Concentration gradient, near interfac

Similar statements can be made about holes. They, too, have to be transported to the interface to be available for the receipt of electrons there. These matters all come under the influence of the Nernst-Planck equation, which is dealt with in (Section 4.4.15). There it is shown that a charged particle can move under two influences. The one is the concentration gradient, so here one is back with Fick s law (Section 4.2.2). On the other hand, as the particles are changed, they will be influenced by the electric field, the gradient of the potential-distance relation inside the semiconductor. Electrons that feel a concentration gradient near the interface, encouraging them to move from the interior of the semiconductor to the surface, get seized by the electric field inside the semiconductor and accelerated further to the interface. 

Figure 6.1 Concentration gradients near the gas-liquid interface in absorption. The liquid phase mass transfer coefficient (rn h ) is defined by...

The dilemma is solved by taking into account the fact that the lack of an equal supply rate for cations and anions carried toward the electrodes by the electric current will create a concentration gradient near the interface for the slower ions, and this concentration gradient will speed up the motion of the slower ions to compensate for their poorer performance. It is this diffusional component that makes Faraday s laws come true. The diffusional gradient pitches in to help the slower ions to the electrode at the same rate as the faster ones. 

Figure 6.1 Concentration gradients near the gas-liquid interface in absorption.

Diffusive Fluxes of Mn(II). If Mn is not transported to the 5-m layer of bottom water by lateral turbulent diffusion or advection, we should observe maximum values of the diffusive fluxes similar to the oxidation rate across the sediment-water interface (up to 3 mmol/m2 per day). Profiles of Mn concentrations in the pore water are shown in Figure 6a. The steep concentration gradients near the sediment-water interface are not at steady state the gradients are at maximum in summer and decrease to a minimum in spring. Sharp peak profiles were observed in June and July 1990. The diffusive flux of Mn(II), Fm in millimoles per square meter per day, was estimated from pore water profiles by using Fick s law with a correction for the porosity, c )... 

Concentration gradients near a gas-liquid interface (a) distillation (i) absorption of a very soluble gas. 

Later Hansen (1961) pointed out that due to a concentration gradient near an interface the... 

When consecutive or parallel reactions are carried out between a gas and a liquid, the concentration gradients near the interface may influence the selectivity as well as the overall rate of reaction. For chlorination or partial oxidation of hydrocarbons, several workers have reported that the yield of intermediate products was influenced by agitation variables [6,7] and was less than predicted from the kinetic constants. Rigorous analysis of multiple reactions is complex, but film theory can be used to show when mass transfer effects are likely to change the selectivity [8]. 

The electrolysis reaction produces both H+ and OH ions in the anode and cathode, respectively. The movement of H+ ions (acid front) advancing through soil toward the cathode can result in the release of Fe°/Fe ions to the EO flow via mineral dissolution (corrosion of the ZVI). At the same time, the OH ion move toward the anode creates a favorable alkaline zone for Cr(VI) desorption from soil. Thus, the chromates are reduced either at the Fe°-water interface in the barrier or by the Fe°/Fe ions in the EO flow path. The existence of Cr(VI) in the cathode reservoir due to the diffusion of soluble Cr(VI) caused by the concentration gradient near the cathode will also be reduced to Cr(III) by Fe ions. In addition, the occurrence of a secondary electrolysis reaction could reduce Cr(VI) to Cr(III)... 

The diffusing fluxes of biogenic elements across sediment-seawater interfaces mainly depend on the diffusion of the concentration difference caused by the concentration gradient near the interfaces. The net diffusing fluxes of biogenic elements across the sediment-water interface in some of China s sea regions can be estimated by the First Fick Law, and the results are listed in Table 1.10. 

In two-phase systems, there may be steep concentration gradients near the interfaces, particularly when rapid reactions are taking place. When mass transfer and chemical reactions can be considered as processes in series, the qualitative effects can be estimated simply (see section 5.3.5). When kinetic data are available, quantitative effects can be calculated. When diffusion and chemical reactions take place in the same zone, calculations become quite complex, but qualitative effects can yet be estimated. This may apply to situations where a reactant dissolves in a liquid and is converted widiin the diffusion layer adjacent to the interface. The dissolving reactant may be introduced as a gas, a solid or a second liquid phase (see section 5.4.2.2). It was shown that in these situations the selection of a reactor type is essential for obtaining a good selectivity (see also section 9.3). Similar effects are encountered with reactions takmg place inside porous solids (see section 5A.3.2), Therefore the structure of solid catalysts may be important in view of process selectivity. 

Dynamic surface tension is the measure of change of surface tension with time when a new surface is created. It is related to how fast the surfactant molecules diffuse from the bulk solution to the new air—solution interface and is, thus, affected by the concentration gradient near the surface. Dynamic surface tension can give information on the rate of adsorption at the interfece. Dynamic surface tension is related to the equilibrium surface tension (yeq), the concentration (C), and the diffusion coefficient (D) of the surfactant and is approximated by the following equation [49] ... 

In contrast, a fast reaction rate will result in steep concentration gradients for the reactants and a higher reaction rate near the solvent interface. This concept is represented diagrammatically in Figure 2.13b, where the concentration of reactant A is almost as high as that in phase 1 at the solvent interface, but plummets as it is rapidly consumed by the reaction. Thus, for a fast reaction, the majority of reactant is converted to product near the phase boundary layer and the rate of the reaction is limited by the rate of phase transfer and diffusion. 

The concentration of the volatile component in the nip is uniform as a result of the cross-channel circulatory motions even though a concentration gradient exists near the vapor-liquid interface. 

The intensity of mass transfer shown by the mass transfer coefficient depends on the flow processes inside the drop or in its surroundings and, thereby, on the various life stages of the drops. During the drop formation, new interfaces and high concentration gradients are produced near the interface. The contact times between liquid elements of the drop and the surroundings that are near the surface are then extremely short. According to Pick s second law for unsteady diffusion, it follows that for the phase mass transfer coefficient [19] ... 

Flow near the interface that is influenced by gradients of interface tension is called Marangoni convection. It may have further modes [27]. Thus, a low Marangoni convection in an interface, which results from small concentration differences, may be increased to a strong flow in the shape of rolling cells by mass transfer. These rolling cells transport liquid out of the... 

Let us consider the interface between two phases, say between a liquid and a vapour, where a solute (i) is dissolved in the liquid phase. The real concentration gradient of solute near the interface may look like Figure 3.1. When the solute increases in concentration near the surface (e.g. a surfactant) there must be a surface excess of solute nf, compared with the bulk value continued right up to the interface. We can define a surface excess concentration (in units of moles per unit area) as ... 

Molecular dynamics (MD) simulation studies also indicate that the initial formation of methane hydrate occurs preferentially near the water-methane interface where there is a significant concentration gradient (Moon et al., 2003). 

EXAMPLE 9.2. Consider the decarburization of a steel having a carbon content of c0 when it is heated into the austenite (y) region and held in air (Figure 9.13). At this temperature the reaction 2C + O2 -> 2CO effectively reduces the carbon concentration at the surface to zero. A layer of a forms at the surface and into the steel to a depth of x. The concentration profile near the surface is shown in Figure 9.14. The concentration gradient is dr /dr = —cjx, where ca is the carbon content of the a in equilibrium with the y. Fick s first law gives the flux, J = — /)dr /dx = Dcjx. As the interface advances a distance, dx (Figure 9.15), the amount of carbon that is removed in a time interval, At, is approximately (Cy—Ca)dx so the flux is... 

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