Diffusivity temperature effect

For effective ultrafiltration, equipment must be optimized to promote the highest transmembrane flow and selectivity. A major problem which must be overcome is concentration polarization, the accumulation of a gradient of retained macrosolute above the membrane. The extent of polarization is determined by the macrosolute concentration and diffusivity, temperature effects on solution viscosity and system geometry. If left undisturbed, concentration polarization restricts solvent and solute transport through the membrane and can even alter membrane selectivity by forming a gel layer on the membrane surface—in effect, a secondary membrane — increasing rejection of normally permeating species. 

Supercritical Mixtures Dehenedetti-Reid showed that conven-tionaf correlations based on the Stokes-Einstein relation (for hquid phase) tend to overpredict diffusivities in the supercritical state. Nevertheless, they observed that the Stokes-Einstein group D g l/T was constant. Thus, although no general correlation ap es, only one data point is necessaiy to examine variations of fluid viscosity and/or temperature effects. They explored certain combinations of aromatic solids in SFg and COg. 

Figure 12.42ft shows the measurements given as a function of the Archimedes number At ATqIuq. This figure is more informative than Fig. 12.42(3. The figure shows that the temperature effectiveness is a function of the Archimedes number. An identical level of j for the two diffusers A and B at the same Archimedes number implies that the temperature effectiveness is rather independent of the diffuser design and the local induction close to the diffuser. The effectiveness is probably more dependent on other parameters that are constant in the experiments, such as heat source and heat source location.

From the coverage made thus far, it may be of interest to record in one place the different factors which influence the rate of chemical reactions. The rate of chemical reaction depends essentially on four factors. The nature of reactants and products is one. For example, certain physical properties of the reactants and products govern the rate. As a specific example in this context mention may be of oxidation of metals. The volume ratio of metallic oxide to metal may indicate that a given oxidation reaction will be fast when the oxide is porous, or slow when the oxide is nonporous, thus presenting a diffusion barrier to the metal or to oxygen. The other two factors are concentration and temperature effects, which are detailed in Sections. The fourth factor is the presence of catalysts. 

For situations where the reaction is very slow relative to diffusion, the effectiveness factor for the poisoned catalyst will be unity, and the apparent activation energy of the reaction will be the true activation energy for the intrinsic chemical reaction. As the temperature increases, however, the reaction rate increases much faster than the diffusion rate and one may enter a regime where hT( 1 — a) is larger than 2, so the apparent activation energy will drop to that given by equation 12.3.85 (approximately half the value for the intrinsic reaction). As the temperature increases further, the Thiele modulus [hT( 1 — a)] continues to increase with a concomitant decrease in the effectiveness with which the catalyst surface area is used and in the depth to which the reactants are capable of... 

How does temperature effect diffusion in solids How do defects influence diffusion in solids ... 

The Mallard-Le Chatelier development for the laminar flame speed permits one to determine the general trends with pressure and temperature. When an overall rate expression is used to approximate real hydrocarbon oxidation kinetics experimental results, the activation energy of the overall process is found to be quite high—of the order of 160kJ/mol. Thus, the exponential in the flame speed equation is quite sensitive to variations in the flame temperature. This sensitivity is the dominant temperature effect on flame speed. There is also, of course, an effect of temperature on the diffusivity generally, the dif-fusivity is considered to vary with the temperature to the 1.75 power. 

What is important to realize from Eq. (8.148a) is that the flame temperature effect is in the log term and thus variations in flame temperature are not significant with regard to increases of soot mass in diffusion flames. The extent of the... 

It is apparent from early observations [93] that there are at least two different effects exerted by temperature on chromatographic separations. One effect is the influence on the viscosity and on the diffusion coefficient of the solute raising the temperature reduces the viscosity of the mobile phase and also increases the diffusion coefficient of the solute in both the mobile and the stationary phase. This is largely a kinetic effect, which improves the mobile phase mass transfer, and thus the chromatographic efficiency (N). The other completely different temperature effect is the influence on the selectivity factor (a), which usually decreases, as the temperature is increased (thermodynamic effect). This occurs because the partition coefficients and therefore, the Gibbs free energy difference (AG°) of the transfer of the analyte between the stationary and the mobile phase vary with temperature. 

E. C. Kumbur, K. V. Sharp, and M. M. Mench. Validated Leverett approach for multiphase flow in PEFC diffusion media. III. Temperature effect and unified approach. Journal of the Electrochemical Society 154 (2007) 1315-1324. 

Taylor (T4, T6), in two other articles, used the dispersed plug-flow model for turbulent flow, and Aris s treatment also included this case. Taylor and Aris both conclude that an effective axial-dispersion coefficient Dzf can again be used and that this coefficient is now a function of the well known Fanning friction factor. Tichacek et al. (T8) also considered turbulent flow, and found that Dl was quite sensitive to variations in the velocity profile. Aris further used the method for dispersion in a two-phase system with transfer between phases (All), for dispersion in flow through a tube with stagnant pockets (AlO), and for flow with a pulsating velocity (A12). Hawthorn (H7) considered the temperature effect of viscosity on dispersion coefficients he found that they can be altered by a factor of two in laminar flow, but that there is little effect for fully developed turbulent flow. Elder (E4) has considered open-channel flow and diffusion of discrete particles. Bischoff and Levenspiel (B14) extended Aris s theory to include a linear rate process, and used the results to construct comprehensive correlations of dispersion coefficients. 

A fourth factor is the flow rate of the eluent (mobile phase). A too high rate decreases resolution because there is no time for molecules to diffuse into the pores of the matrix. In contrast, a very slow migration of solvent decreases the resolution by remixing the components by diffusion. The effect of diffusion is minimized if the chromatography is done at low temperature. If short separation times are necessary, pre-packed columns, elevated pressure, or HPLC columns are indispensable. 

The reaction rate constant and the diffusivity may depend weakly on pressure (see previous section). Because the temperature dependence is much more pronounced and temperature and pressure often co-vary, the temperature effect usually overwhelms the pressure effect. Therefore, there are various cooling rate indicators, but few direct decompression rate indicators have been developed based on geochemical kinetics. Rutherford and Hill (1993) developed a method to estimate the decompression (ascent) rate based on the width of the break-dovm rim of amphibole phenocryst due to dehydration. Indirectly, decompres-... 

Another m3d h arises from the intuition that pressure effect is opposite to the temperature effect. This is not true in kinetics. Therefore, kinetic constants (reaction rate constants, diffusion coefficients, etc.) almost always increase with increasing temperature, but they may decrease or increase with increasing pressure. Both positive and negative pressure dependences are well accounted for by the transition-state theory and are not strange. 

Temperature increases the rate of diffusion through the liquid to the adsoiption sites but since the adsoiption process is exothermic, increases in temperature may reduce the degree of adsoiption. This temperature effect is negligible in water-treatment applications and ambient vapor-phase applications. 

A sensitive parameter in the coupling between chemical reaction and diffusion can be the temperature. In many cases the temperature coefficients are markedly different, and a shift of temperature can have a striking effect on systems coupling, compared with temperature effects on simpler molecules. 

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