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by |
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Department of Chemical Engineering |
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Submitted in partial fulfillment of the requirements |
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April 21, 1998 |
| The undersigned have examined the
dissertation entitled Numerical Simulation and
Experiments on Liquid Drops in a Vertical Temperature
Gradient in a Liquid of Nearly the Same Density
presented by Xiangjiang Ma, a candidate for the
degree of Doctor of Philosophy, and hereby certify
that it is worthy of acceptance. |
| ADVISOR: |
| Dr. R. Shankar Subramanian |
| EXAMINING COMMITTEE: |
| Dr. R. Balasubramaniam |
| Dr. Ruth E. Baltus |
| Dr. Robert Cole |
| Dr. Mark N. Glauser |
| Dr. John B. McLaughlin |
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Abstract |
| The thermocapillary migration of an isolated drop in a
continuous phase subjected to a uniform temperature gradient is studied
theoretically and experimentally.
The governing equations for the motion of an isolated spherical drop, along with the associated boundary conditions, are solved in discretized form using the method of finite differences. The migration velocity, as well as the velocity, temperature, and pressure fields inside and outside the drop are calculated for selected values of the governing parameters. These include the Reynolds and Marangoni numbers in each phase and relevant ratios of physical properties. The results are validated by comparison with those from available analytical and numerical solutions. Predictions from the present model for purely thermocapillary migration are found to be in good agreement with available data from experiments performed in reduced gravity for small to moderate Marangoni numbers. The behavior of liquid drops in a vertical temperature gradient in a second liquid of nearly the same density is observed. Two transparent immiscible pairs of fluids are chosen for the experiments. They are water drops in butylbenzoate and castor oil drops in 50 cS silicone oil. The conditions of the experiments are such that the Reynolds number ranges from 0.00004 to 10 while the Marangoni number varies from approximately 0.02 to 389, both being calculated using continuous phase properties. The results from the experiments are in the form of the final stationary location achieved by a drop as a function of its diameter for each temperature gradient. The results are plotted in dimensionless form and compared with predictions from a numerical solution of the governing equations. In this case, the gravitational force on the drop is included and the velocity of the drop is set equal to zero in the model. The predictions are in good agreement with the experimental data from the water-butylbenzoate system but only in qualitative accord with data from the castor oil-silicone oil system. Possible reasons for the discrepancies include variation of physical properties with temperature, buoyant convection in the cell, and effects of the container walls. |
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Acknowledgments |
| I would like to express my appreciation to my advisor,
Professor R. Shankar Subramanian for his advice, support, understanding,
and encouragement throughout this work.
I am most indebted to Dr. R. Balasubramaniam for his valuable advice on both my numerical work and experiments. I would like to thank Dr. Pericles Kondos, Dr. Claud E. Lacy, Dr. Huailiang Wei, Dr. Santosh Menon, Dr. Peer Hadland, and Mr. Lu Zhang for their many helpful suggestions and valuable discussions. I would also like to thank Dr. Ian Suni and his group for continuously providing me freshly-made doubly distilled water for my experiments. Strong support through [email protected] from the Technical Assistance Group (TAG) of NASA Center for Computational Sciences made it possible to carry out the numerical simulation. Financial support for this work was provided by NASA's Microgravity Sciences and Application Division through NASA Grant NAG3-1122 from the Lewis Research Center to Clarkson University. Also, the allocation of generous resources on the supercomputer CHARNEY (CRAY J90) at Goddard Space Flight Center and on the workstation BENARD at NASA Lewis Center is gratefully acknowledged. Special thanks are due to my family for their love and support
throughout my academic career from China to the United States. |
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Dedicated to My Parents |
| Table of Contents |
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