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The migration of an isolated gas bubble in an immiscible liquid possessing a temperature gradient is analyzed in the absence of gravity. The driving force for the bubble motion is the shear stress at the interface which is a consequence of the temperature dependence of the surface tension. The analysis is performed under conditions for which the Marangoni number is large, i.e. energy is transferred predominantly by convection. Velocity fields in the limit of both small and large Reynolds numbers are used. The thermal problem is treated by standard boundary layer theory. The outer temperature field is obtained in the vicinity of the bubble. A similarity solution is obtained for the inner temperature field. For both small and large Reynolds numbers, the asymptotic values of the scaled migration velocity of the bubble in the limit of large Marangoni numbers are calculated. The results show that the migration velocity has the same scaling for both low and large Reynolds numbers, but with a different coefficient. Higher order thermal boundary layers are analyzed for the large Reynolds number flow field and the higher order corrections to the migration velocity are obtained. Results are also presented for the momentum boundary layer and the thermal wake behind the bubble, for large Reynolds number conditions.

The thermocapillary migration of a bubble in a liquid possessing a temperature gradient is analyzed in the limit of large Reynolds and Marangoni numbers. Crespo and Manuel (1983) performed an analysis in this limit wherein energy conduction is completely neglected and obtained the bubble migration velocity using energy dissipation arguments. In the present analysis, performed in a coordinate system moving with the bubble, the velocity field in the convection term in the energy equation is approximated in an Oseen-like manner by replacing it with the velocity field far away from the bubble (i.e., the migration velocity of the bubble). Conduction is retained to satisfy the zero conductive heat flux boundary condition on the bubble surface. An approximate solution has been obtained for the Oseen-like energy equation. The bubble velocity obtained using energy dissipation considerations is in agreement with the result of Crespo and Manuel. The solution shows the thermal boundary layer and wake structure in the vicinity of the bubble. The Oseen-like analysis, however, has inherent limitations, as the flow penetrates the bubble surface. These issues are discussed and the result are compared to those in the literature.

The migration of a gas bubble under the combined action of buoyancy and a downward temperature gradient is analyzed. Inertial effects are considered negligible, but allowance is made for convective transport of energy in the model. Results from a numerical solution of the governing equations are presented and discussed.

The design of experiments in materials processing for trials on board the Shuttle are described. Thermocapillary flows will be examined as an aid to mixing in the formation of glasses. Acoustically levitated molten glass spheres will be spot heated to induce surface flow away from the hot spot to induce mixing. The surface flows are also expected to cause internal convective motion which will drive entrained gas bubbles toward the hot spot, a process also enhanced by the presence of thermal gradients. The method is called fining, and will be augmented by rotation of the sphere to cause bubble migration toward the axes of rotation to form one large bubble which is more easily removed. Centering techniques to fix the maximum centering accuracy will also be tried. Ground-based studies of bubble migration in a rotating liquid and in a temperature gradient in a liquid drop are reviewed.

A numerical procedure in which the Navier-Stokes equations are discretized using tightly coupled discretizations of pressure derivatives and continuity equations is used here to extend the range of known terminal velocities of gaseous bubbles in liquids well beyond that in previous investigations. Computations performed for Reynolds numbers up to 2000 and Marangoni numbers up to 1000 show only a modest variation of the scaled bubble velocity between 0.16 and 0.5. The bubble velocity is influenced more by the Marangoni number than by the Reynolds number.

The NASA KC-135 microgravity-environment aircraft was used to gather experimental data on the migration of bubbles in rotating liquid fields under reduced gravity conditions. The data thus obtained were compared to those of an analysis for the prediction of fluid particle trajectories in the presence of both gravitational and rotational fields at the limit of quasi-steady creeping flow. Reasonable agreement with experimental results was achieved, despite the large size of the bubbles, their close proximity to a bounding surface over significant portions of their migration time, and their rather nonspherical geometry.

The thermocapillary motion of spherical bubbles present in an unbounded liquid with a linear temperature distribution, when the Reynolds number and the Marangoni number are large is analyzed. Previous calculations of the terminal velocity performed for this parametric range did not take into complete consideration the thermal boundary layer present near the surface of the bubble. A scaling analysis is presented for this problem. The thermal boundary layer is analyzed by an integral method. The resulting terminal velocity is lower than the one previously calculated, though it is of the same order of magnitude.

Results and analysis of ground-based experiments performed to aid in designing experiments on the behavior of bubbles in a rotating liquid body on board the Shuttle in free fall are presented. Spherical shells filled with silicone oil containing a small gas bubble were spun and filmed by high speed motion picture photography. The rotation of the shell and the trajectory of the bubble motion were recorded and the film was exposed to a motion analyzer connected to a keypunch. The analyzer measured Cartesian coordinates as well as angle, frame number, and rotation rate. Optical correction equations were employed to determine the apparent bubble trajectory relative to an inertial frame of reference. An analytical model for the bubble motion was defined, yielding predictions of velocity and position at different times. Rotation of the fluid container is concluded to aid in centering the bubbles.

Two bubbles migrating along their line of centers under the influence of an imposed thermal gradient are considered in the quasi-static limit. Results are reported for representative values of the governing parameters.

Experiments in support of the Pore Formation and Mobility Investigation (PFMI) and the In-Space Soldering Investigation (ISSI) were conducted aboard the International Space Station (ISS) with the goal of promoting our fundamental understanding of melting dynamics , solidification phenomena, and defect generation during materials processing in a microgravity environment. Through the course of many experiments a number of observations, expected and unexpected, have been directly made. These include gradient-driven bubble migration, thermocapillary flow, and novel microstructural development. The experimental results are presented and found to be in good agreement with models pertinent to a microgravity environment. Based on the space station results, and noting the futility of duplicating them in Earth s unit-gravity environment, attention is drawn to the role ISS experimentslhardware can play to provide insight to potential materials processing techniques and/or repair scenarios that might arise during long duration space transport and/or on the lunar/Mars surface.

This section of the Life and Microgravity Spacelab (LMS) publication includes the following articles entitled: (1) Oscillatory Thermocapillary Instability; (2) Thermocapillary Convection in Multilayer Systems; (3) Bubble and Drop Interaction with Solidification Front; (4) A Liquid Electrohydrodynamics Experiment; (5) Boiling on Small Plate Heaters under Microgravity and a Comparison with Earth Gravity; (6) Thermocapillary Migration and Interactions of Bubbles and Drops; and (7) Nonlinear Surface Tension Driven Bubble Migration

The migration of bubbles or drops in a rotating liquid-filled sphere was observed under a variety of experimental conditions, and the trajectory, final equilibrium position, and shape were compared with results of analysis. It was found that small migrating bubbles or drops were spherical and, under the quasi-steady conditions employed, behaved in a predictable manner. Large migrating bubbles were nonspherical yet still behaved predictably except when close to the sphere wall. At low rotation rates, the final equilibrium position was offset from the rotation axis and stationary in the rotating liquid relative to a laboratory (inertial) reference frame. One of the bubble migration experiments was accomplished in the near-free-fall environment provided by the NASA KC-135 flight program. At higher rotation rates and under zero gravity conditions where the rotation axis is the final equilibrium position, the shape was reasonably predictable.

It is possible to manipulate a large, molten mass of material, such as a glass, aboard an orbital platform using acoustic fields. Attention is presently given to the problem of bubble removal from such a melt; it is desirable to make small bubbles coalesce into larger ones through floating melt rotation, to create an artificial convective field in which the bubbles will move centripetally to the axis of rotation. Computer models of bubble migration have been developed in order to define the operational conditions required aboard such experiment platforms as the Space Shuttle Orbiter.

Applications of bubble and drop technologies are discussed and include: low gravity manufacturing, containerless melts, microballoon fabrication, ink printers, laser fusion targets, generation of organic glass and metal shells, and space processing. The fluid dynamics of bubbles and drops were examined. Thermomigration, capillary flow, and interfacial tension are discussed. Techniques for drop control are presented and include drop size control and drop shape control.

A quasi-static analysis is performed for the thermocapillary motion of a bubble located inside a drop in free fall, with arbitrary axisymmetric temperature fields prescribed on the drop surface. It is shown that in the case of an axially symmetric temperature field, the bubble moves along the axis of symmetry toward the nearest warm pole. The bubble velocity as well as the velocity and temperature fields in the drop can be predicted on the basis of the quasi-static assumptions. An approximation is presented which adequately describes bubble migration velocities in the case where the ratio of the bubble radius to the drop radius is relatively small.

Experiments were conducted on bubble migration in rotating liquid bodies contained in a sphere. Experiments were initiated on the migration of a drop in a slightly less dense continuous phase contained in a rotating sphere. A refined apparatus for the study of thermocapillar flow in a glass melt was built, and data were acquired on surface velocities in the melt. Similar data also were obtained from an ambient temperature fluid model. The data were analyzed and correlated with the aid of theory. Data were obtained on flow velocities in a pendant drop heated from above. The motion in this system was driven principally by thermocapillarity. An apparatus was designed for the study of volatilization from a glass melt.

An experiment was carried out on board a Space Processing Applications Rocket with the aim of demonstrating bubble migration in molten glass due to a temperature gradient under low gravity conditions. During the flight, a sample of a sodium borate melt with a specific bubble array, contained in a platinum/fused silica cell, was subjected to a well defined temperature gradient for more than 4 minutes. Photographs taken at one second intervals during the experiment clearly show that the bubbles move toward the hot spot on the platinum heater strip. This result is consistent with the predictions of the theory of thermocapillary driven bubble motion.