Chemical wave generation

Figure 4.21 The moving spiral chemical waves generated during the BZ reaction occurrence in a flat Petri dish. Frames A-F are acquired in successive moments of time.

Any propagating front or chemical wave generates concentration and temperature gradients that create differences in the density of the solution. In Chapter 9, we will consider this issue in detail, but the important point is that natural convection can arise from buoyancy. Such convective flows will distort the front and change the wave velocity. Several methods can be used to eliminate convection. Extremely narrow capillary tubes will often suppress convection, but it becomes difficult to observe the front and two-dimensional phenomena cannot be studied. 

Linear stability analysis provides one, rather abstract, approach to seeing where spatial patterns and waves come from. Another way to look at the problem has been suggested by Fife (1984), whose method is a bit less general but applies to a number of real systems. In Chapter 4, we used phase-plane analysis to examine a general two variable model, eqs. (4.1), from the point of view of temporal oscillations and excitability. Here, we consider the same system, augmented with diffusion terms a la Fife, as the basis for chemical wave generation ... 

The harmonic oscillator is an important system in the study of physical phenomena in both classical and quantum mechanics. Classically, the harmonic oscillator describes the mechanical behavior of a spring and, by analogy, other phenomena such as the oscillations of charge flow in an electric circuit, the vibrations of sound-wave and light-wave generators, and oscillatory chemical reactions. The quantum-mechanical treatment of the harmonic oscillator may be applied to the vibrations of molecular bonds and has many other applications in quantum physics and held theory. 

For chemical systems of interest, photolysis produces intermediates, such as radicals or biradicals, whose energetics relative to the reactants are unknown. The energetics of the intermediate can be established by comparison of the acoustic wave generated by the non-radiative decay to create the intermediate, producing thermal energy , with that of a reference or calibration compound whose excited-state decay converts the entire photon energy into heat, / (ref). The ratio of acoustic wave amplitudes, a, represents the fraction of the photon energy that is converted into heat. 

The Presumed Probability Density Function method is developed and implemented to study turbulent flame stabilization and combustion control in subsonic combustors with flame holders. The method considers turbulence-chemistry interaction, multiple thermo-chemical variables, variable pressure, near-wall effects, and provides the efficient research tool for studying flame stabilization and blow-off in practical ramjet burners. Nonreflecting multidimensional boundary conditions at open boundaries are derived, and implemented into the current research. The boundary conditions provide transparency to acoustic waves generated in bluff-body stabilized combustion zones, thus avoiding numerically induced oscillations and instabilities. It is shown that predicted flow patterns in a combustor are essentially affected by the boundary conditions. The derived nonreflecting boundary conditions provide the solutions corresponding to experimental findings. 

Fig. 9. Successive compartmental lines predicted on the fate map6-7 of the blastoderm by the chemical wave model, with the binary combinatorial code assignment in each compartment generated by the successive lines. A, antenna E, eye Pb, proboscis P, prothorax W, wing and mesothorax H, haltere LI, L2, L3, first, second, and third legs Abd, abdominal segments G, genital.

Figure 3.30 Displacement in the film is a superposition of waves generated at the sub-strate/fllm interface by the surface displacements m,v, and radiated across the film. The surface-normal component Uyo generates compressional waves, while the in-plane components (Ujto, U20) generate shear waves. (Reprinted with permission. See Ref. [501. 1994 American Chemical Society.)...

It is not always true that K sources of chemical variation generate an X matrix of rank K. Consider short-wave near-infrared (800-1000 nm) spectra of mixtures of water and ethanol at different concentrations of water and ethanol and collect these spectra in X. If the Lambert-Beer law holds, X can be modeled as... 

Today there are several other ways of diamond synthesis besides the HPHT method. For example, it is possible to utilize the pressure of a shock-wave generated in an explosion. This process mostly yields powdery products with particle sizes in the range of micrometers (1 mm at max.) that may be employed for industrial purposes as well. Moreover, very small diamonds (5-20 nm) can be made by reacting explosives in confined containers. Diamond films are produced on various substrates by chemical vapor deposition (CVD method using methane as a carbon source. Detonation synthesis and vapor deposition will be described in detail in Chapters 5 and 6. 

Non-linear phenomena such as temporal oscillations and chemical waves in the case of chemical reactions are governed by the autocatalytic reaction (positive feedback) and reaction where the product of autocatalysis is destroyed by some other species (negative feedback). Of course in the case of chemical waves (spatio-temporal oscillations), diffusion does play a role, and the concept of reaction diffusion equation is evoked to predict the dependence of velocity of chemical waves on different parameters. In this chapter, we propose to discuss electrical potential oscillations generated due to coupling of volume flux, solute flux and electric current through solid-liquid interface (membrane systems), liquid-liquid interface, solid-liquid-liquid interface (density oscillator) and liquid-liquid-vapour interface. 

Photoacoustic sensors (PAS) Quantification of air contaminants by PAS involves the use of UV or IR radiation to quantify air contaminants. It involves the absorption of a pulse of light energy by a molecule and the subsequent detection of a pressure wave generated by heat energy released by the molecule upon its return to the ground state. Photoacoustic spectroscopy analysis is nondestructive, can be done in real time, and can be a few orders of magnitude more sensitive than conventional UV-vis spectroscopy. Detection limits are chemical-specific and are reported to be between 0.001 and 1 ppm. 

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