Ph.D. Thesis Defense by Travis S. Laker
Thursday, April 10, 2003

(Dr. S. M. Ghiaasiaan, advisor)

"Transport of Microscopic Particles in Microchannels and Microbubbles"

Abstract

The effect of microscopic particles on hydrodynamics and heat transfer in microchannels subject to turbulent flow was investigated, and a Monte-Carlo simulation of the transport of micro particles in spherical and oscillating bubbles was performed.

The anomalous and opposing trends in published data dealing with turbulent flow friction factor and heat transfer coefficient in microchannels, and their apparent disagreement with macroscale correlations, are investigated. It is shown that the modification of turbulent eddy diffusivities, consistent with the way suspended particles may modify turbulence, can explain the observed higher-than-expected heat transfer coefficients in some data. It is therefore suggested that suspended microscopic particles may be a major contributor to the aforementioned inconsistencies and disagreements in some of the published data.

The dynamic transport and removal of suspended microscopic particles in spherical and oscillating bubbles rising in quiescent liquid pools are modeled based on a hybrid Eulerian—Monte-Carlo numerical analysis. The bubble internal circulation is obtained by assuming that it is similar to Hill’s vortex flow for non-oscillating bubbles. For oscillating bubbles, the latter solution is perturbed to account for the effect of oscillations. The transport of particles is rendered by a Monte-Carlo analysis, based on the simultaneous solution of the equations of motion for a large number of particles in the Lagrangian frame. The particle equations of motion account for sedimentation, inertia, convection, and Brownian (modeled by an appropriately defined random force) displacement mechanisms. For non-oscillating micro bubbles, parametric calculations are presented and compared with relevant Eulerian models, including the widely-used method of Fuchs (1964). The strength of bubble internal circulation is shown to be a key parameter affecting the particles. The Eulerian models predict Brownian motion well, but over predicted the inertial particle removal rates.

Vibrating spherical bubbles are assumed to undergo second-mode shape oscillations while supporting laminar internal circulation. Parametric calculations are presented to examine the effect of oscillations on particle removal rate from bubbles, and its sensitivity to particle and bubble size. The results show that oscillations enhance the particle removal rate from bubbles. The enhancement effect increases with reduction of the particle diameter, increased bubble diameter, and increased oscillation amplitude. For sub-micron particles suspended in mm-size bubbles, for example, oscillations could increase particle removal rates by orders of magnitude.