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dual-**frequency**... **oscillators**... multi-**frequency**

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In this dissertation, some fundamental fluid flow problems, due to **oscillations** in spherical geometry have been studied. It consists of three parts. In the first part, the flow in the annular region between two rigid hemispheres induced by the transverse and torsional **oscillations** of the inner solid hemispherical boundary has been studied. This work was originally motivated by the need to design an experiment system in which we can effectively apply and control the shear stress and correlate it to the protein aggregation rate. In the second part, we consider combined transverse and torsional **oscillations** in the annular region between two spheres, as a fundamental development in streaming phenomenon. In the third part, we aim to mathematically model the flow around bubbles in porous media as ultrasound contrast agents in ultrasonography. However, we consider only solid particulates in the present work. We also consider the basic problem of torsional **oscillation** within a porous fluid-filled sphere. ❧ First, the flow properties of fluid between two concentric hemispheres with inner hemisphere undergoing torsional **oscillation** and transverse **oscillation** are explored in detail in Chapters 2 and 3 respectively, using perturbation method. The Womersley number |M|, which expresses **oscillation** inertia forces in relation to the shear forces is introduced to determine the flow, along with perturbation parameter ε, which is amplitude of the **oscillation** in radians, scaled with the **oscillation** **frequency**. With mathematical analysis, the analytical solutions for the velocity field, shear rate, and the flow pattern of steady streaming are obtained, which can be applied to unrestricted Womersley number |M| values. In Chapter 4, we consider the same system with combined **oscillations** with phase difference β and amplitude ratio α. The leading order velocity field and shear stress profiles, and the steady streaming are discussed not only for unrestricted |M| values, but also in the low **frequency** (|M|≪1) and high **frequency** (|M|≫1) limits. Especially in high **frequency** limit, the flow field has been divided into three regions, two boundary layers and the outer region. The streaming flow field in determined for the limiting case of the streaming Reynolds number R_s ≪1. ❧ In Chapter 5, a mathematical model of flow for fluid through porous medium in a sphere with torsional **oscillation** is described. Darcy number Da is defined to represent the relative effect of the permeability κ of the medium versus its cross-sectional area. The mathematical analysis of both the oscillatory flow and the steady streaming is performed. Finally, the flow outside a sphere in porous medium due to transverse **oscillation** is analyzed in Chapter 6. The effects of Darcy number Da and Womersley number |M| on the flow are provided.

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rotary **oscillations**

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In this thesis the thermo-mechanical properties of single–walled carbon nanotubes are investigated utilizing carbon nanotube based nanoelectromechanical **oscillators**. These resonator devices are highly sensitive to changes in tension on the carbon nanotube. In Chapters 4 the coefficient of thermal expansion of an individual single–walled carbon nanotube is measured in the range 4K - 475K. Experimental observation of this parameter has not been reported before this work and the calculations give different results depending on the models used. The observed negative thermal expansion is attributed to the free configurational space around the carbon atoms of the nanotube. When the nanotube is cooled, the entropy of the system is lowered by expanding the volume of the nanotube through various changes in the structure like pinching twisting or bending. The minimum of the coefficient of thermal expansion is measured as -4.5 ppm•K-1 at 100K. The coefficient of thermal expansion remains negative throughout the entire range. ❧ The mechanical response of carbon nanotube electromechanical **oscillators** at elevated temperatures is studied in Chapter 5. The weak interaction forces between the carbon nanotube and underlying platinum electrodes limit the performance of carbon nanotube electromechanical **oscillators**, where the devices are built as described in Chapter 3. Van der Waals bond between the carbon nanotube and the platinum electrode weaken as the temperature increases. At a critical temperature the nanotube delaminates from the surface completely and a sudden drop is observed in the mechanical resonance **frequency** of the **oscillator**. Using the results obtained, the clamping force between the carbon nanotube and the underlying platinum electrode is measured to be around 3 pN. The small value obtained for the clamping force shows that quality factor of carbon nanotube electromechanical resonators is affected by the clamping efficiency of the nanotube ends. ❧ Carbon nanotubes have unique electron ransport properties at high bias voltages. Due to their one dimensional nature, scattering of electrons by phonon are highly nonlinear. At low bias voltages (across the nanotube) phonon scattering is suppressed and the electrons exhibit ballistic transport. At higher bias voltages optical phonon scattering dominates, and subsequently nanotubes heat suddenly. In Chapter 6, the heating of nanotubes is probed using the mechanical vibrations of a carbon nanotube based nanoelectromechanical **oscillator**. Since the substrate temperature is constant the change in mechanical resonance **frequency** is attributed to the contraction of the nanotube due to its negative thermal expansion. The bias voltage, at which the mechanical resonance shows a sudden drop, corresponds to experimentally observed optical phonon emission onset voltage for single–walled carbon nanotubes.

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