Travelling reaction waves

In this section the whole field of exotic dynamics is considered this term includes not merely oscillating reactions but also oligo-oscillatory reactions, multiple steady states, spatial phenomena such as travelling reaction waves, and chaotic systems. All of these have common roots in autocatalytic processes. This area has continued to expand, and there is a case for treatment in future volumes by a specialist reviewer. An entry into the literature can be gained from a recent series of articles in a chemical education joumal, and in a festschrift issue in honor of Professor R. M. Noyes. Other useful sources are a volume of conference proceedings, and a volume of lecture preprints of a 1989 conference. The present summary is concerned with the chemical rather than the mathematical aspects of the topic. 

Fig. 5 MR images of traveling (reaction-diffusion)waves in the manganese-catalysed Belousov-Zhabotinsky reaction, taken from the centre of a bed packed with 1 mm diameter glass spheres (22). Waves are formed both inside the bed and above it in the liquid phase. Images (a-d) are shown at time intervals of 16 s. 

The photoelectric effect was explained by Albert Einstein in 1905 using the principles of quantum physics developed by Max Planck. Einstein claimed that light was quantized— that is, it appeared in bundles of energy. While these bundles traveled in waves, certain reactions (like the photoelectric effect) revealed their particulate nature. This theory was further supported in 1923 by... 

Rarefaction waves travel from the edges toward the center of the cylinder, causing the reaction wave to travel more slowly at the edges, thus eurving the front. As a consequence, the velocity of the wave depends on the radius of the cylinder, as depicted in Figure 8. 

Under these conditions of excellent mixing of chlorine and hydrocai bim at low temperature and in the absence of an activating agent, no ignition occurs and the resulting mixture has such alow reaction velocity that the reaction wave will not travel backward from the reactor to the mixer. 

We begin with a discussion of a one-dimensional traveling wave solution which is a mathematical representation of the uniformly propagating reaction wave that we are discussing. This discussion is a bit technical but gives a good insight into the combustion theory. 

The BZ reaction is carried out in two-dimensional, i.e., Petri dish filled with the reaction mixture followed by the monitoring of oscillatory phenomenon in the stirred system which can manifest itself formation of traveling chemical waves as could be seen in Fig. 1.6. In the oxidized state of the reaction, the autocatalyst... 

We have shown that multiple travelling front waves can occur in a reaction-diffusion-convection system. These waves can be studied in an unbounded system by using a wave transformation and solving a special boundary value problem with the use of continuation methods. These results provide various parameter dependences of the velocity of the wave. Moreover, in a bounded system the waves move back and forth through the system and form remarkable zig-zag patterns. 

Sonication is an easy method to prepare highly dispersed oxides. Cavitation develops when ultrasounds are applied to a liquid The traveling sound wave causes high pressures, compressing the liquid, followed by low pressure and sudden expansion, forming very small bubbles, which expand and collapse. Such expansion/collapsing of the bubbles creates hot spots (up to 5000 °C) with high pressures (1000 atm), and the reaction proceeds. 

In Eq. (4-29) jc is the distance traveled by the wave, and a is the absorption coefficient. Sound absorption can occur as a result of viscous losses and heat losses (these together constitute classical modes of absorption) and by coupling to a chemical reaction, as described in the preceding paragraph. The theory of classical sound absorption shows that a is directly proportional to where / is the sound wave frequency (in Hz), so results are usually reported as a//, for this is, classically, frequency independent. 

In a moving co-ordinate system, the traveling wave equations typically reduce to a system of parameterized nonlinear ordinary differential equations. The solutions of this system corresponding to pulses and fronts for the original reaction-diffusion equation are called homoclinic and heteroclinic orbits, correspondingly, or just connecting orbits. 

A detonation wave is a very rapid wave of chemical reaction which, once it is initiated, travels at a stable supersonic speed, called the detonation velocity, in a high explosive. Typically, detonation velocities for pressed or cast high explosives range from... 

Stationary, traveling wave solutions are expected to exist in a reference frame attached to the combustion front. In such a frame, the time derivatives in the set of equations disappear. Instead, convective terms appear for transport of the solid fuel, containing the unknown front velocity, us. The solutions of the transformed set of equations exist as spatial profiles for the temperature, porosity and mass fraction of oxygen for a given gas velocity. In addition, the front velocity (which can be regarded as an eigenvalue of the set of equations) is a result from the calculation. The front velocity and the gas velocity can be used to calculate the solid mass flux and gas mass flux into the reaction zone, i.e., msu = ps(l — e)us and... 

Reaction-diffusion systems have been studied for about 100 years, mostly in solutions of reactants, intermediates, and products of chemical reactions [1-3]. Such systems, if initially spatially homogeneous, may develop spatial structures, called Turing structures [4-7]. Chemical waves of various types, which are traveling concentrations profiles, may also exist in such systems [2, 3, 8]. There are biological examples of chemical waves, such as in parts of glycolysis, heart... 

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