Date of Award

Spring 1-1-2011

Document Type


Degree Name

Doctor of Philosophy (PhD)


Chemical & Biochemical Engineering

First Advisor

Robert H Davis

Second Advisor

Alexander Z Zinchenko

Third Advisor

Patrick D Weidman


Understanding the nature of emulsion flows through confined geometries (i.e., packed beds, porous media, and the cardiovascular system) is substantially meaningful to numerous applications, such as food and pharmaceutical manufacturing, oil recovery and fixed-bed catalytic reactors, and also to many fundamental fields of science. When the drops are comparable in size to the constriction pathways, the traditional approach of treating an emulsion flow as a continuous phase is not valid, because complex phenomena, such as pore blockage, circuitous flow pathways, and drop squeezing mechanisms brought on by constrictions need to be considered.

To address some outstanding problems in emulsion flows with drops as large as the constrictions, this dissertation presents modeling and experimental observations of buoyancy-induced drop motion through tight constrictions. It concludes determining the critical conditions, below which a drop becomes trapped in the throat of a constriction, and above which the drop passes through a constriction. The key dimensionless parameter is the Bond number, representing a ratio of gravitational and interfacial forces.

It is found that the drop velocity in the constriction throat typically decelerates a 100-fold or more, and the drop-solid gap thickness typically decreases to 0.1%–1% of the undeformed drop radius. A power-law scaling is obtained, so that the time for a drop to pass through the constriction is inversely proportional to the square of the difference between the Bond number and its critical value, when a drop becomes trapped in the constriction.

Highly-accurate critical Bond numbers and statically trapped drop shapes for axisymmetric constrictions are efficiently calculated by a special static algorithm, and for three-dimensional constrictions, similar results are presented using a different solution approach of an artificial “time-dependent” process to reach the steady state. For both the axisymmetric and three-dimensional steady-state solution methods, a desirable benefit is that prior knowledge of the drop-solid contact is nonessential. Observed for both axisymmetric and three-dimensional constrictions, the critical Bond number nearly linearly increases with an increase in the most significant factor, the undeformed drop-to-hole size ratio. The critical Bond number decreases weakly, with an increase in the constriction cross-section, due to a smoother constriction pathway. Unexpectedly, increasing the tilt angle between the gravity vector and the normal to the plane of the constriction containing the minimum hole size, decreases the critical Bond number, even though the horizontal projection of the hole is decreased.