Heterogeneous reactions Diffusion

I. Rubinstein, Asymptotics front formation in heterogeneous reaction diffusion kinetics, Phys. Chem. Hydrodyn., 6 (1985), pp. 879-899. 

Figure 9.1. Schematic heterogeneous reaction-diffusion system.

Mishra, S.K. et al. (2008) Spatiotempo-ral compound wavelet matrix framework for multiscale/multiphysics reactor simulation case study of a heterogeneous reaction/diffusion system. Int.J. Chem. Reactor Eng., 6 (A28), A28-1-A28-42. 

Mass Transfer. The reaction rate of heterogeneous reactions may be controlled by the rates of diffusion of the reacting species, rather than the chemical kinetics. 

Assume A, B, C, and D have similar diffusivities so that local stoichiometry is preserved. Under what circumstances will conversion be maximized by (a) complete segregation (b) by maximum mixedness Heterogeneous reactions are often modeled as if they were homogeneous. A frequently encountered rate expression is... 

The form of the effective mobility tensor remains unchanged as in Eq. (125), which imphes that the fluid flow does not affect the mobility terms. This is reasonable for an uncharged medium, where there is no interaction between the electric field and the convective flow field. However, the hydrodynamic term, Eq. (128), is affected by the electric field, since electroconvective flux at the boundary between the two phases causes solute to transport from one phase to the other, which can change the mean effective velocity through the system. One can also note that even if no electric field is applied, the mean velocity is affected by the diffusive transport into the stationary phase. Paine et al. [285] developed expressions to show that reversible adsorption and heterogeneous reaction affected the effective dispersion terms for flow in a capillary tube the present problem shows how partitioning, driven both by electrophoresis and diffusion, into the second phase will affect the overall dispersion and mean velocity terms. 

In a manner similar to that used for heterogeneous reactions, we can define diffusion and nuclei growth for a homogeneous solid. We have already stated that homogeneous nucleatlon can be contrasted to heterogeneous nucleatlon in that the former is random within a single compound while the latter involves more than one phase or compound. 

The effect of temperature on the rate of a typical heterogeneous reaction is shown in Figure 3.25. At low temperatures the reaction is chemically controlled and at high temperatures it is diffusion or mass transport controlled. 

The reaction plane model with heterogeneous reactions was discussed at length for acid-base reactions in the previous section. The same modeling technique, of confining the reactions to planes, can be applied to micelle-facilitated dissolution. As with the acid-base model, one starts with a one-dimensional steady-state equation for mass transfer that includes diffusion, convection, and reaction. This equation is then applied to the individual species i, i.e., the solute, s, the micelle, m, and the drug-loaded micelle, sm, to yield... 

Dioxygen and oxidized substances react on the surface of the catalyst only. The pure heterogeneous reaction occurs only after diffusion of reactants to the catalytic surface and back diffusion of products from the surface into the solution. A combination of a few mechanisms of such types are possible. 

Steam reforming is a heterogeneously catalyzed process, with nickel catalyst deposited throughout a preformed porous support. It is empirically observed in the industry, that conversion is proportional to the geometric surface area of the catalyst particles, rather than the internal pore area. This suggests that the particle behaves as an egg-shell type, as if all the catalytic activity were confined to a thin layer at the external surface. It has been demonstrated by conventional reaction-diffusion particle modelling that this behaviour is due to... 

There are some processes occurring in solutions, e.g. quenching of the fluorescence in solution, certain heterogeneous reactions etc., in which the diffusion is the rate controlling. These reactions occur very rapidly, e.g. ionic recombinations. 

Recall the diffusion controlled burning rate of a particle with fast heterogeneous reactions at the surface given by Eq. (9.29)... 

Selectivity in homogeneous reactions is treated in Refs. [2-6], while the selectivi-ties that are influenced in heterogeneous reactions by diffusion and adsorption are dealt with in Refs. [7, 8]. Kinetics and mechanisms of electrochemical reactions are covered in Chap. 1 of this volume and in Refs. [9-11]. 

Char oxidation dominates the time required for complete burnout of a coal particle. The heterogeneous reactions responsible for char oxidation are much slower than the devolatilization process and gas-phase reaction of the volatiles. Char burnout may require from 30 ms to over 1 s, depending on combustion conditions (oxygen level, temperature), and char particle size and reactivity. Char reactivity depends on parent coal type. The rate-limiting step in char burnout can be chemical reaction or gaseous diffusion. At low temperatures or for very large particles, chemical reaction is the rate-limiting step. At... 

At low temperatures (T<1320 °C) and small particles, combustion regime (I) prevails [11,74,75]. Regime (I) is controlled by chemical kinetics intraparticle (reaction control), see Figure 55. The oxygen content is constant at any radius inside the particle since the rate of diffusion is fast compared to the rate of heterogeneous reaction. The particle then burns with reducing density and a constant diameter, see Figure 55. 

The philosophy used to develop detailed chemical kinetic mechanisms for gas-phase reactions can, in principle, be extended to treat heterogeneous reactions, provided diffusion is also considered in the final analysis. Clearly, the problem in heterogeneous catalysis is considerably more complex because of the close proximity of a large number of atoms and their collective effect on reaction kinetics and mechanisms, and the inevitable variation of catalyst structure with time—for example, as a result of sintering and poisoning. 

Fig. 3. The Arrhenius plot for a heterogeneous reaction showing regions in which the rate is diffusion-controlled and reaction-controlled.

The above analysis, which is exceedingly brief and simplified is designed to demonstrate how, even in a pre-mixed flame, the question arises as to what is the appropriate reaction volume (i.e. the flame thickness). In heterogeneous reactions, this is a question that will recur again and ain and the designer of reactors must not attempt to avoid it. It is interesting to note that, in the next but one example to be treated, the overall reaction rate (a flame speed cm s in the above) becomes a mass transfer coefficient (also cms" ) when considering the absorption of gas into a liquid with which it reacts quickly. Furthermore, exactly the same sort of analysis as the above leads to the dependence of the mass transfer coefficient fej on the reaction rate coefficient and the diffusivity, D, in the liquid phase, of ki o. (rD), cf. z a RKY above. 

Chemical reactions may be classified by the number of phases involved in the reaction. If the reaction takes place inside one single phase, it is said to be a homogeneous reaction. Otherwise, it is a heterogeneous reaction. For homogeneous reactions, there are no surface effects and mass transfer usually does not play a role. Heterogeneous reactions, on the other hand, often involve surface effects, formation of new phases (nucleation), and mass transfer diffusion and convection). Hence, the theories for the kinetics of homogeneous and heterogeneous reactions are different and are treated in different sections. 

The scope of kinetics includes (i) the rates and mechanisms of homogeneous chemical reactions (reactions that occur in one single phase, such as ionic and molecular reactions in aqueous solutions, radioactive decay, many reactions in silicate melts, and cation distribution reactions in minerals), (ii) diffusion (owing to random motion of particles) and convection (both are parts of mass transport diffusion is often referred to as kinetics and convection and other motions are often referred to as dynamics), and (iii) the kinetics of phase transformations and heterogeneous reactions (including nucleation, crystal growth, crystal dissolution, and bubble growth). 

In this section, we focus on diffusive mass transfer. The mathematical description of mass transfer is similar to that of heat transfer. Furthermore, heat transfer may also play a role in heterogeneous reactions such as crystal growth and melting. Heat transfer, therefore, will be discussed together with mass transfer and examples may be taken from either mass transfer or heat transfer. 

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