First reaction front

We assume that a steady wavefront with velocity c, exists. The system must be governed now by two travelling coordinate equations for the two concentrations of A and B. These are 

Ahead of the reaction front (at z - + oo), no conversion has occurred, so the boundary condition is 

We do not know the exact conditions after the wavefront has passed. These must emerge from the analysis. 

The first important assumption to be made is that the autocatalyst should decay only slowly, so k2 1. This will lead to a distinct separation between 

Coupled wave equations are not easy to handle. It will help greatly if we can somehow find some sort of approximate relationship between a and / , which will allow us to substitute for a, say, and reduce the system to a single equation. This relationship need only apply during the first wavefront. What should we take The behaviour of this model in a CSTR suggests one such form. By analogy with the stationary-state relationship, eqn (6.50), we try the form 

---

These studies have found that increased confinement leads to flame acceleration and increased damage. The flame acceleration is caused by increased turbulence which stretches and tears the flame front, resulting in a larger flame front surface and an increased combustion rate. The turbulence is caused by two phenomena. First, the unburned gases are pushed and accelerated by the combustion products behind the reaction front. Second, turbulence is caused by the interaction of the gases with obstacles. The increased combustion rate results in additional turbulence and additional acceleration, providing a feedback mechanism for even more turbulence. 

The choice of the temperature of the initial reactive mass (75 - 90°C) is dictated by two requirements firstly, the reactive mass must be liquid secondly, the reaction rate in this temperature range must be negligible. It was established in preliminary experiments that the temperature of the heater surface needs to be 75 - 125°C higher than the initial temperature of the reactive mass. The necessary operation period for the heater depends on the initial temperature of the reactive mixture and its reactivity (i.e., on its composition). The temperature of the heater does not influence the properties of the final product or the stationary kinetics of the process. The local temperature increase inside the adjoining layer must be supplemented by a heater for 30 - 50 min. This is the time required to set up the reaction front after that, the front exists by itself and propagates due to the exothermal heating effects of chemical reaction and crystallization. 

Band-Aging - Especially with fresh catalysts, the reaction occurs over a relatively small zone in a fixed bed. This reaction front marches down the catalyst bed as the coke deposits first deactivate the front part of the bed (Figure 4). Use of a sufficient catalyst volume permits a fixed-bed design in which on-stream periods are long enough to avoid overly frequent regeneration cycles. 

Figure 10.5 shows the modeling results for the first five years. The first thing we notice is that the seepage of acidic tailings fluid into the shallow contaminated aquifer causes chemically distinct zones separated by sharp reaction fronts. Each zone corresponds to the successive buffer reactions with calcite, Al(OH)3(a), and Fe(OH)3(a). 

It is interesting to compare the reaction front formulations of the gasless combustion and frontal polymerization models. First of all, there is an additional differential equation in the FP model, namely, equation (4.132). The equation, however, can be easily solved yielding... 

The ammonia oxidation reaction proceeds in the first part of the catalyst bed [Fig. 16(a)]. This part is subsequently deactivated, mainly by nitrogen species. The high activity of the catalyst is maintained due to the movement of the reaction front to the next positions in the catalyst bed. When [ Nj-NH3 is injected at the moment that the reaction was already 20 seconds on-stream, labelled N species adsorb further on in the catalyst bed. Thus, in time to come, the deactivation front moves to the end of the catalyst bed. When this front reaches the end of the bed, the catalyst is covered with reaction species and the deactivation is observed in the concentration of the products. An experiment with half an amount of the catalyst also supports this reaction front movement. This experiment showed the formation and concentration of the products in the same manner, however, the catalyst remained active for half the time of the normally applied catalyst bed. Thus, below 413 K, the catalyst remains initially active because the reaction zone moves to the next bed positions, after the previous positions became fully covered with the adsorbed reaction species. Injection of a [ N]-NH3 or [ 0]-02 pulse after the initial deactivation, confirmed that the platinum surface is fully covered and that conversion of ammonia and oxygen is low. No significant amount of nitrogen or oxygen species remains adsorbed at the catalyst surface. 

Vemet [234] submitted the example of reaction fronts modeling, in which the precipitation of CD compound firstly occurred, and then of ABn firstly the product with the lower solubility is formed (Fig. 6.62). The CaCOj and Mg(OH)2 layers on the surface of concrete exposed to the sea water attack are the examples. 

Moreover, the influence of the chemical reaction rate constant and some other physical parameters of the liquid flow (density, viscosity) on the conditions of macroscopic front formation in turbulent flows, allow us to make an assumption about the differences in the nature of the reaction front and mixing front formation. In the first case, the key parameters of the process are the kinetic and diffusion parameters in the second case, however, the key parameters of the process are the convective and turbulent transfer. The influence of density and viscosity, i.e., the parameters which define the hydrodynamic motion mode of the liquid flow in the tubular channels, on the... 

Chemical attack by solutions containing sulfates proceeds by an inward movement of a reaction front. In this way a surface region is produced whose thickness increases with time, and in which the reactions that take place first are those taking place in the greatest depth. 

The calculations presented above were done by the two-dimensional version of REBOS. In the case of self-heating first of all the phenomena taking place until ignition are of interest. These phenomena may be treated by REBOS quite well in two dimensions. Calculation concerning the motion of the reaction front after ignition may be treated by the one-dimensional version of REBOS. 

One of the great appeals of nonlinear chemical dynamics lies in the striking visual demonstrations that can be created. It is a rare person who is not impressed the first time he or she sees a clear solution repeatedly turn brown, then blue, then back to clear In this appendix, we explain how to perform demonstrations of oscillating reactions, fronts, and waves. In the next section, we provide information on how some of these systems can be systematically studied in the upper-level undergraduate laboratory. 

If either the monomer or the polymer, or both, are liquid natural convection, caused by the heat liberated by the exothermic reaction, can occur. Consider first the case when the monomer is liquid and the polymer is solid (cf. Section 1). We will discuss separately upward and downward propagating fronts. If the front propagates upward, then the chemical reaction heats the monomer from below which reminds of the classical Rayleigh-Benard problem. If the Rayleigh number is sufficiently large, then the planar front loses its stability and stationary natural convection above the front occurs. For descending planar fronts there is no such convective instability. An approximate analytical approach allows one to find stability conditions for the propagating reaction front and to determine the modes which appear when the front loses stability [22]. 

---