Solution diffusion model single-component

Numerical Solution of the Lumped Pore Diffusion Model (or FOR Model) for Single Component Systems... 

In Chapter 14, we discussed the case of a single-component band. In practice, there are almost always several components present simultaneously, and they have different mass transfer properties. As seen in Chapter 4, the equilibrium isotherms of the different components of a mixture depend on the concentrations of all the components. Thus, as seen in Chapters 11 to 13, the mass balances of the different components are coupled, which makes more complex the solution of the multicomponent kinetic models. Because of the complexity of these models, approximate analytical solutions can be obtained only under the assumption of constant pattern conditions. In all other cases, only numerical solutions are possible. The problem is further complicated because the diffusion coefficients and the rate constants depend on the concentrations of the corresponding components and of all the other feed components. However, there are still relatively few papers that discuss this second form of coupling between component band profiles in great detail. In most cases, the investigations of mass transfer kinetics and the use of the kinetic models of chromatography in the literature assume that the rate constants and the diffusion coefficients are concentration independent. This seems to be an acceptable first-order approximation in many cases, albeit separation problems in which more sophisticated theoretical approaches are needed begin to appear as the accuracy of measru ments improve and more interest is paid to complex... 

At subcritical potentials a single oxidation process with participation of only electronegative component takes place on the surface of the alloy. The surface layer is saturated with nonequilibrium defects (mainly vacancies), maintains morphological stability and represents a diffusion zone in which the atomic fraction of the noble component gradually increases as we approach the interface with the solution [6-9], According to the volume-diffusion model [10, 11], the formation of such zone is limited by the time-dependent interdiffusion of alloy components for the vacancy mechanism. 

Three models were used to simulate the observed extraction rates for the oily components. Each of employed the effective diffusivity De as an adjustable parameter. They were the Characteristic Time Model (3) two other published models here designated Single Sphere Models I (4,5) and II (6). In these models it is assumed that the solute is extracted from a particulate bed composed of porous... 

To reveal the effect of the rate of chemical steps, we consider concentration profiles simulated for the certain model system. To make the mathematics simpler, we explore only a hmited number of components emphasizing that an increase in their number has no effect on general conclusions. Thus, the system to be analyzed would contain only free metal ions (aqua complexes) M", monoUgand complexes ML , and uncharged Ugand L. Then, a single chemical reaction Eq. (3.16) occurs both in the bulk of solution and in the 5-thick diffusion layer. 

---