Diffusion rule

Diffusion rules relate the future state of the target cell to those of neighboring cells. This mimics a second order reaction ... 

Analysis time in diffusion-controlled assays (Nernst- Einstein diffusion rule)... 

The problem of crystal reactivity and diffusion limitations has been considered in detail by Makinen and Fink [170]. They provide a simple treatment for crystals approximated as a plane sheet of material which leads to the definition of a limiting crystal thickness below which kinetic measurements of second-order rate constants are not affected by rate-limiting diffusion processes. For papain [172], ribonuclease A [173] and deoxyhaemoglobin [174], where the crystal thicknesses are comparable to the critical crystal thickness, reactivities are the same in the crystal and solution. In the case of glycogen phosphorylase b Kasvinsky and Madsen [175] demonstrated that the values for both substrates, glucose 1-phosphate (37 + 8mM) and malto-heptaose (176 + 20 mM), were the same in the crystal and solution. The 10-100-fold reduction in rate, despite the fact that crystal thickness was only twice the critical thickness, may be attributable partly to the allosteric nature of this enzyme and partly to the fact that the large substrate maltoheptaose (molecular weight, 1152) may not obey the simple diffusion rules in the crystal. 

ZhangZhigang2012. Resolving of MethaneTime-varying Diffusion Rule in Coal Grain. Coal mining Technology, 17(2) 8-11 (in Chinese). 

The full diffusion-reaction problem is therefore mapped onto a discrete, one-dimensional process that evolves according to the following diffusion "rules" (Grebenkov et al., 2005). Molecules currently at site i move to the left (site f — 1) or right (site i + 1) with probability l/2d, or stay on the current site with probability (1 — cr) (1 — 1/d), wherein (7 = 1/ (1 + A/a) is the absorption probability of the molecule with the surface. Finally, the molecule crosses the surface with probability a (1 — 1/d). Collectively, these rules can be written as a finite difference equation (Grebenkov et al., 2005), which is a discretized version of Eqns. 4 to 6 ... 

Table 2 Summaiy of the Dissolution and Diffusion Rules Used in 2-D and 3-D Computer Simulations... 

Once the radicals diffuse out of the solvent cage, reaction with monomer is the most probable reaction in bulk polymerizations, since monomers are the species most likely to be encountered. Reaction with polymer radicals or initiator molecules cannot be ruled out, but these are less important because of the lower concentration of the latter species. In the presence of solvent, reactions between the initiator radical and the solvent may effectively compete with polymer initiation. This depends very much on the specific chemicals involved. For example, carbon tetrachloride is quite reactive toward radicals because of the resonance stabilization of the solvent radical produced [1] ... 

These selection rules lead to the sharp, principal, diffuse and fundamental series, shown in Figures 7.5 and 7.6, in which the promoted electron is in an x, p, d and / orbital, respectively. Indeed, these rather curious orbital symbols originate from the first letters of the corresponding series observed in the spectrum. 

The combined effects of Knudsen and molecular diffusion may be estimated approximately from the reciprocal addition rule ... 

Permeant movement is a physical process that has both a thermodynamic and a kinetic component. For polymers without special surface treatments, the thermodynamic contribution is ia the solution step. The permeant partitions between the environment and the polymer according to thermodynamic rules of solution. The kinetic contribution is ia the diffusion. The net rate of movement is dependent on the speed of permeant movement and the availabiHty of new vacancies ia the polymer. 

Printing on triacetate follows the same general rules as for polyester. For batch-type pressure steaming, the steam pressure is reduced to 7—10 kPa (50—75 mm Hg) at 115—120°C. Acetate requires a steam pressure of ca 3.5 kPa (25 mm Hg), 108°C for full fixation of disperse dyes. With selected disperse dyes of a higher rate of diffusion ia acetate, ia combination with a suitable carrier, continuous steam fixation under atmospheric pressure at 100—105°C duting 20—30 min is also possible. A light scouting at 40—50°C completes the operation. 

Before using diffusivities from either data or correlations, it is a good idea to check their reasonableness with respect to values that have been commonly observed in similar situations. Table 5-13 is a compilation of sever rules of thumb. These values are not authoritative they simply represent guidelines based on experience. 

TABLE 5-13 Rules of Thumb for Diffusivities (See Cussler, Reid et al / Schwartzberg and Chao)... 

Exceptions to these rules of thumb abound, however. For example, although diffusion is faster at elevated temperatures, dissolved oxygen concentration may be lower. Convective transport is stimulated by high temperatures, but increased... 

The model is intrinsically irreversible. It is assumed that both dissociation of the dimer and reaction between a pair of adjacent species of different type are instantaneous. The ZGB model basically retains the adsorption-desorption selectivity rules of the Langmuir-Hinshelwood mechanism, it has no energy parameters, and the only independent parameter is Fa. Obviously, these crude assumptions imply that, for example, diffusion of adsorbed species is neglected, desorption of the reactants is not considered, lateral interactions are ignored, adsorbate-induced reconstructions of the surface are not considered, etc. Efforts to overcome these shortcomings will be briefly discussed below. 

It must always be remembered that diffusion coatings are produced by a form of heat treatment and that, with the exception of low-temperature zinc diffusion (sherardising), the treated ferrous materials are usually in the annealed condition. Whenever the mechanical properties of the parts must be restored to their original level, a subsequent heat treatment is necessary . This does not as a rule present any difficulty with chromised or boronised steels. In order to prevent undue distortion and internal stresses during treatment and subsequent hardening, it is recommended that high-carbon and alloy steels should be processed in the normalised condition. 

The extension of generic CA systems to two dimensions is significant for two reasons first, the extension brings with it the appearance of many new phenomena involving behaviors of the boundaries of, and interfaces between, two-dimensional patterns that have no simple analogs in one-dimension. Secondly, two-dimensional dynamics permits easier (sometimes direct) comparison to real physical systems. As we shall see in later sections, models for dendritic crystal growth, chemical reaction-diffusion systems and a direct simulation of turbulent fluid flow patterns are in fact specific instances of 2D CA rules and lattices. 

Fig. 3.9 Example of a slow diffusive- ke growth from a simple seed. I lie initial state a = ...0042400... evolves according to the k = 5, r = f totalistic rule T985707700. All sites with <7 > 0 are colored black.

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