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Inertialess swimming and propulsion of slender bodies Peng, Zhiwei


In this thesis, two problems relevant to the biological locomotion in inertialess environments are studied, one is the characteristics of undulatory locomotion in granular media, the other is the optimal flexibility of a driven microfilament in a viscous fluid. Undulatory locomotion is ubiquitous in nature and observed in different media, from the swimming of flagellated microorganisms in biological fluids, to the slithering of snakes on land, or the locomotion of sandfish lizards in sand. Despite the similarity in the undulating pattern, the swimming characteristics depend on the rheological properties of different media. Analysis of locomotion in granular materials is relatively less developed compared with fluids partially due to a lack of validated force models but recently a resistive force theory in granular media has been proposed and shown useful in studying the locomotion of a sand-swimming lizard. In this work, we employ the proposed model to investigate the swimming characteristics of a slender filament, of both finite and infinite length, undulating in a granular medium and compare the results with swimming in viscous fluids. In particular, we characterize the effects of drifting and pitching in terms of propulsion speed and efficiency for a finite sinusoidal swimmer. We also find that, similar to Lighthill's results using resistive force theory in viscous fluids, the sawtooth swimmer is the optimal waveform for propulsion speed at a given power consumption in granular media. Though it is understood that flexibility can improve the propulsive performance of a filament in a viscous fluid, the flexibility distribution that generates optimal propulsion remains largely unexplored. In this work, we employ the resistive force theory combined with the Euler-Bernoulli beam model to examine the optimal flexibility of a boundary driven filament in the small oscillation amplitude limit. We show that the optimality qualitatively depends on the boundary actuation. For large amplitude actuation, our numerics show that complex asymmetry in the waveforms emerge. The results complement our understanding of inertialess locomotion and provide insights into the effective design of locomotive systems in various environments.

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