Reaction film theory

Fig. 4.2. Liquid phase concentration profiles for mass transfer with chemical reaction - film theory...

Several theories have appeared in the Hterature regarding the mechanism of protection by -PDA antiozonants. The scavenger theory states that the antiozonant diffuses to the surface and preferentially reacts with ozone, with the result that the mbber is not attacked until the antiozonant is exhausted (25,28,29). The protective film theory is similar, except that the ozone—antiozonant reaction products form a film on the surface that prevents attack (28). The relinking theory states that the antiozonant prevents scission of the ozonized mbber or recombines severed double bonds (14). A fourth theory states that the antiozonant reacts with the ozonized mbber or carbonyl oxide (3) in Pig. 1) to give a low molecular weight, inert self-healing film on the surface (3). 

Penetration theoiy often is used in analyzing absorption with chemical reaction because it makes no assumption about the depths of penetration of the various reacting species, and it gives a more accurate result when the diffusion coefficients of the reacting species are not equal. When the reaction process is veiy complex, however, penetration theoiy is more difficult to use than film theory, and the latter method normally is preferred. 

There are various theories on how passive films are formed however, there are two commonly accepted theories. One theory is called the oxide film theory and states that the passive film is a diffusion-barrier layer of reaction products (i.e., metal oxides or other compounds). The barriers separate the metal from the hostile environment and thereby slow the rate of reaction. Another theory is the adsorption theory of passivity. This states that the film is simply adsorbed gas that forms a barrier to diffusion of metal ions from the substrata. 

In evaluating their results they assumed the film theory, and, because the oxygen is sparingly soluble and the chemical reaction rate high, they also assumed that the liquid film is the controlling resistance. The results were calculated as a volumetric mass-transfer coefficient based, however, on the gas film. They found that the volumetric mass-transfer coefficient increased with power input and superficial gas velocity. Their results can be expressed as follows ... 

A pure gas is absorbed into a liquid with which it reacts. The concentration in the liquid is sufficiently low for the mass transfer to be covered by Fick s Law and the reaction is first-order with respect to the solute gas. It may be assumed that the film theory may be applied to the liquid and that the concentration of solute gas falls from the saturation value to zero across the film. The reaction is initially carried out at 293 K. By what factor will the mass transfer rate across the interface change, if the temperature is raised to 313 K ... 

The mass balances accompanied by reaction (5) of species A and B, and the boundary conditions based on the film theory are given as follows ... 

According to the Whitman Two-Film theory, the actual concentration profiles, as shown in Fig. 1.28 are approximated for the steady state with no chemical reaction, by that of Fig. 1.29. 

Laubriet et al. [Ill] modelled the final stage of poly condensation by using the set of reactions and kinetic parameters published by Ravindranath and Mashelkar [112], They used a mass-transfer term in the material balances for EG, water and DEG adapted from film theory J = 0MMg — c ), with c being the interfacial equilibrium concentration of the volatile species i. 

All three of these proposals give the mass transfer rate N A directly proportional to the concentration difference (CAi — CAL) so that they do not directly enable a decision to be made between the theories. However, in the Higbie-Danckwerts theory N A a s/Dj whereas NA film theory. Danckwerts applied this theory to the problem of absorption coupled with chemical reaction but, although in this case the three proposals give somewhat different results, it has not been possible to distinguish between them. 

Additional experiments in a loop reactor where a significant mass transport limitation was observed allowed us to investigate the interplay between hydrodynamics and mass transport rates as a function of mixer geometry, the ratio of the volume hold-up of the phases and the flow rate of the catalyst phase. From further kinetic studies on the influence of substrate and catalyst concentrations on the overall reaction rate, the Hatta number was estimated to be 0.3-3, based on film theory. 

The reaction order of one is also in good accordance with the film theory, where the rate of mass transport linearly correlates with the equilibrium concentration of citral in the aqueous phase. As a matter of fact, the mass transport rate is of first order regarding the substrate concentration in the organic phase. Therefore, what is measured is in fact the rate of mass transport and not the rate of chemical reaction. This result is in our opinion a good example of how kinetic parameters could be falsified when the reaction is limited by mass transport and not kinetics. 

The measured G(x) value of representative epoxy polymers is approximately 10, but this value depends strongly on the structure of the polymer, its glass transition temperature and other characteristics. Since the crosslinking reaction that characterizes the COP resist functionality is a chain reaction, in theory, a single, electron-initiated event could result in the insolublization of an entire film of the resist material. Fortunately, because of the existence of chain terminating reactions, this does not occur and high resolution imaging of the resist material can be accomplished. 

The two-film theory is not always applicable to heterogeneous processes and, for example, in gas—solid reactions, only the gas film is considered. 

Since reactant A must move from gas to liquid for reaction to occur, diffusional resistances enter the rate. Here we will develop everything in terms of the two-film theory. Other theories can and have been used however, they give essentially the same result, but with more impressive mathematics. 

Figure 23.2 Setting up the rate equation for absorption of A in the liquid, and reaction in the liquid, based on the two-film theory.

Figure 23.5 Concentration of reactants as visualized by the two-film theory for an infinitely fast irreversible reactions of any order, A + bB - products. Case A high Cg (see Eq. 17).

A more comprehensive analysis of the influences on the ozone solubility was made by Sotelo et al., (1989). The Henry s Law constant H was measured in the presence of several salts, i. e. buffer solutions frequently used in ozonation experiments. Based on an ozone mass balance in a stirred tank reactor and employing the two film theory of gas absorption followed by an irreversible chemical reaction (Charpentier, 1981), equations for the Henry s Law constant as a function of temperature, pH and ionic strength, which agreed with the experimental values within 15 % were developed (Table 3-2). In this study, much care was taken to correctly analyse the ozone decomposition due to changes in the pH as well as to achieve the steady state experimental concentration at every temperature in the range considered (0°C [Pg.86]

The absorption of a gas by a liquid with simultaneous reaction in the liquid phase is the most important case. There are several theories of mass transfer between two fluid phases (see Volume 1, Chapter 10 Volume 2, Chapter 12), but for the purpose of illustration the film theory will be used here. Results from the possibly more realistic penetration theory are similar numerically, although more complicated in their mathematical form0,4. ... 

In the film theory, steady state conditions are assumed in the film such that, in any volume element, the difference between the rate of mass transfer into and out of the element is just balanced by the rate of reaction within the element. Carrying out such a material balance on reactant A the following differential equation results ... 

The individual mass transfer and reaction steps occurring in a gas-liquid-solid reactor may be distinguished as shown in Fig. 4.15. As in the case of gas-liquid reactors, the description will be based on the film theory of mass transfer. For simplicity, the gas phase will be considered to consist of just the pure reactant A, with a second reactant B present in the liquid phase only. The case of hydro-desulphurisation by hydrogen (reactant A) reacting with an involatile sulphur compound (reactant B) can be taken as an illustration, applicable up to the stage where the product H2S starts to build up in the gas phase. (If the gas phase were not pure reactant, an additional gas-film resistance would need to be introduced, but for most three-phase reactors gas-film resistance, if not negligible, is likely to be small compared with the other resistances involved.) The reaction proceeds as follows ... 

Adoption and Use of Modeling Framework The rate of diffusion and species generation by chemical reaction can be described by film theory, penetration theory, or a combination of the two. The most popular description is in terms of a two-film theory, which is... 

The rate-based models usually use the two-film theory and comprise the material and energy balances of a differential element of the two-phase volume in the packing (148). The classical two-film model shown in Figure 13 is extended here to consider the catalyst phase (Figure 33). A pseudo-homogeneous approach is chosen for the catalyzed reaction (see also Section 2.1), and the corresponding overall reaction kinetics is determined by fixed-bed experiments (34). This macroscopic kinetics includes the influence of the liquid distribution and mass transfer resistances at the liquid-solid interface as well as dififusional transport phenomena inside the porous catalyst. 

In rate-based multistage separation models, separate balance equations are written for each distinct phase, and mass and heat transfer resistances are considered according to the two-film theory with explicit calculation of interfacial fluxes and film discretization for non-homogeneous film layer. The film model equations are combined with relevant diffusion and reaction kinetics and account for the specific features of electrolyte solution chemistry, electrolyte thermodynamics, and electroneutrality in the liquid phase. 

A pure gas is absorbed into a liquid with which it reacts. The concentration in the liquid is sufficiently low for the mass transfer to be governed by Fick s law and the reaction is first order with respect to the solute gas. It may be assumed that the film theory may be applied to the liquid and that the concentration of solute gas falls from the saturation value to zero across the film. Obtain an expression for the mass transfer rate across the gas-liquid interface in terms of the molecular diffusivity, D, the first-order reaction rate constant ft, the film thickness L and the concentration Cas of solute in a saturated solution. The reaction is initially carried out at 293 K. By what factor will the mass transfer rate across the interface change, if the temperature is raised to 313 K Reaction rate constant at 293 K = 2.5 x 10 6 s 1. Energy of activation for reaction (in Arrhenius equation) = 26430 kJ/kmol. Universal gas constant R = 8.314 kJ/kmol K. Molecular diffusivity D = 10-9 m2/s. Film thickness, L = 10 mm. Solubility of gas at 313 K is 80% of solubility at 293 K. 

Equations according to film theory, see also Ref. 53. For stoichiometry, see reaction (8). N0l = ozone absorption rate, Ms-1 Ha according to Eq. (9) Ei, according to Eq. (10) = function (Ha, )). In the fast, pseudo first-order kinetic regime equation, a represents the specific interfacial area. 

Another difficulty is related to the mass transfer by convection, as, by definition, the films are stagnant and hence, there should be no mass transport mechanism, except for molecular diffusion in the direction normal to the interface (Kenig, 2000). Nevertheless, convection in films is directly accounted for in correlations. Moreover, in case of reactive systems, the film thickness should depend on the reaction rate, which is beyond the two-film theory consideration. 

As is shown in Figure 2, in the two-phase model the fluid bed reactor is assumed to be divided into two phases with mass transfer across the phase boundary. The mass transfer between the two phases and the subsequent reaction in the suspension phase are described in analogy to gas/liquid reactors, i.e. as an absorption of the reactants from the bubble phase with pseudo-homogeneous reaction in the suspension phase. Mass transfer from the bubble surface into the bulk of the suspension phase is described by the film theory with 6 being the thickness of the film. D is the diffusion coefficient of the gas and a denotes the mass transfer coefficient based on unit of transfer area between the two phases. 6 is given by 6 = D/a. 

According to the film theory, in reactive-absorption processes the resistance to mass transfer is concentrated in a small region near the gas/liquid interface. The ratio between tbe rate of chemical reaction and liquid-phase mass transfer is given by the Hatta number. For a second-order reaction (12.1), the Hatta number is defined as ... 

Probably, for most slurry reactor applications, information on the value of the product kLa is sufficient for design purposes. In some cases, however, information on the individual parameters a and/or ki, can be useful. For instance, the reactor capacity will depend on a, rather than on the product k a, if the reaction is so fast that all conversion takes place within the stagnant film (film theory) around the gas bubbles. For first-order conversion kinetics in the porous catalyst particles this will occur for... 

One of the most important of these new experimental tools has been the development and application of the vacuum microbalance technique in which the sensitive microbalance operates directly in the vacuum or reaction system. The success of the method depends upon the coordination of a number of different experimental as well as theoretical disciplines. Thus, from an experimental point of view precise weighing techniques on properly prepared specimens must be coordinated with high vacuum techniques and the use of ceramic materials at high temperatures. From a theoretical viewpoint thermodynamic calculations must be made for all of the reactions involved and the results interpreted in terms of diffusion process for gas-solid reactions in which a film is formed or the gas diffuses into the solid, or in terms of the absolute reaction rate theory or its equivalent for gas reactions on solids including catalytic reactions and the combustion of fuels. 

Let r- be the net rate of the i reaction at a position x in the diffusion film (defined such that Vij r represents the quantity of jth species produced per unit time per unit volume by that reaction). Then the mass balance equation for the jt 1 species can be formulated based on the film theory as ... 

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