Diffusion shorted

In conclusion, the above analysis shows that in order to obtain a d/y calcination, even with industrially high heating rates and high loading, the crucial point is to design the calcination process so that the evolved gas will only have to diffuse short distances. 

Whether electron hopping or molecular diffusion takes place will depend on which of these processes is faster. In some cases the centres may diffuse short distances to allow electron hopping to occur. This argument was substantiated by previous workers (65) who measured d-d distances of 2.5-3.4 nm for Fe(CN)5". For electron self-exchange to occur, distances of 0.92 nm are required. Where the response is limited by the rate of charge transfer, a small charge carrier additive may prove useful. For example, a ferro-ethylenediaminetetra-acetic acid additive has been used (66). It is most likely that the mechanism of transport will vary with analyte concentration and also with the morphology of the polymer (67). 

In practical applications we are often interested in the early stages of a mixing process, before the process becomes controlled by diffusion (i.e., when striations reach the length scale of diffusion). Short-term mixing dynamics have been extensively studied in the past by tracer dispersion simulations. Consider the sine flow... 

For solid phase sintering, there are fonr ways of diffusion i) surface diffusion, ii) volnme diffusion (often called lattiee diffusion), iii) vapor phase transport (evaporation-eondensation), and iv) grain boundary diffusion the boundaries are very disturbed areas, which allow diffusion short-circuits . For liquid phase sintering, we must add dissolution-reprecipitation effects or a vitreous flow. Finally, for pressure sintering the pressure exerted allows the plastic deformation of the crystallized phases and the viscous flow of the amorphous phases. 

Femtosecond lasers represent the state-of-the-art in laser teclmology. These lasers can have pulse widths of the order of 100 fm s. This is the same time scale as many processes that occur on surfaces, such as desorption or diffusion. Thus, femtosecond lasers can be used to directly measure surface dynamics tlirough teclmiques such as two-photon photoemission [85]. Femtochemistry occurs when the laser imparts energy over an extremely short time period so as to directly induce a surface chemical reaction [86]. 

The scan rate, u = EIAt, plays a very important role in sweep voltannnetry as it defines the time scale of the experiment and is typically in the range 5 mV s to 100 V s for nonnal macroelectrodes, although sweep rates of 10 V s are possible with microelectrodes (see later). The short time scales in which the experiments are carried out are the cause for the prevalence of non-steady-state diflfiision and the peak-shaped response. Wlien the scan rate is slow enough to maintain steady-state diflfiision, the concentration profiles with time are linear within the Nemst diflfiision layer which is fixed by natural convection, and the current-potential response reaches a plateau steady-state current. On reducing the time scale, the diflfiision layer caimot relax to its equilibrium state, the diffusion layer is thiimer and hence the currents in the non-steady-state will be higher. 

Microelectrodes with several geometries are reported in the literature, from spherical to disc to line electrodes each geometry has its own critical characteristic dimension and diffusion field in the steady state. The difhisional flux to a spherical microelectrode surface may be regarded as planar at short times, therefore displaying a transient behaviour, but spherical at long times, displaying a steady-state behaviour [28, 34] - If a... 

This expression is the sum of a transient tenu and a steady-state tenu, where r is the radius of the sphere. At short times after the application of the potential step, the transient tenu dominates over the steady-state tenu, and the electrode is analogous to a plane, as the depletion layer is thin compared with the disc radius, and the current varies widi time according to the Cottrell equation. At long times, the transient cunent will decrease to a negligible value, the depletion layer is comparable to the electrode radius, spherical difhision controls the transport of reactant, and the cunent density reaches a steady-state value. At times intenuediate to the limiting conditions of Cottrell behaviour or diffusion control, both transient and steady-state tenus need to be considered and thus the fiill expression must be used. Flowever, many experiments involving microelectrodes are designed such that one of the simpler cunent expressions is valid. 

The type of treatment described here was originally introduced by Scott and Dullien [4], who confined attention to isothermal isobaric diffusion in binary mixtures. Similar equations were independently published shortly after by Rothfeld [5], and the method was later extended to multi-component mixtures by Silveston [6], Perhaps the most complete exposition is given by Mason and Evans [7],... 

A second form of desolvation chamber relies on diffusion of small vapor molecules through pores in a Teflon membrane in preference to the much larger droplets (molecular agglomerations), which are held back. These devices have proved popular with thermospray and ultrasonic nebulizers, both of which produce large quantities of solvent and droplets in a short space of time. Bundles of heated hollow polyimide or Naflon fibers have been introduced as short, high-surface-area membranes for efficient desolvation. 

There is an intimate connection at the molecular level between diffusion and random flight statistics. The diffusing particle, after all, is displaced by random collisions with the surrounding solvent molecules, travels a short distance, experiences another collision which changes its direction, and so on. Such a zigzagged path is called Brownian motion when observed microscopically, describes diffusion when considered in terms of net displacement, and defines a three-dimensional random walk in statistical language. Accordingly, we propose to describe the net displacement of the solute in, say, the x direction as the result of a r -step random walk, in which the number of steps is directly proportional to time ... 

Oral adrninistration of vacciaes may be ineffective as many vacciaes are deactivated in the digestive tract of the animals the vacciaes are intended to protect. Dip treatment by which the vacciaes enter the animals through diffusion from the water are not generally as effective as injection but can be used to vaccinate large numbers of animals in short periods of time. 

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