Diffusional transport

In order to allow a proper comparison of chemical conversion rates with transport (diffusional) rates of the reactants, it is more convenient to express eqn. (8) in terms of hydrogen conversion and the rate constant for hydrogen conversion, ku2, since rates of conversion depend on hydrogen pressure rather than on carbon monoxide pressure. The relation between ku2 and kco follows from stoichiometry considerations ... 

Laminar flame instabilities are dominated by diffusional effects that can only be of importance in flows with a low turbulence intensity, where molecular transport is of the same order of magnitude as turbulent transport (28). Flame instabilities do not appear to be capable of generating turbulence. They result in the growth of certain disturbances, leading to orderly three-dimensional stmctures which, though complex, are steady (1,2,8,9). 

A further problem is possible if the reinforcements are very small. Coarsening of the particles or whiskers may occur driven by Ostwald ripening, in which large particles grow through diffusional transport at the expense of smaller ones. This can be minimized by choosing matrices in which the reinforcement elements have very low solid solubilities and diffusion coefficients. Platelets, however, have been shown to be more resistant to coarsening than particles or whiskers. 

Rate of Growth Crystal growth is a layer-by-layer process, and since growth can occur only at the face of the crystal, material must be transported to that face from the bulk of the solution. Diffusional... 

The diffusional transport model for systems in which sorbed molecules can be divided in two populations, one formed by completely immobilized molecules and the other by molecules free to diffuse, has been developed by Vieth and Sladek 33) in a modified form of the Fick s second law. However, if linear isotherms are experimentally found, as in the case of the DGEBA-TETA system in Fig. 4, the diffusion of the penetrant may be described by the classical diffusion law with constant value of the effective diffusion coefficient,... 

Diffusion as referred to here is molecular diffusion in interstitial water. During early diagenesis the chemical transformation in a sediment depends on the reactivity and concentration of the components taking part in the reaction. Chemical transformations deplete the original concentration of these compounds, thereby setting up a gradient in the interstitial water. This gradient drives molecular diffusion. Diffusional transport and the kinetics of the transformation reactions determine the net effectiveness of the chemical reaction. 

In ICC 1 there were only a few references to diffusional limitations, but they may have been present in a number of papers. Despite improved attention, problems may still exist particularly in systems involving transport from the gas to the liquid phase. Absent a demonstration that the rate of a hydrogenation was proportional to the amount of catalyst one may suspect that C(H2)(liq.) was not in equilibrium with P(H2)(gas). 

It must be pointed out that in a diffusion layer where the ions are transported not only by migration but also by diffusion, the effective transport numbers t of the ions (the ratios between partial currents ij and total current t) will differ from the parameter tj [defined by Eq. (1.13)], which is the transport number of ion j in the bulk electrolyte, where concentration gradients and diffusional transport of substances are absent. In fact, in our case the effective transport number of the reacting ions in the diffusion layer is unity and that of the nonreacting ions is zero. 

In aqueous solutions Dj = lO cmVs a typical value of 5 is 10 cm. It follows that the convective and diffusional transport are comparable even at the negligible linear velocity of 10 cm/s of the liquid flow. At larger velocities, convection will be predominant. 

It follows that convection of the hqnid has a twofold influence It levels the concentrations in the bnlk liquid, and it influences the diffusional transport by governing the diffusion-layer thickness. Shght convection is sufficient for the first effect, but the second effect is related in a qnantitative way to the convective flow velocity The higher this velocity is, the thinner will be the diffusion layer and the larger the concentration gradients and diffusional fluxes. 

Curve 1 of Fig. 6.8 corresponds to pure kinetic control (i is very large), while the other curves for which the exchange CD has the same value show the influence of a gradual decrease in limiting diffusion CD caused by decreasing diffusional transport constants (e.g., when the electrode is rotated more and more slowly, but not when the concentration is reduced, since this would alter the exchange CD). 

It will be more convenient sometimes to describe the boundaries of the various regions in terms of the overall reaction rate constant and the diffusional transport constant k. In our example, we can replace the ratio by the ratio... 

Diffusion of ions can be observed in multicomponent systems where concentration gradients can arise. In individnal melts, self-diffnsion of ions can be studied with the aid of radiotracers. Whereas the mobilities of ions are lower in melts, the diffusion coefficients are of the same order of magnitude as in aqueous solutions (i.e., about 10 cmVs). Thus, for melts the Nemst relation (4.6) is not applicable. This can be explained in terms of an appreciable contribntion of ion pairs to diffusional transport since these pairs are nncharged, they do not carry cnrrent, so that values of ionic mobility calculated from diffusion coefficients will be high. 

During electrolysis there is no change in composition of an individual melt close to the electrode surfaces only its quantity (volume) will change. The resulting void space is filled again by flow of the entire liquid melt mass. This flow replaces the diffusional transport of ions customarily associated with aqueous solutions. This has particular consequences for the method used to measure ionic transport numbers ... 

For small K, i.e., K = 0.5 in Fig. 17, the response of the equilibrium to the depletion of species Red] in phase 1 is slow compared to diffusional mass transport, and consequently the current-time response and mass transport characteristics are close to those predicted for hindered diffusion with an inert interface. As K is increased, the interfacial process responds more rapidly to the electrochemical perturbation in phase 1. The transfer of the target species across the interface generates an enhanced flux to the UME, causing... 

For the diffusional monitor the steady state mass transport... 

First, consider the transepidermal route. The fractional area of this route is virtually 1.0, meaning the route constitutes the bulk of the area available for transport. Molecules passing through this route encounter the stratum corneum and then the viable tissues located above the capillary bed. As a practical matter, the total stratum corneum is considered a singular diffusional resistance. Because the histologically definable layers of the viable tissues are also physicochemically indistinct, the set of strata represented by viable epidermis and dermis is handled comparably and treated as a second diffusional resistance in series. 

Finally, from the available research into the variety of mechanisms for targetting ophthalmic drugs to specific tissues, means for integrating—both figuratively and literally—combinations of effects are now available [15]. Certainly, the combination of hydrodynamics, retention or sustained release, and diffusional or even active transport can be computed, their influence anticipated, and some specific deficiencies addressed. Nonetheless, many unanticipated interactions may often intrude and still leave the field heavily dependent on empirical assessment. 

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