Reaction modulus

Whereis the reaction modulus,/ /(wrfo) w, is the residence frequency I is the dispersed-phase mixing modulus o i/cor co, is the dispersed-phase mixing frequency and /i(c) dc is the fraction of drops of concentration in the range c to c + dc. 

Reaction modulus, Eq. (108) Length of optical path Linear scale of energy-containing eddies Total number of drops present per unit volume of dispersion... 

Fluid-fluid reactions are reactions that occur between two reactants where each of them is in a different phase. The two phases can be either gas and liquid or two immiscible liquids. In either case, one reactant is transferred to the interface between the phases and absorbed in the other phase, where the chemical reaction takes place. The reaction and the transport of the reactant are usually described by the two-film model, shown schematically in Figure 1.6. Consider reactant A is in phase I, reactant B is in phase II, and the reaction occurs in phase II. The overall rate of the reaction depends on the following factors (i) the rate at which reactant A is transferred to the interface, (ii) the solubihty of reactant A in phase II, (iii) the diffusion rate of the reactant A in phase II, (iv) the reaction rate, and (v) the diffusion rate of reactant B in phase II. Different situations may develop, depending on the relative magnitude of these factors, and on the form of the rate expression of the chemical reaction. To discern the effect of reactant transport and the reaction rate, a reaction modulus is usually used. Commonly, the transport flux of reactant A in phase II is described in two ways (i) by a diffusion equation (Pick s law) and/or (ii) a mass-transfer coefficient (transport through a film resistance) [7,9]. The dimensionless modulus is called the Hatta number (sometimes it is also referred to as the Damkohler number), and it is defined by... 

The calculation procedure is straightforward. We compute e for different values of Xg and a reaction modulus o that is defined as... 

Increasing smface activity (including surface treatment) gives higher abrasion resistance, chemical adsorption or reaction, modulus (at elongation... 

From the above discussion we see that the shrinking-core reaction modulus (Tg provides a simple but general criterion for the relative importance of chemical reaction and diffusion. The effect of is shown in Fig. 3.10 for... 

FIG. 3.10. Effect of the reaction modulus on the conversion versus time relationships. 

FIG. 3.13. The effect of reaction order n on the rate of regression of the reaction interface for various values of the reaction modulus CTs [44]. 

In the previous section we developed a generalized model for the reaction between a porous solid and a reactant gas, for systems with first-order kinetics with respect to the reactant gas. The model provided general criteria for relating structural effects to the reactivity of porous solids, and the reaction modulus defined therein allowed the assessment of the relative importance of pure diffusion and chemical kinetics. 

Tg shrinking-core reaction modulus for the grain defined by Eq. 

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