| Bubble motion induced by temperature gradients in the surrounding fluid--thermocapillary motion--can become important in cases where the usually dominant buoyancy force is negligible. For example, in materials processing in space applications this process is considered to be a potentially viable means of degassing melts before solidification. The interactions of the bubbles with one another are likely to play important roles in determining the rate of gas removal. This thesis focuses on these bubble interactions.; First, a calculation of the motion of two bubbles in a constant temperature gradient is presented for the limit of creeping flow and vanishing Peclet number. The results are valid for undeforming, spherical bubbles of arbitrary size and orientation with respect to the temperature gradient, and for separations up to near-touching. Trajectories of two bubbles as they approach one another in an infinite fluid are then determined from these instantaneous velocity calculations.; On the basis of the two bubble results, a model for the evolution of a statistically homogeneous cloud of bubbles with a given initial size distribution is formulated in terms of a discrete stochastic collection equation. Using this simple model, it is shown that the rate of coalescence in a bubble cloud is related to material properties, as well as to other parameters such as bubble volume fraction and the average temperature gradient. The nature of the initial bubble size distribution also affects the bubble cloud evolution. For example, it is found that a wider initial distribution enhances the collision rate among the bubbles. Finally, the analysis is extended to the case of a one-dimensional slab of finite thickness. For this geometry, both a steady-state temperature gradient and a transient thermal field are analyzed. The concept of bubble cloud "seeding" is also examined. This involves inserting additional bubbles into the melt at the cold end with the intent of increasing the overall rate of gas removal.; This research demonstrates that the rate at which bubbles are removed from the melt can be influenced by process design. The maximization of the rate of coalescence holds the key to optimizing bubble removal. |
