Doctoral Dissertations

Date of Award

12-1994

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Chemical Engineering

Major Professor

Timothy C, Scott

Committee Members

Robert M. Counce, Wayne T. Davis

Abstract

Within the chemical process industries, the behavior of drops and bubbles is a major factor in the operation of most multiphase systems such as reactors and separation equipment. Significant enhancement of such processes has been made by applying external fields to break up drops and bubbles. These external forces are applied more efficiently near resonant frequencies of the drops. Investigations of free and forced oscillations of pendant drops have been carried out to help elucidate the complex drop behavior that occurs near resonance. Experiments employing axisymmetric drops and forcing signals were analyzed with high-resolution imaging and high-speed data acquisition systems. The effects of a wide range of system variables were determined using glycerol/water solutions ranging from 0 to 100% glycerol and with dimensionless parameters, including dimensionless drop size, α, Reynolds number, Re, and gravitational Bond number, G.

Free oscillation frequency is most greatly affected by α and is relatively insensitive to Re over a large range. However, below a size-dependent value, Re has a large negative effect upon frequency, leading to aperiodic motion. Damping is significantly affected by α, Re, and oscillation amplitude. The geometry of the solid support significantly affects damping but has little effect on frequency. Excellent agreement was found in comparison of frequency and damping results with published nonlinear numerical computations.

Dimensionless resonance frequency for small-amplitude forced oscillation is essentially a linear function of the parameter a for each oscillation mode. Deformation of the drops by gravity decreases resonance frequencies, while Re has little impact on frequency. Results obtained for a liquid-liquid system indicate that viscous effects in the surrounding fluid are important in decreasing resonance frequencies. Comparison of the results to pertinent analytic theories defined limitations in their applicability; modifications to the theories rendered more accurate estimation of resonance frequencies. The results will be valuable for predicting the frequency regime needed to optimize dispersion of fluids from nozzles.

Nonlinear effects were exhibited during large-amplitude forced oscillations. The resonance frequency decreases as the forcing amplitude is increased. For forcing amplitude greater than a critical value, the frequency response results exhibit a hysteresis similar to that of a soft Duffing oscillator. Small imperfections in the experiments resulted in asymmetric oscillations at higher forcing amplitude, leading to complex behavior that may ultimately lend itself to interpretation by chaos theory.

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