Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering

Committee Member

Dr. Phanindra Tallapragada, Committee Chair

Committee Member

Dr. Joshua Bostwick

Committee Member

Dr. Ethan Kung

Committee Member

Dr. Xiangchun Xuan


This dissertation develops a modeling framework to address the problem of particle manipulation in low Reynolds number fluid flows. This framework combines singularity methods in low Reynolds number fluid dynamics with the theory of transport in phase space of dynamical systems. While dynamical systems theory offers tools to study the properties of geometric features in systems such as fluid flows, singularity methods enable the construction of models for low Reynolds number flows that are simple to work with and yet, preserve the essential geometric features of the flow. Hence, the combination of these techniques offers a natural framework for the study of particle transport in varied problems of the viscous/low Reynolds number flow regime. The first problem studied is that of inertial particle manipulation in microfluidic channels integrated with acoustically excited micro-bubbles. The Lagrangian Coherent Structures(LCS) of micro-bubble streaming flows serve as a guideline for placement of micro-bubbles within the channel in a manner that enhances focusing and size based separation of inertial particles. Second, the dynamics of viscous micro-rotors within a bounded domain is modeled. The influence of viscous boundary effects on the dynamics is assessed. The application of micro-rotors for the purpose of chaotic micro-mixing is explored using numerical simulations.