Mixed heterogeneous reactions

Equation (4.4.9b) may be compared with the boundary condition for a mixed heterogeneous reaction k c] = D dcldy),. It is evident that Rj = 1 corresponds to a first-order reaction, whereas if R c , there is a correspondence as well for reactions other than first order. For simplicity, let us consider the perfectly rejecting case of R = 1. Here, the appropriate dimensionless parameter characterizing the boundary condition is the ratio of the permeation velocity to the diffusion velocity... 

What is important to recognize from the discussion is that the boundary condition for mass transfer through a semipermeable membrane is directly analogous to that for a mixed heterogeneous reaction. A consequence of this is that what is said about the one problem can be translated to the other, despite the somewhat different physics and chemistry. The example of reverse osmosis is therefore used as an illustration of a mixed heterogeneous reaction. The major part of the discussion will, however, be confined to the developing layer, where... 

Reverse Osmosis and Mixed Heterogeneous Reactions 75 surface. Observing that /"=t7 is a solution of Eq. (4.4.21) suggests the form... 

Our thickness estimation requires the knowledge of the concentration C . If the process is diffusion-controlled, then C = 0. Another example is the surface of a material dissolvable in liquid. If dissolution occurs much faster than removal of dissolved substance into to the bulk of the liquid, then C , = C at, where Cjat is the equUibrium concentration of dissolved substance near the surface. The values of C for mixed heterogeneous reactions and penetrable surfaces will be determined later on in the relevant sections. 

Compare the obtained boundary condition to the condition for a mixed heterogeneous reaction,... 

The analogy between the problem of convective diffusion in a channel with semipermeable walls and the problem of mixed heterogeneous reaction makes it possible to consider these problems together. Conclusions that are true for one problem would be true for the other problem as well, even though these processes are distinct from both physical and chemical viewpoints. Besides, the analogy with chemical reactions allows us to introduce a dimensionless parameter of the problem (see (6.16)) - the Damkoler number ... 

If we consider a diffusion process with the boundary condition at the wall that corresponds to a mixed heterogeneous reaction, then the inequality (6.73) is similar to the inequality Da 1. It means that the rate of formation of reaction products is small in comparison with the diffusion flux. 

An example of reverse osmosis can be used as an illustration of mixed heterogeneous reaction. Reverse osmosis is a pressure-driven membrane process used to separate relatively pure solvents, most often water from solutions containing salts and dissolved organic molecules. The solvent passes through the membrane under the action of hydrostatic pressure leaving the dissolved materials behind. 

Because the highest possible interfacial area is desired for the heterogeneous reaction mixture, advances have also been made in the techniques used for mixing the two reaction phases. Several jet impingement reactors have been developed that are especially suited for nitration reactions (14). The process boosts reaction rates and yields. It also reduces the formation of by-products such as mono-, di-, and trinitrophenol by 50%. First Chemical (Pascagoula, Mississippi) uses this process at its plant. Another technique is to atomize the reactant layers by pressure injection through an orifice nozzle into a reaction chamber (15). The technique uses pressures of typically 0.21—0.93 MPa (30—135 psi) and consistendy produces droplets less than 1 p.m in size. The process is economical to build and operate, is safe, and leads to a substantially pure product. 

The role of mixing in heterogeneous reactions is obvious. In multiphase processes mixing imposed by a stirrer or an external pump is necessary to increase the interface through which reactants pass to meet their partner in the other phase and/or to intensify mass transfer between phases. Mixing can also play a significant role in the case of homogeneous reactions. Chemical reactions occur at the molecular level. Reactant molecules introduced into a reactor encounter the environment in the vicinity of the inlet. The composition of the mixture there is obviously... 

In such an apparatus, a chemical reaction takes place with a conversion of compound A into the products B and C. Typically, a sharp pulse of component A is fed into the column. During the passage through the column, compound A is converted into the products B and C and the amount of component A decreases. Because of their different retention times, the products B and C are concomitantly separated from each other and component A. Due to the removal of the products from the reaction zone, chemical equilibrium is never reached and the reaction will ideally proceed until the total conversion of the compound A. The reaction may take place in the stationary and/or the mobile phase. Heterogeneous reactions maybe either catalyzed by the packed adsorbent or by an additional catalyst, which is mixed with the adsorbent. 

Rule 3 applies to heterogeneous reactions with mixed mechanisms i. e. radical and ionic. These will have their radical component enhanced by sonication although the general mechanical effect from Rule 2 may still apply. Two situations which may occur in heterogeneous systems involving two mechan-... 

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