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Acoustic singularities in interfacial fluid dynamics
- Author / Creator
- Habibi Khoshmehr, Hamed
Formation of singularities in physical phenomena has always fascinated scientists and stimulated both development of mathematical theories accounting for observations and further experimental scrutiny of the governing physics with the goal to resolve the singular behavior. The underlying theme of this Dissertation is to unify the appearance of cavitation phenomena in an impulse-driven drop sitting on a membrane and of folds on a retracting soap film, studied here both experimentally and theoretically, under the umbrella of geometric acoustics and singularity theories. A fundamental difference between wave propagation in two and three dimensions proved to be instrumental in elucidating the phenomena at hand.
The Dissertation consists of two parts. In the first part, we explore impulse-driven drop phenomena. Drop deformation and disintegration regimes have been studied in many contexts ranging from an impact on a solid surface or a liquid layer of varying thickness to a liquid drop suspended in air and hit by a propagating aerodynamic shock wave. As a counterpart, deformation and disintegration of an initially static drop of controlled shape and size sitting on an impulsively driven stiff membrane are explored here experimentally. A significant amount of collected experimental data is used here to map the possible drop morphological changes along with the transitions between them. In order to elucidate the effects of impulse intensity, viscosity, surface tension, and wetting, we measured the crown height and radius in the drop deformation regimes, as well as the drop detachment and breakup times along with probability density functions of the secondary droplets in the drop disintegration regimes. With the goal to convey the physical mechanisms behind these transient responses, the observations are interpreted with phenomenological models, scalings, and estimates highlighting the rich multiscale physics of the impulse-driven drop phenomena. To provide a theoretical background for the cavitation phenomena responsible for the most energetic regimes of drop disintegration, we will explore the behavior of the pressure field near the most singular region -- the cusp -- and then near the caustic with the goal to demonstrate qualitatively that the pressure field develops significant amplitudes capable of leading to cavitation as observed experimentally.
In the second part, we will study the acoustic singularities -- the folds -- on soap films. Soap films have been not only the object of children's play, but also the subject of scientific research since the time of Leonardo Da Vinci. Earlier systematic experimental studies of bursting soap films using high-speed flash photography revealed a precursor wave preceding the expanding hole, with a disturbed region of shrinking film material in between. In 1969 Mysels, famous for his work on soap films, referred to this wave and the disturbed region as the
shock wave'' and theaureole'', respectively. These observations have overturned some misconceptions regarding the bursting process in earlier theoretical and experimental works, which concluded that a rolled up rim collected all of the disappearing film, leaving the rest of the film undisturbed. Also in 1969, Frankel and coworkers qualitatively interpreted this as a shock wave in the surfactant film and showed that any significant aureole preceding the rim of the expanding hole in a punctured soap film is related to large changes in surface tension as the film shrinks and thickens. In this part of the Dissertation, we will report and interpret new phenomena associated with the aureole and accidentally discovered in our laboratory. On the theoretical side, first we will use the basics of geometric acoustics to deduce qualitatively the behavior of acoustic waves on the soap film and to explain the origin of folds along the diagonal of a collapsing soap film. Given the experimental observation that there is an areola -- a wave preceding the retracting soap film edge -- we will revisit the classical theory in order to develop proper equations governing the velocity and thickness of the collapsing soap film, since these variables are crucial for the proper interpretation of the wave propagation superimposed on the evolving in time base state, which will lead to a succinct understanding of the origin of the observed folds.
- Graduation date
- Fall 2020
- Type of Item
- Doctor of Philosophy
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