Factors That Influence Diffusion

This is a diffusion problem in which Equation 5.6b may be employed. Because at both 500°C and 600°C the composition remains the same at some position, say Xq, Equation 5.6b may be written as 

The magnitude of the diffusion coefficient D is indicative of the rate at which atoms diffuse. The diffusing species and the host material influence the diffusion coefficient. For example, there is a significant difference in magnitnde between self-diffusion and carbon interdiffusion in a-iron at 500°C, the D value being greater for the carbon interdiffusion (3.0 X 10 vs. 1.4 X 10 m /s). This comparison also provides a contrast between rates of diffusion via vacancy and interstitial modes, as discussed earlier. Self-diffusion occurs by a vacancy mechanism, whereas carbon diffusion in iron is interstitial. 

Temperature has a profound influence on the coefficients and diffusion rates. For example, for the self-diffusion of Fe in a-Fe, the diffusion coefficient increases approximately six orders of magnitude (from 3.0 x 10 to 1.8 X 10 m /s) in rising temperature from 500°C to 900°C. The temperature dependence of the diffusion coefficients is 

The activation energy may be thought of as that energy required to produce the diffusive motion of one mole of atoms. A large activation energy resnlts in a 

Because Dq, Q, and R are all constants. Equation 5.9b takes on the form of an equation of a straight line  

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In ammonia production, the space velocity is often (0.6—2) x 10 h. In axial flow converters, the velocity of gas flow can be up to several m s the effect of external diffusion should be absent, but the effect of intraparticle diffusion cannot be ignored. The gas flow area In a radial flow converter is very large, the gas velocity is very low, and thus both effects of external and intraparticle diffusion cannot be ignored. Among the many factors that influence diffusion, the particle size of catalyst is the most significant and can be easily adjusted. 

Parenteral products should be formulated to possess sufficient buffer capacity to maintain proper product pH. Factors that influence pH include product degradation, container and stopper effects, diffusion of gases through the closure, and the effect of gases in the product or in the headspace. However, the buffer capacity of a formulation must be readily overcome by the biological fluids thus, the concentration and ratios of buffer ingredients must be carefully selected. 

Various factors that influence the release of drugs from particulate carriers are listed in Table 10. Drugs can be released by diffusion or by surface erosion, disintegration, hydration, or breakdown (by a chemical or an enzymatic reaction) of the particles. The release of drugs from microspheres follows a biphasic pattern that is, an initial fast release followed by a slower... 

The diffusion of an impurity atom in a crystal, say K in NaCl, involves other considerations that influence diffusion. In such cases, the probability that the impurity will exchange with the vacancy will depend on factors such as the relative sizes of the impurity compared to the host atoms. In the case of ionic movement, the charge on the diffusing species will also play a part. These factors can also be included in a random-walk analysis by including jump probabilities of the host and impurity atoms and vacancies, all of which are likely to vary from one impurity to another and from one crystal structure to another. All of these alterations can be... 

Conradi RA, Burton PS and Borchardt RT (1996) Physiochemical and Biological Factors That Influence a Drug s Cellular Permeability by Passive Diffusion. In V Pliska, B Testa, H Van De Waterbeemd (Eds.), Lipophilicity in Drug Action and Toxicology. Weinheim, VCH, pp 233-252. 

Results from equilibrium modelling indicate that the extent of mineral trapping depends strongly on the fugacity of C02. Consequently, the extent of mineral trapping is sensitive to the rate of mineral-brine-C02 reactions relative to the rate of flow and dispersion of C02 away from the site of injection. Reactions must be fast enough to reach carbonate phase saturation before the C02 is overly diluted by outward radial flow, dispersion, and diffusion. The rates of reaction and the factors that influence the rates of reaction must be better constrained. 

Lapse Rate and Atmospheric Stability Apart from mechanical interference with the steady flow of air caused by buildings and other obstacles, the most important factor that influences the degree of turbulence and hence the speed of diffusion in the lower air is the varia-... 

Conradi RA, Burton PS, Borchardt RT. Physico-chemical and biological factors that influence a drug s cellular permeability by passive diffusion methods and principles in medicinal chemistry. Lipophil. Drug Action Toxicol. 1996 4 233-252. 

In real cells, multiple transmembrane pumps and channels maintain and regulate the transmembrane potential. Furthermore, those processes are at best only in a quasi-steady state, not truly at equilibrium. Thus, electrophoresis of an ionic solute across a membrane may be a passive equilibrative diffusion process in itself, but is effectively an active and concentra-tive process when the cell is considered as a whole. Other factors that influence transport across membranes include pH gradients, differences in binding, and coupled reactions that convert the transported substrate into another chemical form. In each case, transport is governed by the concentration of free and permeable substrate available in each compartment. The effect of pH on transport will depend on whether the permeant species is the protonated form (e.g., acids) or the unprotonated form (e.g., bases), on the pfQ of the compound, and on the pH in each compartment. The effects can be predicted with reference to the Henderson-Hasselbach equation (Equation 14.2), which states that the ratio of acid and base forms changes by a factor of 10 for each unit change in either pH or pfCt ... 

In these systems, the donor and acceptor diffuse together to give a precursor complex, D A, whose formation is described by the equilibrium constant Kp. Electron transfer, characterized by rate constant eTj occurs within the associated donor-acceptor pair, converting the precursor complex to successor complex D A. Subsequent separation of the oxidized donor (D+) and reduced acceptor (A ) from the successor complex is described by. s- The rate of m/ermolecular electron transfer depends not only on the factors that influence kpj but also on factors affecting the formation of the precursor complex [19]. More quantitatively, as described by Eq. 2, the expression for intermolecular electron transfer has the form of a consecutive reaction mechanism described by an observed rate constant (A obs) consisting of rate constants for diffusion (A ) and the activated electron transfer. 

The choice of chemical is usually based on trial-and-error procedures hence, demulsifier technology is more of an art than a science. In most cases a combination of chemicals is used in the demulsifier formulation to achieve both efficient flocculation and coalescence. The type of demulsifiers and their effect on interfacial area are among the important factors that influence the coalescence process. Time-dependent interfacial tensions have been shown to be sensitive to these factors, and the relation between time-dependent interfacial tensions and the adsorption of surfactants at the oil-aqueous interface was considered by a number of researchers (27, 31-36). From studies of the time-dependent tensions at the interface between organic solvents and aqueous solutions of different surfactants, Joos and coworkers (33—36) concluded that the adsorption process of the surfactants at the liquid-liquid interface was not only diffusion controlled but that adsorption barriers and surfactant molecule reorientation were important mecha-... 

The effect of flow rate has been examined as a factor that influences bandwidth, and therefore resolution. Figure 14.6 shows a typical plot of band width as a function of flow rate. At low flow rates, longitudinal diffusion is significant, and leads to larger bandwidths than at the optimum. At high flow rates, the kinetics of partitioning becomes the dominant factor that leads to increased bandwidths and decreased resolution. The contribution of eddy diffusion is independent of flow rate. 

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