Cross-diffusion, effect

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. 

If the concentration gradient is in the y-direction, then the Rouse model predicts no change in the mass flux in the y-direction, but does give a cross-diffusion term in the x-direction. If, on the other hand, the concentration gradient is in the x-direction, then - according to the Rouse chain model - the mass flux in the x-direction is altered by the flow, and there is a cross-diffusion effect in the jMlirection. 

Thermal diffusion coefficients should not be confused with the thermal diffusivity, a quantity defined in terms of the thermal conductivity and referring to conduction of heat (see Section E.5). Thermal diffusion one of the cross-transport effects, is a physical process entirely separate from heat conduction. It tends to draw light molecules to hot regions and to drive heavy molecules to cold regions of the gas. Hydrogen is a species that is... 

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. 

For an evaluation of these methods, it is important to analyze the effects of the delays on cross-relaxation and on the efficiency of Hartmann-Hahn transfer. In order to avoid spin diffusion effects, the effective crossrelaxation rate should be averaged to zero on a time scale that is short compared to the inverse cross-relaxation rates. In practice, this implies that the delays must be separated by less than about 10 ms (Bearden et al., 1988). This condition is excellently fulfilled by Methods C and D, and can also be fulfilled by Method B if the delays are introduced after only a few repetitions of the basis sequence. However, in most cases spin diffusion effects cannot be suppressed using Method A. 

Effects similar to those of the lift force are observed when implementing the turbulent dispersion force using the gradient diffusion model. This dispersion force closure smoothes out sharp velocity gradients in the domain. If the model overestimates the diffusive effect, the velocity profiles may become completely flat over the column cross section. 

There can often be more than one resistance to mass transfer. These resistances can include boundary layer and diffusion effects. For example, in adsorption a solute must diffuse through a fluid, cross the boundary layer between the fluid and the solid sorbent,... 

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