Modeling and Scaling Electrostatic Effects in Dilute Solid-Gas Suspensions
Nieh, Sen
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https://hdl.handle.net/2142/70117
Description
Title
Modeling and Scaling Electrostatic Effects in Dilute Solid-Gas Suspensions
Author(s)
Nieh, Sen
Issue Date
1983
Department of Study
Mechanical Engineering
Discipline
Mechanical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Fluid and Plasma
Abstract
An experimental and theoretical investigation of thermocapillary convection in liquid drops is presented. The experiments were conducted on a pendant drop (approximately 1 mm in height) suspended from a thermocouple junction and heated from above. A theoretical model was developed to assist in the interpretation of the experimental data.
The experiments were conducted using Dow Corning DC-200 series silicone oils. For flow visualization, Lycopodium particles, approximately 30 (mu)m in size, were employed. A meridian section of the drop was illuminated using a vertical sheet of light of thickness (TURN) 70 (mu)m. Flow patterns were recorded using a video camera attached to a microscope. Frame-by-frame analysis of the video images was performed to make quantitative determination of velocities in the core region of the drop. The magnitude of the measured velocities was seen to increase with an increase in the temperature difference between the junction and the ambient air and/or a decrease in the viscosity of the liquid.
A mathematical model of the experimental system was formulated. A coordinate transformation was used to map the domain inside the drop to that within a hemisphere. The governing equations were solved using the method of finite differences. The predictions from the model were compared with the experimental data and found to be in excellent agreement.
In addition, several auxiliary theoretical problems were solved. The solutions for the velocity and temperature fields when a spherical drop in a space laboratory is spot-heated are presented in Section 3.2. A regular perturbation series in the Marangoni number was used to account for the convective transport of energy within the drop. The results indicate that for values of Ma (LESSTHEQ) 1, convective transport plays a negligible role in determining the temperature field on the drop surface, and hence motion within the drop.
A model was formulated to assess the role of residual accelerations in a space laboratory in influencing thermocapillary convection in a spherical drop. The model is presented in Section 3.3. The Boussinesq approximation was used to account for the variation of density with temperature. Analytical solutions were obtained for the field variables when the temperature distribution on the drop surface is known. It was demonstrated that qualitative distortion of the basic thermocapillary flow due to buoyancy effects occurs only when the dynamic Bond number is significantly greater than unity.
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