Resistance, liquid diffusion

The gas-phase rate coefficient fcc is not affecded by the fact that a chemic reaction is taking place in the liquid phase. If the liquid-phase chemical reaction is extremely fast and irreversible, the rate of absorption may be governed completely by the resistance to diffusion in the gas phase. In this case the absorption rate may be estimated by knowing only the gas-phase rate coefficient fcc of else the height of one gas-phase transfer unit Hq =... 

Internal circulation occurs inside the bubbles, and the resistance to diffusion in the gas phase is negligible compared to that in the liquid phase. 

Equation (1) consists of various resistance terms. l/Kj a is the gas absorption resistance, while 1/ K,a corresponds to the maleic anhydride diffusion resistance and l/i k represents the chemical reaction resistance. The reaction rate data obtained under the reaction conditions of 250°C and 70 atm were plotted according to equation (1). Although catalytic reaction data with respect to time on stream were not shown here, a linear correlation between reaction rate data and catalyst loading was observed as shown in Fig. 2. The gas absorption resistance (1/ a) was -1.26 h, while the combined reaction-diffusion resistance (lJK,a + 1 T]k) was determined to be 5.57 h. The small negative value of gas absorption resistance indicates that the gas-liquid diffusion resistance was very small and had several orders of magnitude less than the chanical reaction resistance, as similarly observed for the isobutene hydration over Amberlyst-15 in a slurry reactor [6]. This indicates that absorption of malei c anhydride in solvent was a rapid process compared to the reaction rate on the catalyst surface. 

When diffusion is assumed to be controlled by the boundary him, by implication, all other resistances to diffusion are negligible. Therefore, concentrations are uniform through the solid and local equilibrium exists between huid and solid. The whole of the concentration difference between bulk liquid and solid is conhned to the him. The rate of transfer into a spherical pellet may then be expressed as ... 

Since the experiments of Tung and Drickamer, the resistance to diffusion through an interface has been further studied in gas-liquid systems by Emmert and Pigford (E2), who studied the absorption and desorption of CO 2 and 02 in water in a wetted-wall tower and interpreted their results in terms of accommodation coefficients. They... 

Equation (2), derived for dilute solutions, is valid when the flow of solute from the gas to the gas film is balanced by an equal flow of the inert component from the film to the gas similarly, it requires that the flow of solute from the liquid film to the solvent be balanced by an equal flow of solvent from the liquid into the liquid film. This is a good approximation when both the gas and the liquid are dilute solutions. If either or both are concentrated solutions, the flow of gas out of the film, or the flow of liquid into the film, may contain a significant quantity of solute. These solute flows counteract the diffusion process, thus increasing the effective resistance to diffusion. 

Figure 5 shows that a fast reaction takes place only in the liquid film. In such instances, the dominant mass transfer mechanism is physical absorption and the diffusion model above is applicable, but the resistance to mass transfer in the liquid phase is lower because of the reaction. On the other hand, a slow reaction occurs in the bulk of the liquid, and its rate has little dependence on the resistances to diffusion in either the gas or liquid film. Here the dominant mass transfer mechanism is that of chemical reaction therefore, this case is considered part of chemical reaction technology, as distinct from absorption technology. 

Viscosity. Efficiency increases as liquid viscosity diminishes (5,149, 150,186). As discussed earlier (Sec, 7.2.2), lower liquid viscosity usually implies higher liquid diffusivity, and therefore, lower resistance to mass transfer in the liquid phase. It was also argued that bubbles formed in high-viscosity liquids are larger and generate less interfa-cial area (186). 

Solution The full numerical model needs to include shrinkage since the material is 50 percent water initially and the thickness will decrease from 100 to 46.5 lm during drying. Assuming the layer is viscous enough to resist convection in the liquid, diffusion is the dominant liquid-phase transport mechanism. 

The reaction was carried out by dissolving gaseous HCl in a stirred vessel containing the alcohol. The resulting concentration-time data could be correlated with a rate equation half-order in alcohol concentration. However, the rate constant was found to vary with the gas (HCl) flow rate into the reactor, suggesting that the observed rate was influenced by the resistance to diffusion of dissolved HCl in the liquid phase. A method of analysis which took into account the diffusion resistance indicated that the chemical step was probably first order in dissolved HCl and zero order with respect to lauryl alcohol. 

Not all of the four resistances indicated in Eq. (10-46) are significant in every instance. For example, in hydrogenations pure hydrogen is normally used as reactant. Then there is no resistance to diffusion from bulk gas (in the bubble) to bubble-liquid interface. Hence Cg = and Eq. (10-46)... 

In Fig. 10-9 the resistance to solution of hydrogen in the slurry is represented by the horizontal dashed line. The total resistance is the ordinate of the solid line. At low catalyst concentrations the combined resistance of diffusion to the particle and chemical reaction on the catalytic surface is large, although it does not determine the rate by itself. At high concentrations the resistance to transfer of hydrogen from bubble to the bulk liquid dominates the rate. In fact at Qaj = 0.28%, 0.18/0.20, or 90%, of the total resistance is for this step. The results show that ajog increases enough, as the catalyst concentration increases to 0.28%, that the first term in Eq. (10-47) dominates the whole quantity. The results also indicate that increases in Qat beyond 0.28% would do little to speed up the reaction. 

Since the resistance to diffusion will be lower in the mixture critical region than that in the liquid phase it is expected that the (A B ) radical pair should be more readily diffuse apart in the critical region. Although applied hydrostatic pressure favors the recombination of (A B ) to form AB, it seems reasonable to assume that the rate of diffusion dominates the pressure effect as long as the system pressure is maintained below approximately 1,000 bar. Therefore, the formation of free radicals should be facilitated in the SCF phase, as compared with the liquid phase, and shorter reaction times are to be expected. 

For the case of evaporation of a pure liquid into a gas or the condensation of a component in a vapor into its own pure liquid, the only resistance to diffusion is in the gas phase, since there are no concentration gradients in the pure liquid. A test tube, beaker, graduated cylinder, tank, or the Great Salt Lake will all eventually empty by evaporation if the liquid contents are not replenished regularly. One knows intuitively that spills evaporate faster if they are spread over a large area, if the temperature is high, or if we blow air on the spill and also that liquid in a bottle takes longer to evaporate the farther the surface of the liquid is from the top of the bottle. 

The diffusion coefficient (or diffiisivity) and viscosity represent transport properties which affect rates of mass transfer. In general, these properties are at least an order of magnitude higher and lower, respectively, compared with liquid solvents. This means that the diffusion of a species through an SCF medium will occur at a faster rate than that obtained in a liquid solvent, which implies that a solid will dissolve more rapidly in an SCF. In addition, an SCF will be more efficient at penetrating a microporous solid structure. However, this does not necessarily mean that mass transfer limitations will always be absent in an SCF process. For example, in the extraction of a solute from a liquid to an SCF phase, the resistance to diffusion in the liquid phase will probably control the overall rate of mass transfer. Stirring will therefore continue to be an important factor in such systems. 

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