Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2006. / Includes bibliographical references (leaves 128-136). Also available in electronic version.

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We observed the evolution of unstable fluid interfaces in experiments on viscous fingering, pinch-off, and bouncing jets. If we can first identify classes of universal behavior, then we can begin building a unified framework to understand nonlinear processes. We performed the first experimental test of the harmonic moments of viscous fingering patterns, grown by injecting air into a thin layer of silicone oil, which was confined between two closely spaced plates, called a Hele-Shaw cell. We observed that the predicted decay of the moments was accurate within our measurement uncertainty, which confirmed the predicted conservation of the moments for zero surface tension. With greater forcing, the air bubble will undergo a secondary tip-splitting instability, where the fingers of air fork into two or more fingers. We discovered two selection rules for the changing base width and the nearly invariant opening angle of fjords, which are the regions of oil between the fingers of air. We then compared our experiments on viscous fingering with diffusion-limited aggregation (DLA), a model of un-stable growth. We calculated that DLA and viscous fingering have the same spectrum of singularities [called f([alpha])] within measurement uncertainty. Since the spectrum is a global encapsulation of the growth dynamics and scaling properties, we say that the two processes are in the same scaling universality class. All of these results for viscous fingering are expected to apply to other physical systems which approximate Laplacian growth, a model of an interface where its growth rate is determined by the local gradient of a field [phi] obeying Laplace's equation [gradient² phi] = 0. Next we present preliminary work on the experimental test of two predictions for flows in Hele-Shaw cells: 1) soliton-like behavior of two viscous domains and 2) self-similar, universal pinch-off of an inviscid bubble in a viscous liquid. Finally, we report our observations and analysis of a liquid stream with constant viscosity (i.e. Newtonian) which rebounds from the free surface of a moving bath. The stream bounces on a thin layer of lubricating air which is replenished by the relative motion of the jet and the bath.

Study of the dynamics of strings and filaments has broad applications, for instance, macroscopic coil motion in petroleum engineering and microscopic one-armed swimmers in biological science. In this work, we study the motions of flexible strings and thin filaments in two different regimes, inertial and viscous, theoretically and experimentally. Quantitative experiments on the whirling string show that steady motion exists only when the string whirls at its natural frequencies and that whirling motions for other frequencies exhibit rich dynamics. Furthermore, three kinds of response have been observed experimentally for the planar excitation: planar steady oscillation; two-dimensional (2D) to three-dimensional (3D) transient response; 3D steady whirling motion. These phenomena repeat as the driving frequency is increased. The forced response of a string subjected to planar excitation is analyzed through a perturbation technique and multiple time scale method. The steady-state whirling motion of linear elastic filaments under self-weight with rotary excitation at one end and free at the other has been examined; specifically, the effect of bending stiffness has been investigated both theoretically and experimentally. The theoretical predictions have been compared with the experimental results for thin filaments with different bending stiffness to demonstrate the effect of bending stiffness directly. The dynamic response of thin filaments under planar excitation has also been studied experimentally. The two-dimensional dynamics of an Euler elastica in low-Reynolds number regime has been studied. Tension effects have been shown to be either comparable to or dominant over the bending contributions for the microscopic one-armed swimmers. Hence one may change the tension in situ through the externally or internally generated forces, thus changing the effective bending stiffness, and as a consequence controlling the swimming velocity and the propulsion efficiency. Finally, the low-Reynolds-number dynamics of a micro-string has been studied, in order to understand the physics underpinning eukaryotic sperm flagellar swimming. Both linear analysis of small-amplitude swimming and fully numerical simulations show that time-reversal symmetry is broken, which leads to the propulsion. Numerical studies have been performed for different boundary conditions and different forcing levels. Comparison with previous bending model illustrated that, for the same equivalent bending stiffness, the micro-string has higher propulsion efficiency with similar swimming velocity. Excellent agreement between the simulation predictions and the experimentally observed flagellar wave-forms has been obtained. With this theoretical model, observations of swimming characteristics of the sperm of different species are reconciled into a single scaling relationship, characterized by the so-called \string sperm number". Our results imply that tension plays a crucial role in flagellar elasticity and provides impetus for studying a different model underlying the physics of flagellar swimming. For example, it is possible to postulate alternate hypotheses for active force generation by the dynein motors; it also enables the formulation of a different role to the micro-filaments in general, one based on tension rather than one based on bending.

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Typescript (photocopy) / xiii, 363 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Civil Engineering, 1981