Diffusion, coefficients interfacial

The existing data indicate that fcja is proportional to the square root of the solute-diffusion coefficient, and since the interfacial area a does not depend on Dl, it follows that /cl is proportional to Dl. An analysis of the design variables involved indicates that /cl should be proportional to Nsc when the Reynolds number is held constant. 

A number of metals, such as copper, cobalt and h on, form a number of oxide layers during oxidation in air. Providing that interfacial thermodynamic equilibrium exists at the boundaries between the various oxide layers, the relative thicknesses of the oxides will depend on die relative diffusion coefficients of the mobile species as well as the oxygen potential gradients across each oxide layer. The flux of ions and electrons is given by Einstein s mobility equation for each diffusing species in each layer... 

The work of Porter et al. has shown that for copper in phosphoric acid the interfacial temperature was the main factor, and furthermore this was the case for positive or negative heat flux. Activation energies were determined for this system they indicated that concentration polarisation was the rate-determining process, and by adjustment of the diffusion coefficient and viscosity for the temperature at the interface and the application of dimensional group analysis it was found that ... 

In addition, it was concluded that the liquid-phase diffusion coefficient is the major factor influencing the value of the mass-transfer coefficient per unit area. Inasmuch as agitators operate poorly in gas-liquid dispersions, it is impractical to induce turbulence by mechanical means that exceeds gravitational forces. They conclude, therefore, that heat- and mass-transfer coefficients per unit area in gas dispersions are almost completely unaffected by the mechanical power dissipated in the system. Consequently, the total mass-transfer rate in agitated gas-liquid contacting is changed almost entirely in accordance with the interfacial area—a function of the power input. 

In addition to the environmentally benign attributes and the easily tunable solvent properties, other important characteristics such as low interfacial tension, excellent wetting behavior, and high diffusion coefficients also make SCCO2 a superior medium for the synthesis of nanoscale materials [2]. Previous works on w/c RMs showed that conventional hydrocarbon surfactants such as AOT do not form RMs in scCOi [3] AOT is completely insoluble in CO2 due to the poor miscibility of the alkyl chains with CO2, restricting the utilization of this medium. Recently, we had demonstrated that the commonly used surfactant,... 

The investigations of interfacial phenomena of immiscible electrolyte solutions are very important from the theoretical point of view. They provide convenient approaches to the determination of various physciochemical parameters, such as transfer and solvation energy of ions, partition and diffusion coefficients, as well as interfacial potentials [1-7,12-17]. Of course, it should be remembered that at equilibrium, either in the presence or absence of an electrolyte, the solvents forming the discussed system are saturated in each other. Therefore, these two phases, in a sense, constitute two mixed solvents. 

The effect of increasing y is to increase the diffusion coefficient of the solute in phase 2 compared to that in phase 1. For a given value of this means that when a SECMIT measurement is made, the higher the value of y the less significant are depletion effects in phase 2 and the concentrations at the target interface are maintained closer to the initial bulk values. Consequently, as y increases, the chronoamperometric and steady-state currents increase from a lower limit, characteristic of an inert interface, to an upper limit corresponding to rapid interfacial solute transfer, with no depletion of phase 2. 

Under conditions of nonlimiting interfacial kinetics the normalized steady-state current is governed primarily by the value of K y, which is the relative permeability of the solute in phase 2 compared to phase 1, rather than the actual value of or y. In contrast, the current time characteristics are found to be highly dependent on the individual K. and y values. Figure 16 illustrates the chronoamperometric behavior for K = 10, log(L) = —0.8 and for a fixed value of Kf.y = 2. It can be seen clearly from this plot that whereas the current-time behavior is sensitive to the value of Kg and y, in all cases the curves tend to be the same steady-state current in the long-time limit. This difference between the steady-state and chronoamperometric characteristics could, in principle, be exploited in determining the concentration and diffusion coefficient of a solute in a phase that is not in direct contact with the UME probe. 

The influence of an interfacial kinetic barrier on the transfer process is readily illustrated by fixing the concentrations and the diffusion coefficients of Red for the two phases and examining the current response of the UME as K is varied. For illustrative purposes, we arbitrarily set and y = 1, i.e., initially the equilibrium conditions are such that there are equal concentrations of the target solute in the two phases, and the solute diffusion coefficient is phase-independent. Figure 17 shows the chronoamperometric characteristics for several K values from zero up to 1000. Under the defined conditions, these values of K reflect the ease with which the transfer process can respond to a perturbation of the local concentration of Red in phase 1, due to electrolytic depletion. 

The theoretical results described have implications for the design of experimental approaches for the study of transfer processes across the interface between two immiscible phases. The current response in SECMIT is clearly sensitive to the relative diffusion coefficients and concentrations of a solute in the two phases and the kinetics of interfacial transfer over a wide range of values of these parameters. 

For comparable diffusion coefficients of the target solute in the two phases and nonlimiting transfer kinetics, systems characterized by different should be resolvable on the basis of transient and steady-state current responses to a value of up to 50 at practical tip-interface separations. If the diffusion coefficient in phase 2 becomes lower than that in phase 1, diffusion in phase 2 will be partly limiting at even higher values of K. On the other hand, as the value of y increases or interfacial kinetics become increasingly limiting, lower values of suffice for the constant-composition assumption for phase 2 to be valid. 

FIG. 25 Typical DPSC data for the oxidation of 10 mM bromide to bromine (forward step upper solid curve) and the collection of electrogenerated Br2 (reverse step lower solid curve) at a 25 pm diameter disk UME in aqueous 0.5 M sulfuric acid, at a distance of 2.8 pm from the interface with DCE. The period of the initial (generation) potential step was 10 ms. The upper dashed line is the theoretical response for the forward step at the defined tip-interface separation, with a diffusion coefficient for Br of 1.8 x 10 cm s . The remaining dashed lines are the reverse transients for irreversible transfer of Br2 (diffusion coefficient 9.4 x 10 cm s ) with various interfacial first-order rate constants, k, marked on the plot. (Reprinted from Ref. 34. Copyright 1997 American Chemical Society.)... 

As reversible ion transfer reactions are diffusion controlled, the mass transport to the interface is given by Fick s second law, which may be directly integrated with the Nernst equation as a boundary condition (see, for instance. Ref. 230 232). A solution for the interfacial concentrations may be obtained, and the maximum forward peak may then be expressed as a function of the interfacial area A, of the potential scan rate v, of the bulk concentration of the ion under study Cj and of its diffusion coefficient D". This leads to the Randles Sevcik equation [233] ... 

Both reactions are slow compared to the film diffusion in the liquid phase13-15. Hence, the reactions can be assumed to take place predominantly in the bulk phase of the liquid. The rate of mass transfer can be calculated using Equation 7.2. The interfacial concentration can be calculated using Henry Law. Mass transfer coefficients, interfacial area and gas hold-up data are required. Gas hold-up is defined as ... 

These studies showed that sulfonate groups surrounding the hydronium ion at low X sterically hinder the hydration of fhe hydronium ion. The interfacial structure of sulfonafe pendanfs in fhe membrane was studied by analyzing structural and dynamical parameters such as density of the hydrated polymer radial distribution functions of wafer, ionomers, and protons water coordination numbers of side chains and diffusion coefficients of water and protons. The diffusion coefficienf of wafer agreed well with experimental data for hydronium ions, fhe diffusion coefficienf was found to be 6-10 times smaller than the value for bulk wafer. 

At high frequencies, a semicircle is expected as a result of a parallel combination of R and Cg. At low frequencies a Warburg impedance may be found as part of the interfacial impedance. In some cases it may dominate the interfacial impedance as in Fig. 10.13(a), in which case only the diffusion coefficient of the salt will be determinable. It should be noted that, in the absence of a supporting electrolyte, the electroactive species, in this case Li, cannot diffuse independently of the anions. 

By solving Eqs. (5.82a-d) for the interfacial concentrations [ ] after taking into acconnt the correlation between the fluxes [see Eqs. (5.83) and (5.84)] and introducing the simplification that the diffusion coefficients depend only on the natnre of the phase, that is,... 

Interfacial transfer of chemicals provides an interesting twist to our chemical fate and transport investigations. Even though the flow is generally turbulent in both phases, there is no turbulence across the interface in the diffusive sublayer, and the problem becomes one of the rate of diffusion. In addition, temporal mean turbulence quantities, such as eddy diffusion coefficient, are less helpful to us now. The unsteady character of turbulence near the diffusive sublayer is crucial to understanding and characterizing interfacial transport processes. 

The necessary condition to have a NG mechanism is that the second phase can nucleate from the homogeneous solution. The nucleation rate depends on interaction parameter, interfacial tension between both phases, and diffusion coefficient. 

In the same manner, with decreasing of diffusion coefficient and interaction parameter, the spinodal is reached during the evolution of the system in the pregel stage. The very low values of interfacial tension in rubber modified epoxies (interfacial tension of polymer-polymer-solvent system were reported in range of 10-4-10-1 mN/m) therefore lead to an NG mechanism for phase separation. 

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