Diffuse wave

Foam rheology has been a challenging area of research of interest for the yield behavior and stick-slip flow behavior (see the review by Kraynik [229]). Recent studies by Durian and co-workers combine simulations [230] and a dynamic light scattering technique suited to turbid systems [231], diffusing wave spectroscopy (DWS), to characterize coarsening and shear-induced rearrangements in foams. The dynamics follow stick-slip behavior similar to that found in earthquake faults and friction (see Section XU-2D). 

The reaction involving chlorite and iodide ions in the presence of malonic acid, the CIMA reaction, is another that supports oscillatory behaviour in a batch system (the chlorite-iodide reaction being a classic clock system the CIMA system also shows reaction-diffusion wave behaviour similar to the BZ reaction, see section A3.14.4). The initial reactants, chlorite and iodide are rapidly consumed, producing CIO2 and I2 which subsequently play the role of reactants . If the system is assembled from these species initially, we have the CDIMA reaction. The chemistry of this oscillator is driven by the following overall processes, with the empirical rate laws as given ... 

This is observed for example with a solution containing Fe(III) ions and hydrogen peroxide Fe(II) ions formed at the electrode are converted back to Fe(III) ions by the hydrogen peroxide such behaviour results in an enhanced diffusion wave. 

Determine the half-wave potential from the current-voltage curve as described in Section 16.6 the value in 1M potassium chloride should be about — 0.60 vs S.C.E. Measure the maximum height of the diffusion wave after correction has been made for the residual current this is the diffusion current Id, and is proportional to the total concentration of cadmium ions in the solution. 

Although NMRI is a very well-suited experimental technique for quantifying emulsion properties such as velocity profiles, droplet concentration distributions and microstructural information, several alternative techniques can provide similar or complementary information to that obtained by NMRI. Two such techniques, ultrasonic spectroscopy and diffusing wave spectroscopy, can be employed in the characterization of concentrated emulsions in situ and without dilution [45],... 

Y. Hemar, D. N. Pinder, R. J. Hunter, H. Singh, P. Hebraud, D. S. Home 2003, (Monitoring of flocculation and creaming of sodium-caseinate-stabilized emulsions using diffusing-wave spectroscopy), /. Colloid Interface Sd. 264, 502. 

Y. Nicolas, M. Paques, A. Knaebel, A. Steyer, J.-P. Munch, T. B. J. Blijdenstein, G. A. van Aken 2003, (Microrheology structural evolution under static and dynamic conditions by simultaneous analysis of confocal microscopy and diffusing wave spectroscopy), Rev. Sci. Instrum. 74, 3838. 

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. 

Slow release rates and remarkable long shelf-life (months) were obtained compared to typical multiple emulsions stabilized by two short surfactants (SMO and polyoxyethylene (20) sorbitan monolaurate). Finally, the long lifetime of the emulsions allowed study via diffusing wave spectroscopy (DWS) of the interactions between the droplets and the globule surface [37],... 

Alexander, M., Dalgleish, D.G. (2007). The interaction of casein micelles with K-carra-geenan studied by diffusing wave spectroscopy. Food Hydrocolloids, 21, 128-136. 

FIG. 5.1 Multiple scattering is viewed as a random walk of the photon in diffusing wave spectroscopy (DWS). 

Chu 1991 Schmitz 1990). For example, the dynamic version of the diffusing wave spectroscopy described in Vignette V is a form of DLS, although in diffusing wave spectroscopy the method of analysis is different in view of multiple scattering. Most of the advanced developments are beyond the scope of this book. However, DLS is currently a routine laboratory technique for measuring diffusion coefficients, particle size, and particle size distributions in colloidal dispersions, and our objective in this section is to present the most essential ideas behind the method and show how they are used for particle size and size distribution measurements. 

Weitz, D. A., and Pine, D. J., Diffusing-Wave Spectroscopy. In Dynamic Light Scattering The Method and Some Applications (W. Brown, Ed.), Clarendon Press, Oxford, England, 1993. 

Fig. 11.3. The reaction-diffusion wave for cubic autocatalysis in wave-fixed coordinates. The five fronts correspond to z0 = — 4, — 2, 0, 2, and 4.

Thus, with the simple cubic autocatalytic rate law, we have been able to find an analytical expression for the time and space dependence of a steady reaction-diffusion wave and make various quantitative and qualitative comments about the behaviour of the wave in terms of the kinetic and diffusion parameters. We now turn to the apparently simpler kinetics of a quadratic autocatalysis, hoping for similar rewards. 

In the various situations we have seen before, allowing a finite decay rate for the catalyst B has had significant results. The concentrations of A and B are then decoupled and this has allowed oscillations, isolas, and mushrooms. In the present case of reaction-diffusion waves, the uncoupling is again an important step upwards in complexity, sufficiently so as to prevent any completely general form of analysis. 

Lee, C. Bailey, J. E. 1974 Diffusion waves and selectivity modifications in cyclic operation of a porous catalyst. Chem. Engng. Sci. 29,1157. 

For small amplitude (final state B1 with D < c ) the curves N and n are located as shown in Fig. 2, and solution of the equation yields a diffuse wave front (Fig. 3) whose width is proportional to the product Dt and inversely proportional to the amplitude of the wave.1... 

General Considerations. The continuity equations for a column vector of species taking place in a reaction-diffusion wave phenomenon take the form... 

Cytidine undergoes a one-step reduction in the pH range 2-7 l,37) with formation of an irreversible kinetic-diffusion wave 37). Coulometric determinations point to a 3-electron wave at pH 4.5 and a 4-electron wave at pH 7, , 84). 

Alexander, M., Corredig, M., and Dalgleish, D.G. (2006). Diffusing wave spectroscopy of gelling food systems the importance of the photon transport mean free path (I ). Food Hydrocolloids. 20, 325-331. 

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