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Title: Rotational motion at low Reynolds number
Author: Box, Stuart James
ISNI:       0000 0004 5917 4881
Awarding Body: University of Bristol
Current Institution: University of Bristol
Date of Award: 2015
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Driven cyclic or periodic motion is a recurrent feature of many of the microscopic mechanical systems that support life. For example, fields of cilia, nano-scale hair-like structures, beat together to transport fluids though mammalian tracts. Bacteria and other micro-organisms are able to swim using similar organelles known as flagella, while "molecular motors" provide traction in muscle tissue. These mechanisms rely on the hydrodynamics and statistical mechanics of driven cyclic motion at the micro-scale. The purpose of this thesis is to investigate these principles in an abstract sense, in order to better understand these aspects of biology and to provide a framework for the design of future biomimetic devices. In particular, two aspects of rotational motion at low Reynolds number, the viscous dominated regime occupied by microorganisms and micro-machines,are investigated in this work. First, hydrodynamic synchronisation at low Reynolds number is considered. A model system is created that comprises two colloidal spheres driven along circular paths. The driving forces are applied using optical tweezers, a tool that employs a highly focussed laser beam to exert known forces on micro-particles. Each sphere is driven such that it experiences a given optical force profile, but the net force, and thus the resulting rotation rate, are free to vary. A fluid-mediated interaction force also acts on the spheres, and spontaneously induces synchronisation of their rotational motion. This system is an experimental demonstration of minimal models that were previously proposed to describe the synchronous behaviour of flagella. Synchronisation is only possible under certain conditions at low Reynolds number. In the system employed here, synchronisation can occur either via small deformations of each sphere's circular path, or by modulation of the optical driving force. Synchronisation strength is found to depend on these two mechanisms as predicted by theory. Next, the effect of thermal fluctuations on a rotating system are considered. A micro-rotor that experiences a torque when optically trapped is fabricated using photo-polymerisation. This rotor is used to experimentally demonstrate a rotational Fluctuation Theorem, which describes the probability of observing a trajectory over which the surrounding medium does work on the rotor. In the macro-world, a trajectory of this kind would be said to violate the second law of thermodynamics, but is made possible at the micro-scale because the relevant forces and energies are similar in magnitude to the thermal energy of the system. The probability of observing these trajectories is shown to decrease exponentially with the time over which the rotor is studied, as predicted by the Fluctuation Theorem.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available