Reaction zone, thickness

Since 8 is the reaction zone thickness, it is possible to relate 8 to SL. The total rate of mass per unit area entering the reaction zone must be the mass rate of consumption in that zone for the steady flow problem being considered. Thus... 

In this description < L represents not only the reaction zone thickness S in the Mallard-Le Chatelier consideration, but also the total of zones I and II in Fig. 4.4. Substituting Eq. (4.17) into Eq. (4.18) gives... 

Diameter-Dependence of Detonation Velocity in Solid Composite Propellants, I. Attempts to Calculate Reaction-Zone Thickness", 4thONRSympDeton (1965), pp 96-101 9) B. Hayes, "On Electrical... 

Green 8c E. James Jr, "Radius of Curvature Effect on Detonation Velocity , 4th-ONRSympDeton (1965), pp 86-91 (The effect of the radius of curvature of the detonation front on the detonation velocity of certain explosives were measured. The results were used to calculate the reaction zone thicknesses for various expls. For example, such thickness was found as 0.064 mm for 85/15-HMX/Viton, using Holston HMX, whereas for the same type plastic-bonded expl made from British Bridgwater HMX it was 0.182mm) 28) C.G. Dunkle, private... 

The strong influence exerted by many. of these factors, especially degree of confinement and charge diameter, shows that the energy release which is initiated in the deton front does not occur instantaneously. Hence, any theory (such as "curved-front or "nozzle ) must take into consideration the lateral expansion (See Ref 61, pp 188-201). This expansion (if at all appreciable during time t, where reaction zone thickness is a-Dt) will modify the deton process because a) part of the energy released is used in the expansion (See Ref 61, p 201), hence does not contribute to propaga tion of rhe wave front, and b) peak temp and pressure are lower than when lateral expansion... 

Exptl results indicated a reaction zone thickness varying inversely with initial pressure for hydrogen-oxygen mixtures. This was in agreement with the data for U versus d if Fay s theory is accepted as correct... 

The question considered is a description of the conditions which must be met by a localized initiator if a spherical detonation wave is to be formed. The first problem is a determination of the possibility of the existence of such a wave. Taylor analyzed the dynamics of spherical deton from a point, assuming a wave of zero-reaction zone thickness at which the Chapman-Jouguet condition applies. He inquired into the hydrodynamic conditions which permit the existence of a flow for which u2 +c2 = U at a sphere which expands with radial velocity U (Here U = vel of wave with respect to observer u2 = material velocity in X direction and c -= sound vel subscript 2 signifies state where fraction of reaction completed e = 1). Taylor demonstrated theoretically the existence of a spherical deton wave with constant U and pressure p2equal to the values for the plane wave, but with radial distribution of material velocity and pressure behind the wave different from plane wave... 

However, since insufficient information is available regarding the dependence of gx, and especially k, upon r, eqn. (33) is of only formal rather than practical value at the present time. Since the reaction zone thickness is liable to be of molecular dimensions, the conventional procedure of estimating the effective work terms for a single reaction site at the expected plane of closest approach is probably acceptable, although it is nonetheless important to recognize its limitations. 

This close distance determines also the dr value. Therefore, the product K°dr may be considered as an effective reaction zone thickness [139], where k° is the electronic transmission coefficient at a distance of closest approach of the reactant to the electrode surface. For adiabatic reactions the value of k° should approach 1. 

For the purpose of the simple model, the Von Neumann spike is ignored and the reaction zone thickness is assumed to be zero. The gas expansion or rar-... 

This water dissociation model developed by Strathmann et al. [59] is described as being a combination of the second Wien effect, the protonation-deprotonation phenomena of functional groups in the membrane, and the reaction zone thickness A. This model was developed under some assumptions [59] ... 

Fig. II. SiC/W monofilament strength as a function of the reaction zone thickness, c.

In this expression N. is the Avogadro constant, R is the average separation between reacting centers on electron transfer, and A/ is the effective reaction zone thickness. This latter factor has been discussed extensively in papers by Weaver and coworkers. It is immediately obvious that R is the same as the intersite jump distance S discussed previously. The reaction layer thickness AR expresses a range of nuclear separations within which the electron transfer reaction proceeds with a rate constant Aet- Majda notes that the magnitude of AR is strongly... 

This concentration profile is illustrated in Fig. 2.31 as a fimction of the Thiele modulus 3>. From this diagram we note that when <1> is small, concentration profiles are fairly shallow, since the entire layer is being used. However when 4> is large, the concentration of substrate falls rapidly with distance into the polymer film. The reaction is essentially complete within a thin reaction zone (thickness 2fjt) near the polymer/solution interface. 

The formation of the reaction zone in the pressure-volume plane is shown in Figure 1.8 that in the pressure-distance plane in Figure 1.9. The steady-state reaction zone profiles of pressure, temperature and mass fraction are shown in Figure 1.10. The shock-front pressure and reaction zone thickness are shown as functions of time in Figure 1.11. Formation of an approximately stable reaction zone profile requires many ( 10) reaction zone lengths. 

Figure 1.11 Shock-front pressure and reaction zone thickness as a function of time for nitromethane with a piston velocity of 0.4 cm/psec (until complete decomposition occurs at the piston, then the velocity is stepped to 0.3 cm/)usec), with a 0.3 cm/psec constant velocity piston, which form steady-state detonations, and with a 0.4/0.05 cm/psec stepped-velocity piston which forms a failing wave. E = 53.6, Z = 4 x 10, 7 = 0.68, mesh = 5-A.

The formation of an overdriven detonation by a piston, whose initial velocity of 0.4 cm/yusec is decreased to 0.3 cm/jisec when complete decomposition occurs at the pis-ton/nitromethane interface, was computed using a 5-A mesh and realistic viscosity values. The initial reaction zone was about 100-A thick, and the shock-front pressure was 360 kbar. The steady-state reaction zone thickness for a 0.3 cm/yusec piston is 620-A, the shock-front pressure is 272 kbar as described in section 1.1. The formation of the reaction zone in the pressure-volume plane is shown in Figure 1.13. The shock-front pressure and the reaction zone thickness are shown as functions of time in Figure 1.11 for the 0.3 cm//isec constant-velocity piston, and for the 0.4/0.3 cm/yitsec stepped-velocity piston. The 0.4/0.3 stepped-velocity piston results in a reaction zone thickness of 100-A at 3 x 10 /isec which increases to a maximum of 920-A at 4.25 x 10 /itsec and then decreases to 610-A by 7 X 10 /isec. The 0.4/0.3 stepped-velocity piston produces an initial shock-front pressure of 365 kbar, which decreases to 248 kbar by 1.5 x 10 /itsec and remains almost constant for the next 10 /isec during this time the reaction zone thickness increases from 300 to 600-A. Once the reaction zone thickness exceeds the steady-state thickness, the shock-front pressure begins to increase toward the steady-state shock-front pressure. 

Figure 1.11 shows the shock-front pressure and reaction zone thickness for 0.4/0.3 and 0.4/0.05 cm/nsec pistons. The 0.4/0.05 cm/yusec piston produces a detonation that fails to propagate in the time scale of interest. 

Figure 1.14 Shock-front pressure and reaction zone thickness as a function of time for nitromethane with various saw-tooth pistons that form steady-state detonations. Up is piston particle velocity and St = nAt where At is time increment and n is cycle number.

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