Theories of transverse structures

Instability analyses do not provide good indications of fully developed transverse structures of detonations because these structures correspond to highly nonlinear phenomena. A great deal of nonlinear evolution would occur between onset of instability and attainment of a mature multidimensional detonation structure. Intersections of oblique shocks are known to constitute a central element in transverse structures of detonations [69], [72]. Oblique-shock relations are therefore relevant to the nonplanar structure. 

FIGURE 6.9. Schematic diagram of reactive triple-shock interaction. 

FIGURE 6.10. Sketch of a regular pattern of smoked-foil inscriptions on the wall of a detonation tube with a rectangular cross section. 

The spacing s varies with the initial pressure, temperature, and chemical composition in the same way that the induction length varies. Thus the ratio s/l may be taken as constant in a first approximation. The value of s is appreciably larger than perhaps s/l 10 or 30 [101]. Thus s/vq 

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The theory of bulk liquid turbulent structure control in combination with the transverse lift force (Drew et al., 1978 Lahey, 1988)... 

Four salient characteristics contributing to the originality of the theory are briefly outlined the structure, the computing ability, the way space-time is handled, and the proposal of transverse models for constitutive properties. 

Thus by computing the longitudinal structure we eliminate all information on transverse correlation of domains fix>m the scattoing pattern and reduce the problem to the case of one-dimoisional scattmng curves, which is well-known from the theory of lamellar two-phase systems. For the solution of the ID problem api opriate data analysis methods are at hand [2,8,10,15,16], As has been mentioned above, analysis of... 

The proposal that transverse sectioning of natural cellulose fibres can be used to test theories on the structure of microfibrils has been examined theoretically. It was concluded that fibre-sectioning experiments described in the literature do not disprove the folded-chain model, and it was suggested that clearly divided sections exist along the axis of the microfibril at intervals of 200 A. This cannot be explained in terms of a fringed micelle model. However, it is possible that cellulose II has a folded-chain conformation, since a single molecule of cellulose can be folded back and forth in the (101) plane to form a sheet-like structure that fits into the unit cell. A cellulose molecule can achieve a sharp U-tum in the... 

Some recent results in the theory of the interface between continuous fluid phases at equilibrium are described. Emphasis is given to the role played by the external field in determining the microscopic structure of the interface, its anomalous effect on the critical behavior of fluid interfaces in two dimensions, the success of capillary wave theory and the failure of traditional van der Waals theory to describe not only transverse but also longitudinal interfacial correlations, as well as to account for the optical reflectivity of the interface of simple fluids and binary mixtures near the critical point. 

Calculation of the dynamic parameters using a ZND wave structure model do not agree with experimental measurements, mainly because the ZND structure is unstable and is never observed experimentally except under transient conditions. This disagreement is not surprising, as numerous experimental observations show that all self-sustained detonations have a three-dimensional cell structure that comes about because reacting blast wavelets collide with each other to form a series of waves which transverse to the direction of propagation. Currently, there are no suitable theories that define this three-dimensional cell structure. 

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