Diffusion/diffusivity

Without interlayer With interlayer Without interlayer With interlayer diffusion diffusion diffusion diffusion... 

Reactant molecule Diffusion Diffusion Diffusion Forced convection... 

Sorption Rates in Batch Systems. Direct measurement of the uptake rate by gravimetric, volumetric, or pie2ometric methods is widely used as a means of measuring intraparticle diffusivities. Diffusive transport within a particle may be represented by the Fickian diffusion equation, which, in spherical coordinates, takes the form... 

In the oxidation process, a layer of dopant is apphed to the surface of sihcon and patterned sihcon dioxide for subsequent thermal diffusion into the sihcon. The masking property of the Si02 is based on differences in rates of diffusion. Diffusion of dopant into the oxide is much slower than the diffusion into the sihcon. Thus, the dopants reach only the sihcon substrate. Oxide masks are usually 0.5—0.7 p.m thick. 

Fig. 8. Combined flow reactor models (a) parallel flow reactors with longitudinal diffusion (diffusivities can differ), (b) internal recycle—cross-flow reactor (the recycle can be in either direction), comprising two countercurrent plug-flow reactors with intercormecting distributed flows, (c) plug-flow and weU-mixed reactors in series, and (d) 2ero-interniixing model, in which plug-flow reactors are parallel and a distribution of residence times dupHcates that...

Rate of Diffusion. Diffusion is the process by which molecules are transported from one part of a system to another as a result of random molecular motion. This eventually leads to an equalization of chemical potential and concentration throughout the system, and in the case of dyeing an equihbrium between dye in the fiber and dye in the dyebath. In dyeing there are three stages to diffusion diffusion of dye through the bulk solution of the dyebath to the fiber surface, diffusion through this surface, and diffusion of dye from the surface into the body of the fiber to allow for more dye to diffuse through the surface layer. These processes have been summarized elsewhere (9). 

There are two mechanisms of creep dislocation creep (which gives power-law behaviour) and diffusiona creep (which gives linear-viscous creep). The rate of both is usually limited by diffusion, so both follow Arrhenius s Law. Creep fracture, too, depends on diffusion. Diffusion becomes appreciable at about 0.37 - that is why materials start to creep above this temperature. 

By way of example, Volume 26 in Group III (Crystal and Solid State Physics) is devoted to Diffusion in Solid Metals and Alloys, this volume has an editor and 14 contributors. Their task was not only to gather numerical data on such matters as self- and chemical diffusivities, pressure dependence of diffusivities, diffusion along dislocations, surface diffusion, but also to exercise their professional judgment as to the reliability of the various numerical values available. The whole volume of about 750 pages is introduced by a chapter describing diffusion mechanisms and methods of measuring diffusivities this kind of introduction is a special feature of Landolt-Bornstein . Subsequent developments in diffusion data can then be found in a specialised journal. Defect and Diffusion Forum, which is not connected with Landolt-Bdrnstein. 

Table 10.2. Diffusivities (diffusion coefficients) of gases and vapours in air at 298 K and atmospheric...

Table 10.7. Diffusivities (diffusion coefficients) and Schmidt numbers, in liquids at 293 K 41...

Molecules must come into contact for a reaction to occur, and the mechanism for the contact is molecular motion. This is also the mechanism for diffusion. Diffusion is inherently important whenever reactions occur, but there are some reactor design problems where diffusion need not be explicitly considered, e.g., tubular reactors that satisfy the Merrill and Hamrin criterion. Equation (8.3). For other reactors, a detailed accounting for molecular diffusion may be critical to the design. 

One possibility for increasing the minimum porosity needed to generate disequilibria involves control of element extraction by solid-state diffusion (diffusion control models). If solid diffusion slows the rate that an incompatible element is transported to the melt-mineral interface, then the element will behave as if it has a higher partition coefficient than its equilibrium partition coefficient. This in turn would allow higher melt porosities to achieve the same amount of disequilibria as in pure equilibrium models. Iwamori (1992, 1993) presented a model of this process applicable to all elements that suggested that diffusion control would be important for all elements having diffusivities less than... 

It ought to be verified, however, in all cases, that the experimental Q-9 curve truly represents the distribution of surface sites with respect to a given adsorbate under specified conditions. The definition of differential heats of adsorption [Eq. (39) 3 includes, in particular, the condition that the surface area of the adsorbent A remain unchanged during the experiment. The whole expanse of the catalyst surface must therefore be accessible to the gas molecules during the adsorption of all successive doses. The adsorption of the gas should not be limited by diffusion, either within the adsorbent layer (external diffusion) or in the pores (internal diffusion). Diffusion, in either case, restricts the accessibility to the adsorbent surface. 

Film diffusion Diffusion of azo dyes through the boundary layer to the surface of the adsorbent... 

Despite a large body of literature examining the intracellular events that follow solute adsorption and precede cellular responses, in most cases, this remains an active area of research, especially with respect to the kinetics of the pathways that mediate the processes. It is known that most trace metals are moved down their electrochemical gradients by simple diffusion, diffusion... 

Substrate transport through the film may be formally assimilated to membrane diffusion with a diffusion coefficient defined as12 Ds = Dch( 1 — 9)/pjort. In this equation, the effect of film structure on the transport process in taken into account in two ways. The factor 1—0 stands for the fact that in a plane parallel to the electrode surface and to the coating-solution interface, a fraction 9 of the surface area in made unavailable for linear diffusion (diffusion coefficient Dcj,) by the presence of the film. The tortuosity factor,, defined as the ratio between the average length of the channel and the film thickness, accounts for the fact that the substrate... 

Passive Diffusion Diffusion is the random movement of molecules in fluid. If a fluid is separated by a semipermeable membrane, more dissolved molecules will diffuse across the membrane from the higher concentration side to the lower concentration side than in the reverse direction. This process will continue until equihbrium is achieved, whereby both sides have the same concentration. When equilibrium is reached, there are equal numbers of molecules crossing the membrane in both directions. 

We now want to apply the component continuity equation for reactant A to a small differential slice of width dz, as shown in Fig. 2.4. The inflow terms can be split into two types bulk flow and diffusion. Diffusion can occur because of the concentration gradient in the axial direction. It is usually much less important than bulk flow in most practical systems, but we include it here to see what it contributes to the model. We will say that the diffusive flux of A, (moles of A per unit time per unit area), is given by a Pick s law type of relationship... 

The equilibrium (also known as the Donnan effect) established across a semipermeable membrane or the equivalent of such a membrane (such as a solid ion-exchanger) across which one or more charged substances, often a protein, cannot diffuse. Diffusible anions and cations are distributed on the two sides of the membrane, such that the sum of concentrations (in dilute solutions) of diffusible and nondiffusible anions on either side of the membrane equals the sum of concentrations of diffusible and nondiffusible cations. Thus, the diffusible ions will be asymmetrically distributed across the membrane and a Donnan potential develops. 

Point defects and diffusion diffusivity and oxygen fugacity... 

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