Thickness of the reaction zone

When a hydrophobic polymer with a physically dispersed acidic excipient is placed into an aqueous environment, water will diffuse into the polymer, dissolving the acidic excipient, and consequently the lowered pH will accelerate hydrolysis of the ortho ester bonds. The process is shown schematically in Fig. 6 (18). It is clear that the erosional behavior of the device will be determined by the relative movements of the hydration front Vj and that of the erosion front V2- If Vj > V2, the thickness of the reaction zone will gradually increase and at some point the matrix will be completely permeated with water, thus leading to an eventual bulk erosion process. On the other hand, if V2 = Vj, a surface erosion process wiU take place, and the rate of polymer erosion will be completely determined by the rate at which water intrudes into the matrix. 

The thickness of the reaction zone in high explosives is usually in the range 1-10 mm. 

In order to clarify the combustion wave structure of AP composite propellants, photographic observations of the gas phase at low pressure are very informative. The reaction rate is lowered and the thickness of the reaction zone is increased at low pressure. Fig. 7.3 shows the reduced burning rates of three AP-HTPB composite propellants at low pressures below 0.1 MPa.FI The chemical compositions of the propellants are shown in Table 7.1. The burning rate of the propellant with the composition ap(0-86) is higher than that of the one with ap(0-80) at constant pressure. However, the pressure exponents are 0.62 and 0.65 for the ap(0-86) and Iap(0.80) propellants, respectively that is, the burning rate is represented by r for the p(0.86) propellant and by r for the p(0.80) propellant. 

The heat flux transferred back from the gas phase to the burning surface is dependent on the temperature gradient in the gas phase, which is inversely proportional to the thickness of the reaction zone in the gas phase. Since the reaction in the gas phase is complete at the upper end of the bluish flame, the heat flux defined by Am conforms to the proportionality relationship Am l/6g p0- . The observed pressure dependence of the burning rate, is caused by the pressure depend-... 

In contrast to the detonation of gaseous materials, the detonation process of explosives composed of energetic solid materials involves phase changes from solid to liquid and to gas, which encompass thermal decomposition and diffusional processes of the oxidizer and fuel components in the gas phase. Thus, the precise details of a detonation process depend on the physicochemical properties of the explosive, such as its chemical structure and the particle sizes of the oxidizer and fuel components. The detonation phenomena are not thermal equilibrium processes and the thickness of the reaction zone of the detonation wave of an explosive is too thin to identify its detailed structure.C - ] Therefore, the detonation processes of explosives are characterized through the details of gas-phase detonation phenomena. 

Combustion models which consider the thickness of the reaction zone usually accentuate cither heat conduction mechanisms (thermal theory) or the diffusion mechanisms (diffusion theory) and the models are of necessity of limited value. Simpler models in which the reaction zone or flame front is considered to be an infinitesimally thin discontinuity in the flow, while not simulating exactly the observed conditions, allow the model to be of more general utility and many combustion phenomena become easier to understand because of this simplification. It is the latter approach which is discussed first in this paper—i.e., the combustion process is regarded as a wave phenomenon. 

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. 

In the absence of stirring, the front propagation speed reaches an asymptotic value, vo = 2 jD/x, and the thickness of the reaction zone is E, = 8VDx [9,10]. While in the presence of a velocity field the front propagates usually with an average speed v/ greater than vo [13-15], Moreover, if/(0) is not convex, under special conditions, the flow may stop ( quench ) the reaction [16]. 

Synchrotron radiation studies [92] have identified systematic changes in the interplanar spacing in the vicinity of the microscopically visible reaction interface, showing that the thickness of the reaction zone is about 150 pm. There is apparently significant loss of water fi-om the zone ahead of the recrystallization plane identified as the advancing reaction interface. 

When the reaction is infinitely fast the thickness of the reaction zone will be reduced to that of a plane situated at a distance yx from the interface as illustrated in Fig. 6.3.C-1. In the zone of the liquid film between the interface and the reaction plane at yx, varies between C j and zero and there is no more B as shown in Fig. 6.3.C-1. In the zone between y, and y there is no more A, only B. which varies between zero and Cgt,. The location of the reaction plane is dictated by the concentrations Cjii and Cgg, but also by the diffusion rates. 

Many of the problems connected with the study of flame structure stem from the narrowness of the spatial region to be studied, for example the stoichiometric acetylene-air flame at atmospheric pressure has a primary reaction zone smaller than one-tenth of a millimeter (0.004 inch). It is not possible with present-day techniques to measure the properties of such a flame with sufficient spatial resolution to obtain meaningful second derivatives. The thickness of the reaction zone, however, depends inversely on both pressure and burning velocity. This behavior is... 

Assume that the reaction and diffusion model is applicable, as presented in section 5,4,3.1, When the Thiele modulus cp > 3, only a fraction of l/(p of the porous particle, close to the outer surface, will take part in the reaction. As the solid is converted to a solid product with a larger volume, the pore diameter will decrease. The effective diffusivity is thereby reduced, so that the thickness of the reaction zone is also reduc. The higher the reaction rate constant, the higher the Thiele modulus was at the beginning, and the sooner the pore mouth will be plugged. A rough estimate indicates that the maximum degree of conversion of the solid reactant will be smaller than the effectiveness factor, which is tank (p/(p. 

The authors propose that can not increase any further as soon as the effective reaction zone has been reduced, due to the enhancement, to a dimension in the order of the particle diameter. With an effective thickness of the reaction zone, according to film theory, given by 6 = /E, this reasoning results in ... 

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