Transfer Complicated by a Surface Chemical Reaction

Mass Transfer Complicated by a Surface Chemical Reaction 

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. 

The corresponding problem for the concentration distribution in the continuous medium is stated as follows  

Here the dimensionless functions and parameters are related to the original dimensional variables by the formulas 

In particular, for an nth-order surface reaction we have Fs = Cn and /s = (1 -c)n. In the general case, the function /s has the properties 

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When chemisorption is involved, or when some additional surface chemical reaction occurs, the process is more complicated. The most common combinations of surface mechanisms have been expressed in the Langmuir-Hinshelwood relationships 36). Since the adsorption process results in the net transfer of molecules from the gas to the adsorbed phase, it is accompanied by a bulk flow of fluid which keeps the total pressure constant. The effect is small and usually neglected. As adsorption proceeds, diffusing molecules may be denied access to parts of the internal surface because the pore system becomes blocked at critical points with condensate. Complex as the situation may be in theory,... 

In the last two chapters, relatively simple linear problems of mass and heat transfer were discussed. However, no processes of mass transfer complicated by surface (heterogeneous) or volume (homogeneous) chemical reactions with finite rates have been considered so far. Moreover, it was assumed that the basic parameters of the fluid are temperature- and concentration-independent. This assumption permitted the hydrodynamic part of the problem to be solved first and then the linear thermal or diffusion problem to be considered for a known velocity field. 

In voltammetric experiments, electroactive species in solution are transported to the surface of the electrodes where they undergo charge transfer processes. In the most simple of cases, electron-transfer processes behave reversibly, and diffusion in solution acts as a rate-determining step. However, in most cases, the voltammetric pattern becomes more complicated. The main reasons for causing deviations from reversible behavior include (i) a slow kinetics of interfacial electron transfer, (ii) the presence of parallel chemical reactions in the solution phase, (iii) and the occurrence of surface effects such as gas evolution and/or adsorption/desorption and/or formation/dissolution of solid deposits. Further, voltammetric curves can be distorted by uncompensated ohmic drops and capacitive effects in the cell [81-83]. 

The reaction is carried out over a silver gauze or low surface supported catalyst at 600—700°C, indicating a very fast chemical reaction. This implies that determination of the intrinsic reaction rate in laboratory reactors is complicated by the interference of heat and mass transfer limitations. To avoid this problem, studies have been made at much lower temperatures, which in turn run the risk of being non-representative. 

A gas-solid reaction usually involves heat and mass transfer processes and chemical kinetics. One important factor which complicates the analysis of these processes is the variations in the pore structure of the solid during the reaction. Increase or decrease of porosity during the reaction and variations in pore sizes would effect the diffusion resistance and also change the active surface area. These facts indicate that the real mechanism of gas-solid noncatalytic reactions can be understood better by following the variations in pore structure during the reaction. 

Most reactions on surfaces are complicated by variations in mass transfer and adsorption equilibrium [70], It is precisely these complexities, however, that afford an additional means of control in electrochemical or photoelectrochemical transformations. Not only does the surface assemble a nonstatistical distribution of reagents compared with the solution composition, but it also generally influences both the rates and course of chemical reactions [71-73]. These effects are particularly evident with photoactivated surfaces the intrinsic lifetimes of both excited states and photogenerated transients and the rates of bimolecular diffusion are particularly sensitive to the special environment afforded by a solid surface. Consequently, the understanding of surface effects is very important for applications that depend on chemical selectivity in photoelectrochemical transformation. 

Reactions that occur between components in the bulk solution and vesicle-bound components, i.e., reactions occurring across the membrane interface, can be treated mathematically as if they were bimolecular reactions in homogeneous solution. However, kinetic analyses of reactions on the surface of mesoscopic structures are complicated by the finiteness of the reaction space, which may obviate the use of ordinary equations of chemical kinetics that treat the reaction environment as an infinite surface populated with constant average densities of reactant molecules. As was noted above, the kinetics of electron-transfer reactions on the surface of spherical micelles and vesicles is expressed by a sum of exponentials that can be approximated by a single exponential function only at relatively long times [79a, 81], At short times, the kinetics of the oxidative quenching of excited molecules on these surfaces are approximated by the equation [102]... 

Fig 6 shows the single-stage system, which is referred to as plasma-driven catalysis [77]. In the PDC process, catalysts arc directly placed in the NTP reactor. These catalysts arc activated by NTP at low temperature region, where the thermal catalysis docs not occur. The shape of catalyst is cither of honeycomb, foam or pellet. In contrast to the PEC system, all reactions of gas-phase, surface and their interaction lake place simultaneously. In this sense, it is quite complicate to understand and optimize the chemical reactions in the PDC system. In an early USA patent, Henis proposed a PDC reactor for NO.r removal. Figure 7 shows the schematic diagram of the PDC reactor proposed by Henis [78], which is quite similar to those used in recent studies. The gases arc introduced to the reaction zone through the contact materials for heat transfer purpose. The catalysts listed in the patent are alumina, zirconium silicate, cobalt oxide, Thoria, activated carbon, molecular sieves, silica gel etc. 

A to products by considering mass transfer across the external surface of the catalyst. In the presence of multiple chemical reactions, where each iRy depends only on Ca, stoichiometry is not required. Furthermore, the thermal energy balance is not required when = 0 for each chemical reaction. In the presence of multiple chemical reactions where thermal energy effects must be considered becanse each AH j is not insignificant, methodologies beyond those discussed in this chapter must be employed to generate temperature and molar density profiles within catalytic pellets (see Aris, 1975, Chap. 5). In the absence of any complications associated with 0, one manipulates the steady-state mass transfer equation for reactant A with pseudo-homogeneous one-dimensional diffusion and multiple chemical reactions under isothermal conditions (see equation 27-14) ... 

The electrode reaction is rarely as simple as described above. In many cases the product is either insoluble, or partly adsorbed at the electrode surface. Besides, the reactants of many reactions are also surface active. Furthermore, the electrode reaction can be either preceded or followed by chemical reactions. Hence, the choice of the working electrode also depends on the reaction mechanism. For instance, the reduction of lead ions on a platinum electrode is complicated by nucleation and growth of lead micro-crystals, while on a mercury electrode lead atoms are dissolved in mercury and the reduction is fast and reversible. Similarly, the well-known pigment alizarin red S and the product of its reduction are both strongly adsorbed on the surface of mercury and carbon electrodes [17]. In this case, the liquid mercury electrode is analytically much more useful because the adsorptive accumulation on the fresh electrode surface can be easily repeated by creating a new mercury drop. However, on the solid electrode, the film of irreversibly adsorbed substance is so stable that it can be formed in one solution and then transferred into another electrolyte for the measurement of the kinetics of the electrode reaction. After each experiment... 

Step), and leave the reaction area into bulk solution (second mass transfer). The mass transfer step, as well as the electrochemical one, are always present in any electrochemical transformation. Importantly, the electrochemical step is always accompanied by transfer of a charged particle through the interface. That is why this step is called the transfer step or the discharge-ionization step. Other complications are also possible. They are related to the formation of a new phase on the electrode (surface diffusion of adatoms, recombination of adatoms, formation of crystals or gas bubbles, etc.). The transfer step may be accompanied by different chemical reactions, both in bulk and on the electrode surface. A set of all the possible transformations is called the electrode process. Electrochemical kinetics works with the general description of electrode processes over time. While related to chemical kinetics, electrochemical kinetics has several important features. They are specific to the certain processes, in particular - the discharge-ionization step. Determination of a possible step order and the slowest (rate-determining) step is crucial for the description of the specific electrode process. 

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