Abstract.It is well known that the classical three-shock theory of yon Neumann (1943) does not adequately describe the configuration of the shocks close to the triple-point of a Mach reflection of an incident shock with a Mach number less than about 1.5. The assumptions on which the threeshock theory is based have been examined and several of them are shown to be invalid. The assumption that may be of most significance is that the normal components of the flows behind the reflected and the Mach stem shocks are parallel. Dropping this assumption removes an essential equation in the three-shock solution. An alternative assumption, based on experimental observation, is that there is an approximate linear relationship between the pressure behind the reflected shock and the triple-point trajectory angle. This assumption permits a revised three-shock solution which gives results that are in agreement with experimental observations of reflections of incident shocks with Mach numbers between 1.l. and 1.5.
The governing equations describing the propagation of a moderate planar normal shock wave into a homogeneous dust-gas suspension were formulated and solved numerically using the flux-corrected transport (FCT) technique. The numerically predicted attenuation of the shock wave was compared with the experimental results of Sommerfeld. Good agreement was obtained. It was found that the attenuation of moderate normal planar shock waves propagating into dusty gases with relatively high loading ratios of solid particles can be described by a general attenuation law.
The four distinct stages of silicon wafer processing which are relevant to features such as trenches, vias, and topology are: (1) feature wetting, (2) chemical transport into and (3) out of the feature, and (4) feature drying. The present investigation is focused on hydrophilic surfaces. The time scales on which the mechanisms dominating these stages occur have been established. These time scales, while different, are nevertheless significantly shorter than the process time scale. In addition to that, the drying stage is analyzed under “worst case scenario” assuming that all the water in the feature evaporates within the feature leaving a solid silica particle. It is shown that this particle is several orders of magnitude smaller than a particle whose size may have a detrimental effect on the device. The findings exemplify the advantages of spray technology by demonstrating the importance of (i) fresh liquid at the feature top and (ii) rapid exchange of chemicals.
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