Instability, quantitative approach

The substantial effect of secondary breakup of droplets on the final droplet size distributions in sprays has been reported by many researchers, particularly for overheated hydrocarbon fuel sprays. 557 A quantitative analysis of the secondary breakup process must deal with the aerodynamic effects caused by the flow around each individual, moving droplet, introducing additional difficulty in theoretical treatment. Aslanov and Shamshev 557 presented an elementary mathematical model of this highly transient phenomenon, formulated on the basis of the theory of hydrodynamic instability on the droplet-gas interface. The model and approach may be used to make estimations of the range of droplet sizes and to calculate droplet breakup in high-speed flows behind shock waves, characteristic of detonation spray processes. 

Quantitation of synthetic, conjugated bilirubin, after its direct separation from the incubation mixtures, offers the most valid approach to the determination of conjugation rates. However, for the present, such methods are unlikely to find wide application because of instability of... 

Polyether antibiotics are hydrophobic compounds that are characterized chemically by their low polarities and their instability under acidic conditions. These antibiotics can be quantitatively extracted from the primary organic extract into carbon tetrachloride (393-395). When partitioning from a sodium chloride solution into an organic solvent, high yields have been achieved using dichloromethane (396, 397), carbon tetrachloride (391, 399), and chloroform (14, 398) as extraction solvents. In a different approach, water extracts containing lasalocid residues have been purified by partitioning into the mobile phase, which was a complex mixture of tetrahydrofuran, methanol, n-hexane, and ammonia (387, 389, 390, 392). To remove lipids, sample extracts have often been partitioned with n-hexane. 

Even though many compounds discussed in the above presentation are thought to be important in meat flavor, a delicate blend of these compounds and other ingredients at the appropriate concentration is needed to synthesize acceptable flavor. In view of the possible instability of the flavor compounds themselves, precursors that supply the precise mixture of volatiles upon heating will be needed. Attempts have already been made to use this approach as judged by the numerous patented mixtures of precursors listed in the literature. More effort should be given to the quantitative aspects of meat flavor production and work must be continued on the qualitative aspects of the volatiles and the appropriate Maillard reaction precursors chosen. 

Reversed-phase HPLC is the method of choice for the quantitative analysis of procyanidins. In view of the known instability of procyanidins and the problem of developing suitable sample clean up procedures direct analysis of crude extracts is probably the best approach for quantitation. However, the separation capacity of HPLC in combination with the most commonly used UV detection at 280 nm is generally insufficient to generate useful quantitative results. Direct chromatographic determination of procyanidins in qualitative analysis has been frequently performed for example in the analysis of wine [168,252], beer [32], grape seeds [28], rhizomes of tormentil (Potentilla tormentilla) [253], Sesbania sesban... 

The disadvantages of CE compared to IC include lower sensitivity, higher concentration detection limits, and somewhat poorer reproducibility of qualitative and quantitative data owing to instability of the electroosmotic flow (EOF). IC has so far been developed more extensively. Validated procedures and computer optimization approaches are available... 

The macroscopic desaiption has been impressively successful in a number of areas, such as fluid mechanics, for studying complex flows and fluid instabilities, including the Rayleigh-Taylor, Kelvin-Helmholz, and Richtmyer-Meshkov instabilities. But it becomes inaccurate for problems in which the detailed atomistic processes affect the macroscopic behavior of the medium, or when the scale of the medium is small enough that the continuum approximation becomes questionable. Such situations are often found in studies of properties and defects of micro- or nanosystems where the continuum methods can describe only qualitative tendencies, the quality of quantitative results may be difficult to ascertain. Also, the approach has limited applicability since it does not incorporate molecular-scale enthalpic interactions between different species present in the system and requires input (viscosities. 

Fig. 13.7 (triangles), is reproduced by the theory in a rather robust fashion, whereas the actual position depends crucially on the material parameters and is very sensitive to approximations. Thus using standard MBBA parameters the ZZ instability comes out too high within the order-parameter approach, which involves an expansion up to cubic order in the pattern amplitude (Section 13.3) [24, 111]. One needs the full Galerkin computations (Section 13.3), which lead to rather good quantitative agreement (triangles and broken line in Fig. 13.8a) [112]. We conclude that higher order terms in the amplitude become important already at quite low values of .

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