments in Section III as i2 ab) - Thus this cross-diffusion-reaction term is... 

We have made an addition approximation in writing (C.9) the coupling between the singlet A and singlet B fields has been dropped. This coupling is due to elastic collisions between A and B molecules, and it gives rise to cross-diffusion coefficients, which can be neglected in a dilute system. Most elastic collisions are with solvent molecules. 

This equation shows that a gradient in concentration c can induce a flow of component/. Dfj is called a cross-diffusion coefficient. Equation (13.6.4a) can be expressed in matrix form... 

Let us restrict ourselves, as before, to small deviations from equilibrium 6 Cj (6 Cj c°). Then the following diffusion equations can be written neglecting the cross diffusion fluxes ... 

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