Equations and properties of flows with drifting and oscillating bubbles.

We study liquid flows with many small spherical gas bubbles. Heat transfer, surface tension and gas mass are neglected. Viscosity and gravity are added in the second part of the dissertation. The bubbles have two basic motions: radial oscillation and drifting. We first consider flows with a finite number of bubbles. We derive the velocity potential as a converging series using a method similar to Schwartz alternating method. Kinetic energy and potential energy are then calculated. The variational principle is applied and the Euler-Lagrange equations give the exact equations of motion. Based on these equations, we derive effective equations treating the flows as continuum. In the second part of this dissertation, viscosity and gravity are added to consideration. Void wave speeds are calculated, and the result is in good agreement with experimental data. The cause of discrepancy between experiments (no bubble clustering) and numerical simulations (bubble clustering found) is explained. We also prove the correct formula for the drag force on each bubble.Ph.D.Applied SciencesMathematicsMechanicsPlasma physicsPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/132272/2/9959885.pd