Reaction waves

See Detonation Waves Steady-state, One-Dimensional Reaction Waves with Finite Reaction Rate in Vo 4, D7Q3-R to D704-R. Ref S. Brinkley, Jr J.M. Richardson, 4th SympCombstn, Williams Wilkins, Baltimore (1952), 450-57 CA 49, 6608 (1955)... 

The analysis showed that the part cures by reaction wave polymerization. The rate of propagation of the waves from the walls toward the center of the part was proportional to the molding temperatures and was a function of the polymer formulation. 

Part cures were characterized by exothermic reaction wave propagation. Figures 6a-9b show the development of the reaction waves. The waves propagate from the walls of the part towards the center. A comparison of the temperature and epoxide conversion profiles revealed that the highest temperature corresponded to the highest conversion. As the part initially heats the resin/glass matrix nearest the walls heats fastest however, as the part exotherms the temperatures in the interior of the part exceeded the wall temperatures. The center temperature does not become the hottest temperature until the waves intersect. It must be noted that the hottest temperature does not always occur at the center of the part. The wave velocities are proportional to the wall temperatures. In Figures 6a to 9b the mold temperature was 90 C and the press temperature was elevated to 115 C. Since the press does not heat the part until after it is wound, the press temperature was elevated to accelerate the reaction wave from the press so that the waves would intersect in the center of the part. 

Many physical and process constraints limit the cycle time, where cycle time was defined as the time to the maximum exotherm temperature. The obvious solution was to wind and heat the mold as fast and as hot as possible and to use the polymer formulation that cures most rapidly. Process constraints resulted in a maximum wind time of 3.8 minutes where wind time was defined as the time to wind the part plus the delay before the press. Process experiments revealed that inferior parts were produced if the part gelled before being pressed. Early gelation plus the 3.8 minute wind time constrained the maximum mold temperature. The last constraint was based upon reaction wave polymerization theory where part stress during the cure is minimized if the reaction waves are symmetric or in this case intersect in the center of the part (8). The epoxide to amine formulation was based upon satisfying physical properties constraints. This formulation was an molar equivalent amine to epoxide (A/E) ratio of 1.05. 

Transition to detonation in charmels without obstacles was recently successfully simulated numerically [11,12]. In these simulations, it was shown that shock compression of the unreacted mixture forms the hot spots resulting from shock-shock, shock-wall, and shock-vortex interactions. The hot spots contain temperature gradients that produce spontaneous reaction waves and detonations. 

Imaging on a larger scale, in particular when large numbers of adsorbate molecules organize themselves in patterns of micrometer size, is possible by using recently developed methods based on photoemission (PEEM) and ellipsometry (EMSI). These techniques have provided us with spectacular movies of reaction wave fronts moving over surfaces. These phenomena are characteristic of oscillating surface reactions, a subject that has fascinated many in catalysis and surface science [81. 

As regards the low energy-low sensitivity expls of the AN/FO type, the axial priming. with a high energy fuse (20 g/m) generated a reaction wave which attacked the wall of the cylinder in a direction nearly perpendi-... 

Chaiken (Ref 5) reported that his prior streak camera studies of the shock initiation to deton of NM indicated the existence of a "hypervelocity wave moving behind the initiating shock front. It was suggested that the deton reaction wave originated be-... 

Detonation, Strong and Weak. This subject is discussed by Evans 8t Ablow (Ref 2, pp 141-42), but prior to this it. is necessary to discuss the existence and uniqueness of classes of reaction waves for specific boundary conditions , as given in the book of Courant 8c Friedrichs (Ref 1, pp 215-22) and in Ref 2... 

Let the rear boundary of reaction wave move with.a specific velocity Up along the line P in the x,t-plane as in Fig 9 of Ref 2 (our Fig 1). Then initial data are prescribed along two lines. One is the x-axis, which is spacelike with. respect to the material behind it and carries the quantity u = 0 (if. the material is initially at rest), and p=p0. The other line is P, which is timelike, or subsonic to the gas flow, since it is identical with the path of the adjacent gas particles it carries velocity Up. The discontinuity of the reaction wave is represented by the line W. The deductions on uniqueness which. can be Used for non-reactive flow (See Ref 2, pp 136-37) cannot be applied here directly because of the interference of the unknown discontinuity W. 

Evans Ablow (Ref 66) described the following one-dimensional waves "One-dimensional Steady-State Reaction Waves with Instantaneous Reaction (pp 137-45) wOne-Dimensional Steady-State Reaction Waves with Finite Reaction Rate ... 

See also under "DETONATION WAVES STEADY-STATE, ONE-DIMENSIONAL, REACTION WAVES WITH INSTANTANEOUS REACTION , and under "Detonation Waves, Transient, One Dimensional ... 

ONE- DIMENSIONAL REACTION WAVES WITH FINITE REACTION RATI... 

DETONATION WAVES STEADY-STATE, ONE-DIMENSIONAL REACTION WAVES WITH INSTANTANEOUS REACTION... 

Section III entitled "One- Dimensional, Steady-- State Reaction Waves with Instantane -ous Reaction a comprehensive description divided into the following subsections ... 

Since the equations of continuity, momentum, energy, and state do not suffice to determine the five unknowns, it. is necessary to inquire into the conditions under which solutions exist and whether solns are unique. The information which has thus far been omitted is a specification of the flow field of die reaction products, that is to say, since this section is restricted to one--dimensional flow, of the rear boundary condition. Before discussing the question of determinancy it is necessary to deduce from the equations of Section II of Ref 66, the general properties of flow ahead and behind reaction waves. To do this the Hugoniot curve for the products... 

Certain general statements can be made regarding the character of flow relative to the reaction front for the six classes of reaction waves, shown in Fig 6. The state m ents known collectively as Joaguet s rule are listed on p 139 of Ref 66 as (aX (b), (c),... 

Wood Kirkwood (Ref 36a) assumed a curved shock front leading a zone which is cylindrically symmetric. Their coordinates were x, coincident with the axis of the cylindrical chge, and r, the radial distance from the axis. The vector mass velocitytf has an axial component u and a radial component >. Fig 3Oof Ref 66, p 157 is a sketch of the flow in a coordinate system which moves with.the deton wave. Here = space coordinate within reaction wave ... 

Detonation Wave Transient, One-Dimensional. In the discussion entitled One-Dimensional Transient Reaction Waves by Evans Ablow (Ref 66, Section VI, pp 167-68), a model is assumed according to which a detonation wave is a shock followed by a deflagration wave. In a steady wave the reaction at a given layer of unreacted material is initiated by the leading shock. 

M-W. Evans C.M. Ablow, Chem Revs 61 (1961), p 147 (Definition of term detonation wave) p 152 (Steady detonation waves in real fluids) p 157 (Cylindrically symmetric flow in the steady zone of detonation wave) p 159 (Spherically symmetric flow in the steady zone of detonation wave) p 166 (Stability of detonation waves in which reaction is not complete) p 167 (One- dimensional transient reaction waves) 172,... 

Again the scenario we envisage is similar to that shown qualitatively in Fig. 11.7 we expect our best chance of such behaviour if the decay rate is small, i.e. k2 1. The reaction wave has a leading front moving with a steady velocity c1, through which most of the conversion of A to B occurs. After this front, the dimensionless concentration of A is almost zero and that of B is almost unity. At some distance, the first front is followed by a recovery wave, possibly more diffuse, in which A is completely removed and the autocatalyst also decays. The velocity of the recovery wave is c2. If ct exceeds c2, the first front will move away from the second, so the pulse will increase in width if c, = c2, the pulse will move with a constant shape if, however, c2 exceeds c, we can expect the second wave to catch the first, in which case propagation may fail. 

Detonation waves, steady state one-dimensional reaction waves with finite reaction rate 4D703... 

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