Surface phases, reaction rate

The burning rate of a double-base propellant can be calculated by means of Eq. (3.59), assuming the radiation from the gas phase to the burning surface to be negligible. Since the burning rate of a double-base propellant is dominated by the heat flux transferred back from the fizz zone to the burning surface, the reaction rate parameters in Eq. (3.59) are the physicochemical parameters of choice for describing the fizz zone. The gas-phase temperature, Tg, is the temperature at the end of the fizz zone, i. e., the dark-zone temperature, as obtained by means of Eq. (3.60). 

The temperature gradient in the fizz zone just above the burning surface increases from 1.9 K pm to 2.5 K pm at 0.7 MPa when 2.4% LiF and 0.1 % C are added. The gas-phase reaction rate in the fizz zone is increased and the heat flux feedback from the fizz zone to the burning surface is increased by the addition of the catalysts. However, the effect of the addition of the catalysts is not seen in the dark zone. 

Three obvious models which could describe the observed reaction rate are (a) concentration equilibrium between all parts of the intracrystalline pore structure and the exterior gas phase (reaction rate limiting), (b) equilibrium between the gas phase and the surface of the zeolite crystallites but diffusional limitations within the intracrystalline pore structure, and (c) concentration uniformity within the intracrystalline pore structure but a large difference from equilibrium at the interface between the zeolite crystal (pore mouth) and the gas phase (product desorption limitation). Combinations of the above may occur, and all models must include catalyst deactivation. 

The form of the resulting expression differs from the gas phase reaction rate expressions due to the presence of a denominator which represents the reduction in rate due to adsorption phenomena and of which the individual terms represent the distribution of the active sites among the possible surface complexes and vacancies. These expressions are termed the Langmuir-Hinshelwood-Hougen-Watson (LHHW) rate expressions. 

In Refs. an analytical solution of the two-dimensional problem of flame spread over a horizontal surface is described. Formulas for the determination of the location of the chemical reaction, fuel flow to the latter, and temperature in the reaction zone have been derived. From these formulas it follows that the distance between the material surface and the chemical reaction zone is greater farther away from the flame front. Also the influx of fuel and oxidant to the reaction zone is smaller and the temperature is higher, and attains in the limit a level corresponding to adiabatic combustion. Thus, the temperature in the flame front may be substantially below the adiabatic temperature of combustion because of heat transfer to the combustible material. A criterion determining the effect of the gas-phase reaction rate on the com-... 

AHj is the combustion enthalpy, is the maximum gas-phase reaction rate, 5j, 5, and 5 are, respectively, the thickness of the hot layer, heated polymer layer and half-thickness of the reaction zone in the flame a is the angle of inclination of the reaction zone to the polymer surface AHo = cT -h Yp AH is the heat necessary for polymer gasification and heating of combustible vapors. 

The rate constant 2 shows a typical Arrhenius form, at least over a modest range of temperature, while k involves a combination of diffusion to the walls and a subsequent surface-phase reaction. 

Problem 9.5 Considering reaction between A and B catalyzed by a solid there are two possible mechanisms by which this reaction could occur. The first is that one of them, say A gets adsorbed on the solid surface and the adsorbed A then reacts chemically with the other component B which is in the gas phase or in solution and is not adsorbed on the surface. The second mechanism is that both A and B are adsorbed, and the adsorbed species undergo chemical reaction on the surface. The reaction rate expression derived for the former mechanism is the Rideal rate law and that for the second mechanism is the Langmuir-Hinshelwood rate law. Obtain simple derivations of these two rate laws. 

The second-phase reaction is heterogeneous and occurs at the surface of the particle. The reaction causes the reacting surface to shrink and to leave an ash layer as the particle moves through the reactor. Unlike the first-phase reaction, which is only slightly affected by temperature, the second-phase reaction is quite sensitive to variations in temperature for tests conducted in a semiflow system (10). Since a high gas flow rate was maintained in semiflow tests, gas diffusion probably does not affect the rate. At temperatures below 1700°F., the first-phase reaction rate is an order or two larger than the second-phase reaction rate, but as the temperature approaches 2000°F., the two rates become comparable. This is, of course, true only when the reaction is controlled by the chemical step. 

Estimated values (EPIWIN USEPA 2007) in lack of experimental data are given in braekets On graphite partieles. Second order rate eoefHcients were calculated similarly to gas-phase reaction rate coefficients, suggesting that reactions occuned between a gaseous OH radical and a surface-bounded PAH molecule (Perraudin et al. 2007)... 

An optimized mechanism for homogeneous combustion of C1-C3 species by Qin et al. (70 species, 14 irreversible and 449 reversible reactions) [2] was employed for modeling gas-phase chemistry. Thermodynamic data were included in the provided scheme. Surface and gas-phase reaction rates were evaluated with Surface-CHEMKIN [3] and CHEMKIN [4] respectively. Mixture-average difihi-sion was the transport model, using the CHEMKIN transport database [5]. 

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