Diffusion constant enhancement factor

Interest in the use of SC solvents as a reaction media is founded upon recent advances in our understanding of their unique thermo-physical and chemical properties. Worthy of special note are those thermophysical properties (6) which can be manipulated as parameters to selectively direct the progress of desirable chemical reactions. These properties include the solvent s dielectric constant (7), ion product (8,9), electrolyte solvent power (10,11), transport properties"[viscosity (12), diffusion coefficients (13) and ion mobilities (14)], hydrogen bonding characteristics (15), and solute-solvent "enhancement factors" (6). All these properties are strongly influenced by the solvent s density P in the supercritical state. 

If Ha < EJ2, the point representing the enhancement factor falls very close to the limiting diagonal in Fig. 4. Physically this means that reactant B diffuses toward the surface fast enough to prevent the reaction from causing any significant depletion there, so that Cbo is kept virtually constant. The local rate of reaction of dissolved gas is jCbo a-... 

Temperature the results compiled in Tables 4.1-4.6 were obtained at different temperatures, and in some studies the temperature was not controlled. The results reported in Table 3.11 and Fig. 3.104 indicate that the PZC of oxides and related materials shifts to low pH when the temperature increases (with a few exceptions). Most surfaces carry more negative charge at elevated temperature (at given pH), and this creates favorable conditions for adsorption of cations and unfavorable conditions for adsorption of anions. Therefore elevated temperature would enhance uptake of cations, and low temperature would enhance uptake of anions at constant pH, if the electrostatic interaction was the only factor. On the other hand, the rate of chemical reactions and diffusion is enhanced at elevated temperatures. Thus, the kinetic and electrostatic effect on cation adsorption add up and the uptake increases with temperature. With anions these effects act in opposite directions the uptake increases with temperature when the kinetic factor prevails the uptake decreases with temperature when the electrostatic factor prevails, finally the both effects can completely cancel out. 

The results obtained in equations (8-136) to (8-142) assume constant B, i.e., the reaction is pseudo-first-order in A. Another limiting case that yields to analytical solution is that in which the rate of reaction is very rapid and the reaction occurs wholly within the film. Here we consider the reaction A -I- P to occur very rapidly compared to mass-transfer/diffusion rates. The profiles look as in Figure 7.17b, and the overall flux and enhancement factor are given by... 

Design a two-phase gas-liquid CSTR that operates at 55°C to accomplish the liquid-phase chlorination of benzene. Benzene enters as a liquid, possibly diluted by an inert solvent, and chlorine gas is bubbled through the liquid mixture. It is only necessary to consider the first chlorination reaction because the kinetic rate constant for the second reaction is a factor of 8 smaller than the kinetic rate constant for the first reaction at 55°C. Furthermore, the kinetic rate constant for the third reaction is a factor of 243 smaller than the kinetic rate constant for the first reaction at 55°C. The extents of reaction for the second and third chlorination steps ( 2 and 3) are much smaller than the value of for any simulation (i.e., see Section 1-2.2). Chlorine gas must diffuse across the gas-liquid interface before the reaction can occur. The total gas-phase volume within the CSTR depends directly on the inlet flow rate ratio of gaseous chlorine to hquid benzene, and the impeller speed-gas sparger combination produces gas bubbles that are 2 mm in diameter. Hence, interphase mass transfer must be considered via mass transfer coefficients. The chemical reaction occurs predominantly in the liquid phase. In this respect, it is necessary to introduce a chemical reaction enhancement factor to correct liquid-phase mass transfer coefficients, as given by equation (13-18). This is accomplished via the dimensionless correlation for one-dimensional diffusion and pseudo-first-order irreversible chemical reaction ... 

In this chapter, a fast reaction is one whose chemical kinetics is the same speed or faster than diffusion, but one where the reagents can coexist. In this case, the actual rate is a function both of diffusion coefficients and of reaction rate constants, as detailed in Section 17.1. This interaction leads both to the enhancement factors used in reactive gas treating and to the effectiveness factors important for porous catalysts. 

Both the mass transfer kinetic parameters (diffusion in the phases, D, D j, surface renewal frequency, s) and chemical reaction rate constants (kg, kj) strongly influence enhancement of the absorption rate. The particle size, dp, the dispersed liquid holdup, e and the partition coefficient, H can also strongly alter the absorption rate [42-44,46,48]. Similarly, the distance of the first particle from the gas-liquid interface, 6q is an essential factor. Because the diffusion conditions are much better in the dispersed phase (larger solubility and, in most cases, larger diffusivity, as well) the absorption rate should increase with the decrease of the (5g value. 

In Fig. 20.13 flux enhancement V / is shown as a function of the reaction/diffusion parameter q for different equilibrium constants Kr. Remember that q2 is basically the ratio of reaction time kr and diffusion time k (Eq. 20-52). Thus, q 1 corresponds to case (1) mentioned at the beginning of this section flux enhancement should not occur (V / = 1). The other extreme (vp 1, that is tT /w) was discussed with the example of proton exchange reactions (Eq. 8-6). We found from Eq. 20-49 that for this case the water-side exchange velocity v/w is enhanced by the factor (1 + Ka /[H+]). By comparing Eqs. 8-6 and 12-17 we see that for the case of proton exchange ATa/[H+] plays the role of the equilibrium constant KT between the two species. Thus, flux enhancement is ... 

In this connection, it is helpful to look first at the reactivity of the anions. There is no generally acceptable measure of nucleophilic reactivity since both the scale and order of relative reactivities depend on the electrophilic centre being attacked (Ritchie, 1972). However, in the present reaction, the similarity in the reactivity of the different anions is remarkable. Thus, the Swain and Scott n-values (cf. Hine, 1962) indicate that the iodide ion should be 100 times more reactive than the chloride ion in nucleophilic attack on methyl bromide in aqueous acetone. In the present reaction, the ratio of the rate coefficients for iodide ions and chloride ions is 1.4. This similarity led to the suggestion that these reactions are near the diffusion-controlled limit (Ridd, 1961). If, from the results in Table 5, we take this limit to correspond to a rate coefficient (eqn 19) of 2500 mol-2 s 1 dm6 then, from the value of ken for aqueous solutions at 0° (3.4 x 109 mol-1 s 1 dm3 Table 1), it follows that the equilibrium constant for the formation of the electrophile must be ca. 7.3 x 10 7 mol-1 dm3. This is very similar to the equilibrium constant reported for the formation of the nitrosonium ion (p. 19). The agreement is improved if allowance is made for the electrostatic enhancement of the diffusion-controlled reaction by a factor of ca. 3 (p. 8) the equilibrium constant for the electrophile then comes to be ca. 2.4 x 10-7. 

Equation (58) indicates that an increase in initiatior concentration will not enhance the rate of polymerization. It can be used for estimating the molecular mass of the polymer assuming, of course, the absence of transfer. The ratio N/q corresponds to the mean time of polymer growth and molecular mass is equal to the product of the number of additions per unit time and the length of the active life time of the radical, kpN/e. An increase in [I] also means a higher value of q, and thus a shortening of the chains. As in Phase II, the polymerized monomer in the particles is supplemented by monomer diffusion from the droplets across the aqueous phase a stationary state is rapidly established with constant monomer concentration in the particle. The rate of polymerization is then independent of conversion (see, for example the conversion curves in Fig. 7). We assume that the Smith-Ewart theory does not hold for those polymerizations where the mentioned dependence is not linear [132], The valdity of the Smith-Ewart theory is limited by many other factors. 

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