The harmonic excitation of a cylindrical bubble pinned to a plane surface: flow field and oscillation dynamics

This work aims to describe the response of a hemicylindrical gas bubble pinned to rigid substrate to an imposed oscillatory far field pressure, and subsequently describe the resulting steady flow that results in the fluid in the exterior of such a bubble. We first derive an analytical expression for the allowable shape oscillations of a two-dimensional bubble pinned to a wall, in the limit of a thin oscillatory boundary layer, based on the boundary conditions at the bubble surface and at the wall. We show that the shape of the bubble oscillations must depend on the Stokes boundary layer thickness, both close to and away from the wall. We discuss also the implications of the oscillatory flow on the steady streaming. We show that in order to properly describe the steady streaming, the flow must be resolved to obey simultaneously the correct slip velocity at the wall and the correct stresses at the bubble surface, both of which are specified by the exact shape of the bubble. We evaluate the steady streaming flow by means of an eigenfunction expansion, and compare the results to experimental observations. Finally, we examine the dynamics of a pinned bubble in response to an imposed oscillatory pressure by a balance of dynamic stresses across the interface. We propose a mechanism by which surface modes may be linearly coupled to the volume oscillations of a pinned bubble, which is otherwise absent for a bubble oscillating in bulk fluid. We compare the frequency responses of the oscillation mode amplitudes and phases to experimental data.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Theoretical & Applied Mechans

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2012

Author dc:creator

• Rallabandi, Venkatarama Bhargav

Contributors dc:contributor

• Hilgenfeldt, Sascha

• Bubble
• Oscillation
• Streaming
• Viscosity
• Wall streaming
• Pinning
• Boundary layer
• Frequency response
• Surface mode
• Flow
• Stokes

Statement dc:rights

• Copyright 2012 Venkatarama Bhargav Rallabandi

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/31192

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/31192