Transfer, mass with chemical reaction, regime

In the overall picture, different expressions are proposed for the rate of gas absorption with chemical reaction, depending on the forms of the enhancement factor E corresponding to different kinetic regimes, going from reaction-controlling to mass transfer-controlling. Typical cases are ... 

Axial dispersion in packed beds, and Taylor dispersion of a tracer in a capillary tube, are described by the same form of the mass transfer equation. The Taylor dispersion problem, which was formulated in the early 1950s, corresponds to unsteady-state one-dimensional convection and two-dimensional diffusion of a tracer in a straight tube with circular cross section in the laminar flow regime. The microscopic form of the generalized mass transfer equation without chemical reaction is... 

Here, we are concerned with regimes in which the reaction occurs exclusively in the bulk and is controlled by either chemical reaction (regime 1) or diffusion, that is, mass transfer across the liquid film (regime 2), as well as with the intermediate regime in which there is a mass transfer resistance in the film but the reaction still occurs exclusively in the bulk. 

These intriguing situations, which are similar to the so-called "diffusion falsification" regime of fluid-porous catalytic solid systems (5), can be successfully handled by the "theory of mass transfer with chemical reaction". Indeed, they can be deployed to obtain kinetics of exceedingly fast reactions in simple apparatuses, which in the normal investigations in homogeneous systems would have required sophisticated and expensive equipment. Further, it is possible, under certain conditions, to obtain values of rate constants without knowing the solubility and diffusivity. In addition, simple experiments yield diffusivity and solubility of reactive species which would otherwise have been - indeed, if possible - extremely difficult. 

The previous assumptions together with the classical relationships of the different specific absorption rates, depending on the chemical reaction regime used to determine interfacial parameters, lead to the theoretical mean reduced values of the gaseous reactant in the gas exit stream and to absorption efficiency for a gas-liquid dispersion, where a is the geometrical specific interfacial area and Rl is the mean true liquid-side mass transfer coefficient defined for a bubble of diameter dg. ... 

Reaction Kinetics Regime of Mass Transfer with Chemical Reaction... 

If the time scale of a chemical reaction is short compared to the time scale of mass transfer, the mass transfer slows the chemical reaction but can also cause the concentration in the liquid-side mass transfer film to be decreased, resulting in an increased driving force and an enhanced mass transfer rate. Levenspiel (1999) and Middleton (1992) present diagrams for the interface concentration profiles likely to happen at the various reaction rates relative to the mass transfer rate. Those are shown in Table 13-10 along with estimates of the ranges of variables for the various regimes [similar to those of Doraiswamy and Sharma (1984)] and important variables for design and scale-up. 

Over 25 years ago the coking factor of the radiant coil was empirically correlated to operating conditions (48). It has been assumed that the mass transfer of coke precursors from the bulk of the gas to the walls was controlling the rate of deposition (39). Kinetic models (24,49,50) were developed based on the chemical reaction at the wall as a controlling step. Bench-scale data (51—53) appear to indicate that a chemical reaction controls. However, flow regimes of bench-scale reactors are so different from the commercial furnaces that scale-up of bench-scale results caimot be confidently appHed to commercial furnaces. For example. Figure 3 shows the coke deposited on a controlled cylindrical specimen in a continuous stirred tank reactor (CSTR) and the rate of coke deposition. The deposition rate decreases with time and attains a pseudo steady value. Though this is achieved in a matter of rninutes in bench-scale reactors, it takes a few days in a commercial furnace. 

Chemical reactions on solid surfaces can be realized in gas-solid and liquid-solid systems. In both cases the reaction takes place on the surface of the solid matrix, and therefore the molecules to be reacted need to get in contact with the reactive surface. Several transport regimes and interaction mechanisms define the mass transfer efficiency. They can be summarized as follows [6] ... 

Four different regimes of the I-V curve for moderately doped silicon electrodes in an HF electrolyte are shown in Fig. 3.2. These regimes will now be discussed in terms of the charge state of the electrode, the dependence on illumination conditions, the charge transfer, the mass transport, and accompanying chemical reactions. Transient effects are indicated in Fig. 3.2 by a symbol with an arrow. 

On-Bottom Motion or Partial Suspension Regime This state is characterized by the complete motion of all particles around the bottom of the vessel. It excludes the formation of fillets, i.e., loose aggregations of particles in corners or other parts of the vessel bottom. As the particles are in constant contact with the base of the vessel and with one another, not all the particle surface area is available for chemical reaction, mass, or heat transfer. 

Off-Bottom or Complete Suspension (Just-Suspended) Regime This state is characterized by the complete off-bottom motion of all particles with no particle remaining on the base of the vessel for more than 1-2 sec (Zwietering criterion).Under this condition, the total surface area of the particles is exposed to the fluid for chemical reaction, mass or heat transfer. The just-suspended regime refers to the minimum agitation conditions at which all particles attain complete suspension. 

Remark. The problem of mass transfer to a drop for the diffusion regime of reaction on its surface under the conditions of thermocapillary motion is stated in the same way as in its absence (see Section 4.4) taking into account the corresponding changes in the fluid velocity field. In [144], a more complicated problem is considered for the chemocapillary effect with the heat production, which was described in [147-149,419], It was assumed that a chemical reaction of finite rate occurs on the drop surface. 

Consider two-dimensional steady-state mass transfer in the liquid phase external to a solid sphere at high Schmidt numbers. The particle, which contains mobile reactant A, dissolves into the passing fluid stream, where A undergoes nth-order irreversible homogeneous chemical reaction with another reactant in the liquid phase. The flow regime is laminar, and heat effects associated with the reaction are very weak. Boundary layer approximations are invoked to obtain a locally flat description of this problem. 

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