Coupling of fluxes

In summary, junctions are more or less extended zones in crystals in which the disorder type changes and transport occurs along with simultaneous (local) reactions of the SE s. Junctions exhibit complex kinetic behavior due to the coupling of fluxes and reactions. The (p-n) junction is an interesting limiting case but has served to introduce the fundamental concepts of junctions. 

Diffusion in multicomponent system is difficult to analyze. Transport of one component is affected by the presence of the other component due to their mumal interaction. This results in the coupling of fluxes. Thus, single-component diffusion equation cannot be used to predict diffusion in a multicomponent system. Greenlaw et al. [38] proposed a simple relationship in which the diffusion coefficients for components i and j are interdependent on both component concentrations ... 

Separation from mixtures is achieved because the membrane transports one component more readily than the others, even if the driving forces are equal. The effectiveness of pervaporation is measured by two parameters, namely flux, which determines the rate of permeation and selectivity, which measures the separation efficiency of the membrane (controlled by the intrinsic properties of the polymer used to construct it). The coupling of fluxes affecting the permeability of a mixture component can be divided into two parts, namely a thermodynamic part expressed as solubility, and a kinetic part expressed as diffusivity. In the thermodynamic part, the concentration change of one component in the membrane due to the presence of another is caused by mutual interactions between the permeates in the membrane in addition to interactions between the individual components and the membrane material. On the other hand, kinetic coupling arises from the dependence of the concentration on the diffusion coefficients of the permeates in the polymers [155]. 

In this case, the most likely mechanism is the counterdiffusion of cations, i.e., the mechanism of Fig. 3.3c, where the electroneutrality is maintained by the coupling of flux of the cations. When the formation rate of the product is controlled by diffusion through the layer of the product, the thickness of the product layer will follow a parabolic growth law, which is given by ... 

In real systems, one comes across steady states and metastable states. Since coupling of fluxes and forces goes on uninterrupted, equilibrium state is hardly attained. It is... 

Under normal conditions, both demand and supply affect the price variation, and coupling of fluxes occurs. The resulting situation can be represented in terms of linear phenomenological equation as discussed in Part One as follows ... 

In order to demonstrate the principles of the formation of multiphase non-porous reduction layers, we shall now discuss the reduction of magnetite to iron. Even though the limiting case of non-porous reduced layers is only observed in exceptional cases, this discussion will nevertheless serve to illustrate the essential points, such as the coupling of fluxes at the phase boundaries. 

To take into account this coupling of fluxes, the model below employs the following assumptions. 

For a two-component system, a very brief excursion into the role of the coupling of fluxes is illustrative. For the system of solute i and solvent s and equations (3.1.208) and (3.1.209), eliminate the force and rearrange the equations to get (Johnson et al., 1966, 1980 Meares, 1976)... 

Although direct coupling of a camera to a scintillator can give acceptable results one of its major drawback is the degradation of the quantum noise mainly related to the low transmission of the optics. The following schematics summarizes the particles flux (photons and electrons) across the different stages of the detector ... 

A consequence of this theoretical approach which includes kinetic parameters is the establishment and coupling of certain ion fluxes across the phase boundary (equality of the sum of cathodic and anodic partial currents leading to a mixed potential). If a similar approach can be applied to asymmetric biological membranes with different thermodynamic equilibrium situations at both surfaces, the active ion transport could also be understood. 

The overall set of partial differential equations that can be considered as a mathematical characterization of the processing system of gas-liquid dispersions should include such environmental parameters as composition, temperature, and velocity, in addition to the equations of bubble-size and residence-time distributions that describe the dependence of bubble nucleation and growth on the bubble environmental factors. A simultaneous solution of this set of differential equations with the appropriate initial and boundary conditions is needed to evaluate the behavior of the system. Subject to the Curie principle, this set of equations should include the possibilities of coupling effects among the various fluxes involved. In dispersions, the possibilities of couplings between fluxes that differ from each other by an odd tensorial rank exist. (An example is the coupling effect between diffusion of surfactants and the hydrodynamics of bubble velocity as treated in Section III.) As yet no analytical solution of the complete set of equations has been found because of the mathematical difficulties involved. To simplify matters, the pertinent transfer equation is usually solved independently, with some simplifying assumptions. 

Similarly, we can pick another example in crystal growth in melt. In this case, the growth occurs at the interface between the melt and a substrate that is kept at a constant temperature that is lower than the critical temperature for crystallization. The morphology characteristic of the instability is formed by the coupling of the heat flux and the surface-form fluctuation. This problem was first theoretically analyzed by Mullins and Sekerka.57-62... 

Zhang, Y. and Kanner, B. I. (1999) Two serine residues of the glutamate transporter GLT-1 are crucial for coupling the fluxes of sodium and the neurotransmitter. Proc. Natl. Acad. Sci. USA 96,1710-1715. 

So far, water management models have assumed a controlled net water flux, through the PEM. The basic case in Eikerling et al. considered = 0. This approach is incomplete because it does not allow coupling of wafer fluxes in the membrane to water fluxes in other components and to externally... 

The liquid bulk is assumed to be at chemical equilibrium. Contrary to gas-liquid systems, for vapour-liquid systems it is not possible to derive explicit analytical expressions for the mass fluxes which is due to the fact that two or more physical equilibrium constants m, have to be dealt with. This will lead to coupling of all the mass fluxes at the vapour - liquid interface since eqs (15c) and (19) have to be satisfied. For the system described above several simulations have been performed in which the chemical equilibrium constant K = koiAo2 and the reaction rate constant koi have been varied. Parameter values used in the simulations are given in Table 5. The results are presented in Figs 9 and 10. 

How is a concentration gradient of protons transformed into ATP We have seen that electron transfer releases, and the proton-motive force conserves, more than enough free energy (about 200 lcJ) per mole of electron pairs to drive the formation of a mole of ATP, which requires about 50 kJ (see Box 13-1). Mitochondrial oxidative phosphorylation therefore poses no thermodynamic problem. But what is the chemical mechanism that couples proton flux with phosphorylation ... 

In order to do so we must first evaluate the chemical diffusion coefficients of the pair of majority defects (e.g., V and h ) in the semiconducting oxide A O. The coupling of the defect fluxes (jh--2jV = 0) to maintain electroneutrality results in a chemical diffusion coefficient Dv. This controls the change in nonstoichiometry, <5( ,/)> through defect transport and reads... 

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