Fluctuations composition

Eisel et al, Combustion of Ammonium Perchlorate-Polyurethane Propellants. Pressure, Temperature, and Gas Phase Composition Fluctuations , AIAAJ 10 (12), 1655-61 (Engl) (1972) CA 81, 172450 (1974) 9) L. Lake... 

Sankaran, R. and Im, H.G., Dynamic flammability limits of methane-air premixed flames with mixture composition fluctuations, Proc. Combust. Inst., 29, 77, 2002. 

Three-way catalysts are used in most 1981 gasoline-fueled automobiles to lower the levels of NO, CO, and hydrocarbons in engine exhaust. These catalysts normally operate under dynamic conditions catalyst temperature increases rapidly after the engine starts (during catalyst "warmup"), and exhaust flowrate and composition fluctuate under most modes of operation. The warmup of automotive catalysts is reasonably well understood (1). The operation of three-way catalysts in the dynamic exhaust environment after warmup is complex and less well understood. 

Phases may also become unstable with regard to compositional fluctuations, and the effect of compositional fluctuations on the stability of a solution is considered in Section 5.2. This is a theme of considerable practical interest that is closely connected to spinodal decomposition, a diffusion-free decomposition not hindered by activation energy. 

If (a 3G / a 3 ) =0 0, it is possible to choose the sign of so that (-Ak s negative. Hence the equilibrium is unstable since small compositional fluctuations can have any sign. The stability criteria are summarized in Table 5.1. 

In Section 4.2, the LES composition PDF was introduced to describe the effect of residual composition fluctuations on the chemical source term. As noted there, the LES composition PDF is a conditional PDF for the composition vector given that the filtered velocity and filtered compositions are equal to U and 0, respectively. The LES composition PDF is denoted by U, 0 x, /), and a closure model is required to describe it. 

The energy increase related to a compositional fluctuation resulting in a two-phase splitting may be considered as an energy threshold of activation of the de-mixing process. The spinodal curve thus defines a kinetic limit, not a phase boundary line. 

Using coprecipitation methods with a suitable mixture of solutions described above, the resulting LDH materials are often poorly crystallized and exhibit compositional fluctuations due mainly to the difference in the values of the pH at which the precipitation of M(II)(OH)2 and M(III)(OH)3 hydroxides occurs. Consequently, the chemical formula of the final material may not reflect the composition of the solution prior to the precipitation as noted in Chapter 1. Controlling the amount of anion incorporated under such conditions is very difficult. A "chimie douce method has been proposed by Delmas et al. in an effort to overcome this problem [181,182]. The process is illustrated schematically in Fig. 8. Since the synthesis starts from a highly crystalline layered y-oxyhydroxide precursor, it was suggested that this favored the formation of very crystalline LDHs with controllable M(1I)/M(III)... 

Figure 3J2 Energy relationships between solvus and spinodal decompositions. (A) Portion of Gibbs free energy of mixing curve in zone between binodal (X ) and spinodal (X ) points. (B) Gibbs free energy variation as a consequence of compositional fluctuations around intermediate points X and X(2). ...

The Gibbs free energy difference between the system with compositional fluctuations and an analogous homogeneous system of composition Xq is given by... 

Compositional fluctuations may be represented through a Fourier expansion, and are sufficiently approximated (for our interests) by the first sinusoidal term... 

Because there is no energy barrier opposed to compositional fluctuations for compositions within the spinodal field, the decomposition mechanism is entirely a diffusional process. Unmixing effectively begins with a minimal compositional fluctuation that extends over the entire volume of the system. 

Fet us now consider an initial composition C2. We are within the two spinodal points on the Gibbs free energy coherent curve G decomposition takes place spontaneously throughout the entire phase, with modulated compositional fluctuations whose amphtudes increase as the process advances. We always obtain pigeonite plus diopside, although theoretically the orthopyroxene plus diopside paragenesis, also in this case, corresponds to the minimum energy of the system. 

Independent of the type of exsolutive process, pyroxene exolutions usually develop on the (001) and (100) planes, probably because coherence energy is minimal along the axis perpendicular to these planes (development of compositional fluctuations is maximum along the direction that minimizes the value of G cf eq. 3.212 see also Morimoto and Tokonami, 1969, for an example of calculation). 

They also note that since R(B) has a sharp maximum at B B /2 the initial composition fluctuation with wave number B wilf have the maximum growth rate. 

Detector sensitivity is one of the most important properties of the detector. The problem is to distinguish between the actual component and artifact caused by the pressure fluctuation, bubble, compositional fluctuation, etc. If the peaks are fairly large, one has no problem in distinguishing them however, the smaller the peaks, the more important that the baseline be smooth, free of noise and drift. Baseline noise is the short time variation of the baseline from a straight line. Noise is normally measured "peak-to-peak" i.e., the distance from the top of one such small peak to the bottom of the next. Noise is the factor which limits detector sensitivity. In trace analysis, the operator must be able to distinguish between noise spikes and component peaks. For qualitative purposes, signal/noise ratio is limited by 3. For quantitative purposes, signal/noise ratio should be at least 10. This ensures correct quantification of the trace amounts with less than 2% variance. The baseline should deviate as little as possible from a horizontal line. It is usually measured for a specified time, e.g., 1/2 hour or one hour and called drift. Drift usually associated to the detector heat-up in the first hour after power-on. 

We note that all the films designed by e,f and g in Fig. 12 are transparent and exhibit no phase structure when examined by TEM, but differ somewhat in the degree of mixing when studied by the fluorescence technique. In fact, it was found that Ic/Ia for film e was sHghtly but definitely larger than those of the others. For the donor-acceptor pair used in this study, the characteristic distance is 2.7-2.9 nm [106], so that composition fluctuation on this scale in the films could be detected by routine TEM observations. The failure to see the phase structure in e, therefore, may be due to a great decrease in composition fluctuation by a strong intercomponent interaction. 

---