Mechanism of wave propagation

In a region with a high [Br ], a new wave cannot be initiated. HBrOj and Br diffuse in opposite directions through the boundary of the moving edge as indicated in Fig. 10.2. Their mutual reaction 

A quantitative theory of wave propagation based on the above ideas has been developed by Field and Noyes [18] using Fick s second law, FKN mechanism of B-Z reaction and non-linear kinetics. 

Basic steps of FKN mechanism which are used in the formulation are as follows  

It is assumed that the velocity of band propagation is controlled by the concentration of Br (B) and bromous acid (A) in the band front and that trailing band does not affect the velocity of band propagation. Wave is due to (i) autocatalytic production and destruction of HBr02 and (ii) diffusion of HBr02. 

Both chemical reaction and diffusion are involved in concentration changes at any position X and time f. The resulting reaction-diffusion equation can be written as follows  

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This chapter discusses propagation of polymerization waves. In a polymerization wave, a spatially localized reaction zone, in which the polymerization reactions occur, propagates into initial reactants (the monomer) leaving the reaction product (the polymer) in its wake. Two types of polymerization waves, thermal and isothermal, have been observed experimentally, and the mechanism of wave propagation for each is markedly different. Thermal polymeriza-... 

Future directions will call for additional insight into the physics and mechanics of wave propagation in the utilization of oblique incidence to provide us with additional sensitivity on defect analysis inside a structure. Information on the utilization of surface and plate waves by way of oblique incidence can be found elsewhere,( 0,32,33) together with some knowledge useful in the inspection of adhesively bonded structures and composite materials, to be summarized briefly in the following paragraphs. 

Expansion waves are the mechanism by which a material returns to ambient pressure. In the same spirit as Fig. 2.2, a rarefaction is depicted for intuitive appeal in Fig. 2.7. In this case, the bull has a finite mass, and is free to be accelerated by the collision, leading to a free surface. Any finite body containing material at high pressure also has free surfaces, or zero-stress boundaries, which through wave motion must eventually come into equilibrium with the interior. Expansion waves are also known as rarefaction waves, unloading waves, decompression waves, relief waves, and release waves. Material flow is in the same direction as the pressure gradient, which is opposite to the direction of wave propagation. 

The fluid mechanics origins of shock-compression science are reflected in the early literature, which builds upon fluid mechanics concepts and is more concerned with basic issues of wave propagation than solid state materials properties. Indeed, mechanical wave measurements, upon which much of shock-compression science is built, give no direct information on defects. This fluids bias has led to a situation in which there appears to be no published terse description of shock-compressed solids comparable to Kormer s for the perfect lattice. Davison and Graham described the situation as an elastic fluid approximation. A description of shock-compressed solids in terms of the benign shock paradigm might perhaps be stated as ... 

Investigation of Transverse Mode Combustion in Liquid Propellant Rocket Motors (PhD Thesis), Princeton Univ, June 1, 1961 E) L.A. Dickinson, "Command Initiation of Finite Wave Axial Combustion Instability in Solid Propellant Rocket Motors , ARS 32, 643(1962) F) S.Z. Burstein V.D. Agosta, "Combustion Instability Non-Linear Analysis of Wave Propagation in a Liquid Propellant Rocket Motor , Polytechnic Institute of Brooklyn, Dept of Mechanical Engineering,... 

To test the fit of the theoretical mechanism to the experimentally observed phenomena, it seemed principally important to try to realize experimentally the second mode of the autowave process. Its initiation was performed, in accordance with the theory, not by pulse heating but with the help of a heater whose temperature could be raised slowly. Under such conditions the slower wave could not be excited either in liquid helium or nitrogen, that is, there was only one mode of wave propagation. This was possibly connected with the fact that under conditions of intense heat release into liquid media, high (close to critical) transverse temperature gradients occurred in the samples, which might be a source of severe disturbances impeding the realization of the slower wave mode. 

Rogachev, A. S., Khomenko, I. O., Varma, A., Merzhanov, A. G., and Ponomarev, V. I., The mechanism of self-propagating high-temperature synthesis of nickel aluminides. Part II Crystal structure formation in a combustion wave. Int. J. SHS, 3,239 (1994a). 

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