Mass transfer with surface reaction

E will be different from 1 only if R4 is small relative to / 2, resulting in a bulk concentration of c — 0 and in a real parallel mechanism of the enhancement. The advantage of the concept of the enhancement factor as defined by eq 33 is the separation of the influence of hydrodynamic effects on gas-liquid mass transfer (incorporated in Al) and of the effects induced by the presence of a solid surface (incorporated in E ), indeed in a similar way as is common in mass transfer with homogeneous reactions. The above analysis shows that an adequate description of mass transfer with chemical reaction in slurry reactors needs reliable data on ... 

For mass transfer with surface chemical reaction (as, e.g., in a tube wall catalytic reactor), Eqs. 1.3.2 and 1.3.14 yield... 

The global transformation rate of a gas-liquid reaction catalyst by a solid catalyst is influenced by the mass transfer between the gas-liquid and the liquid-solid mass transfer. Mass transfer and surface reaction are in series and, for fast chemical reactions, mass transfer will influence the reactant concentration on the catalytic surface and, as a consequence, influence the reactor performance and the product selectivity. Forthe gaseous reactantthree mass transfer steps can be identified [96] (1) the transfer from the bubble through the liquid film to the catalyst (fecs Gs). (2) the transfer from the caps of the gas bubbles to the liquid slug (fecs Gs) and (3) the transfer of dissolved gas to the catalytic surface (fersaLs). Steps 2 and 3 are in series and in parallel with respect to step 1, respectively. The following expression describes the overall mass transfer (feov ) ... 

The latter is a well-known quantity in the reaction-diffusion analysis in catalytic media (see Section 8.2.3) and can be written as the ratio between the average reaction rate over the washcoat cross-sectional area at a given axial position and its value at the surface. The former compares the driving force for mass transfer toward the coating, with the total potential for concentration decay (due to mass transfer and surface reaction). For a first-order reaction, 0 reduces to the Carberry number (see Chapter 3), and >/ is a concentration ratio between the averaged value inside the washcoat and the one at the surface. 

After discussing various aspects of external mass transfer and surface reactions, transport and reaction inside a porous catalyst will now be dealt with. 

Carbon dioxide gas diluted with nitrogen is passed continuously across the surface of an agitated aqueous lime solution. Clouds of crystals first appear just beneath the gas-liquid interface, although soon disperse into the bulk liquid phase. This indicates that crystallization occurs predominantly at the gas-liquid interface due to the localized high supersaturation produced by the mass transfer limited chemical reaction. The transient mean size of crystals obtained as a function of agitation rate is shown in Figure 8.16. 

For mass transfer with irreversible and reversible reactions, the film-penetration model is a more general concept than the film or surface renewal models which are its limiting cases. 

In general, the concentration of the reactant will decrease from CAo in the bulk of the fluid to CAi at the surface of the particle, to give a concentration driving force of CAo - CAi)-Thus, within the pellet, the concentration will fall progressively from CAi with distance from the surface. This presupposes that no distinct adsorbed phase is formed in the pores. In this section the combined effects of mass transfer and chemical reaction within the particle are considered, and the effects of external mass transfer are discussed in Section J 0.8.4. 

Results such as these suggest that dissolution may be treated mathematically via generalized solution mass transfer correlations, with surface reaction having a negligible effect on determining the over-all rate. However, more systems should be tested before sweeping conclusions are drawn. 

The absorption of ozone by cyanide solutions in stirred reactors is complicated by mass transfer considerations. The presence of ozone gas in the exhaust from such a reactor does not indicate that equilibrium has been obtained between ozone gas bubbles and ozone in solution, but rather that the mass transfer through the individual bubbles is not complete, because of the resistance on the gas side. In other words, mass transfer controls the reaction, as the ozone will react almost instantaneously with the cyanide ion in solution. The presence of some metals, particularly copper, appears to speed up the absorption by acting as oxygen carriers. A solution of ozone in dilute acid decomposes somewhat more quickly when a trace of cupric ion is added. The presence of these metal catalysts, if this be their function, does not appear to be a necessary condition to ozone oxidation. What is important is that adequate mass transfer time and surface be available, as would be found in a countercurrent packed tower. 

Entrapment methods of immobilization of bioreceptors utilized the lattice structure of particular base material. They include such methods as entrapment behind the membrane, covering the active surface of biosensors, entrapment within a self-assembled monolayers on the biosensor surface, as well as on freestanding or supported bilayer lipid membranes, and also entrapment within a polymeric matrix membranes, or within bulk material of sensor. All these mentioned methods are widely employed in design of biosensors. The essential condition of success of these methods of immobilization is preservation of sufficient mobility of substrate or products of biochemical reaction, involved in sensing mechanism, as matrix may act as a barrier to mass transfer with significant implications for... 

In this chapter, some problems of mass and heat transfer with various complicating factors are discussed. The effect of surface and volume chemical reactions of any order on the convective mass exchange between particles or drops and a translational or shear flow is investigated. Linear and nonlinear nonstationary problems of mass transfer with volume chemical reaction are studied. Universal formulas are given which can be used for estimating the intensity of the mass transfer process for arbitrary kinetics of the surface or volume reaction and various types of flow. 

Statement of the problem. In the preceding chapters we considered processes of mass transfer to surfaces of particles and drops for the case of an infinite rate of chemical reaction (adsorption or dissolution.) Along with the cases considered in the preceding chapters, finite-rate surface chemical reactions (see Section 3.1) are of importance in applications. Here the concentration on the surfaces is a priori unknown and must be determined in the course of the solution. Let us consider a laminar fluid flow with velocity U past a spherical particle (drop or bubble) of radius a. Let R be the radial coordinate relative to the center of the particle. We assume that the concentration is uniform remote from the particle and is equal to C. Next, the rate of chemical reaction on the surface is given by Ws = KSFS(C), where Ks is the surface reaction rate constant and the function F% is defined by the reaction kinetics and satisfies the condition Fs(0) = 0. 

Kovatcheva, N. P., Polyanin, A. D., and Kurdyumov, V, N., Mass transfer from a particle in a shear flow with surface reactions, Acta Mech. (Springer-Verlag), Vol. 101, pp. 155-160, 1993. 

In applications where the temperature range of operation is between 1000 and 1400 °C, there is still a lack of heat-resistant materials. For these applications, a ceramic catalyst system, extruded and completed with support and active phase in one piece, would be the ultimate solution. A surface area-enhancing washcoat is probably not needed at these temperatures, since both mass transfer limitations and reaction rates are high. Probably, only a surface area around 1-10 m g would be sufficient, which could be achieved with fine-tuned extrusion techniques. Hence, complicated washcoat-support interactions can be avoided. Among the several materials that are reported suitable for support extrusion in this review, there is a possibility for some of them to be used as the active component. For example, promising support materials like NZP may be active, depending on the specific ionic substitution. On the other hand, metal structures probably have too low a surface area to be used without washcoat. 

The immobilized-catalysts are confined to a region in space defined by the dimensions of the polymer particle. Reactant(s) must diffuse ftom the external surface to the catalytic sites within the particle before any chemical reaction can occur. This sequential process, mass transfer with reaction, has been treated extensively for catalytic reactions in porous solids (13,14,15). A limited number of studies have shown that the mathematical formalism which is applied to heterogeneously-catalyzed reactions can be used to interpret mass transfer with reaction in immobilized catalysts which employ polymers as supports (11,16,17). 

At the opposite extreme, it may be required to disperse very fine particles into a highly viscous liquid. For example, the incorporation of carbon black into rubber is such an operation. Here, as with emulsification in liquid-liquid mixing, the product is stable, highly viscous and may well exhibit complex rheology. Such processes often involve surface phenomena and physical contacting only, in contrast to the mass transfer and chemical reactions described in the previous paragraph. The dispersion of fine particles in liquids is considered in detail in Chapter 6. 

Slurry reactors are commonly used in situations where it is necessary to contact a liquid reactant or a solution containing the reactant with a solid catalyst. To facilitate mass transfer and effective utilization of the catalyst, one usually suspends a powdered or granular form of the catalyst in the liquid phase. This type of reactor is useful when one of the reactants is normally a gas at the reaction conditions and the second reactant is a liquid (e.g., in the hydrogenation of various oils). The reactant gas is bubbled through the liquid, dissolves, and then diffuses to the catalyst surface. Mass transfer limitations on reaction rates can be quite significant in those instances where three phases (the solid catalyst and the liquid and gaseous reactants) are present and necessary to proceed rapidly from reactants to products. 

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