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The molten pool shape and thermocapillary convection during melting or welding of metals or alloys are self-consistently predicted from scale analysis. Determination of the molten pool shape and transport variables is crucial due to its close relationship with the strength and properties of the fusion zone. In this work, surface tension coefficient is considered to be negative, indicating an outward surface flow, whereas high Prandtl number represents a thinner thickness of the thermal boundary layer than that of momentum boundary layer. Since Marangoni number is usually very high, the domain of scaling is divided into the hot, intermediate and cold corner regions, boundary layers on the solid-liquid interface and ahead of the melting front. The results find that the width and depth of the pool, peak and secondary surface velocity, and maximum temperatures in the hot and cold corner regions can be explicitly and separately determined as functions of working variables or Marangoni, Prandtl, Peclet, Stefan, and beam power numbers. The scaled results agree with numerical data, different combinations among scaled equations, and available experimental data.

The molten pool shape and thermocapillary convection in melting or welding of metals or alloys having negative surface tension coefficients and Prandtl number greater than unity are determined from a scale analysis. Negative surface tension coefficient indicates that the surface flow is in outward direction, while Prandtl number greater than unity represents that boundary layer thickness of conduction is less than that of momentum. Determination of the molten pool shape is crucial due to its close relationship with the strength, microstructure and properties of the fusion zone. Since Marangoni and Reynolds number are usually greater than ten thousands, transport processes can be determined by scale analysis. In this work, the molten pool is divided into the hot, intermediate and cold corner regions on the flat free surface, boundary layers on the solid-liquid interface and ahead of the melting front for analysis. The results find that the pool shape, surface speed and temperature profiles can be self-consistently evaluated as functions of Marangoni, Prandtl, Peclet, Stefan, and beam power numbers. The predictions agree with numerical computations and experimental data in the literature.

The lack of significant buoyancy effects in zero-gravity conditions poses an issue with fluid transfer in a stagnant liquid. In this thesis, the movement of a bubble or droplet in both stagnant and rotating liquids is analysed and presented numerically using computational fluid dynamics (CFD). The governing continuum conservation equations for two-phase flow are solved using the commercial software package (2011). The Volume of Fluid (VOF) method is used to track the liquid/gas interface in 2D and 3D domains. User-Defined Functions (UDFs) are employed in order to include the effect of surface tension gradient and fluid properties as a function of temperature, with a view to efficiently investigating temperature effects on the properties of the two phases. The flow is driven via Marangoni influence induced by the surface tension gradient, which in turn drives the bubble/droplet from the cold to the hot region. For stationary liquid, the results indicate that the scaled velocity of the bubble decreases with an increase in the Marangoni number, which agrees with the results of previous space experiments. An expression for predicting the scaled velocity of a bubble has been regressed based on the obtained data from the present numerical study for thermal Marangoni numbers up to 10,721. An expression for predicting the scaled velocity of a Fluorinert droplet migrating in oil has also been presented for an MaT range from 24.05 to 2771. The interactions of two droplets in thermocapillary motion have also been studied and compared with the results obtained for the isolated droplet. The results have shown that the leading droplet will not move faster than if it were isolated, as the trailing droplet has no influence on the velocity of the leading droplet. Three-dimensional results show that no bubbles broke in any of the cases observed and agglomeration could occur during thermocapillary migration for bubbles placed side by side. The results of the motion of a singular and multiple bubbles incorporating thermocapillary forces in a rotating liquid in a zero-gravity environment have been presented for the first time. When the Rossby number is 1, the effects of rotation are important. Furthermore, the deflection of the gas bubble motion increases towards the axis of rotation with a decrease in the Rossby number (Ro). Bubble population balance modelling has been investigated in normal gravity using Luo kernels for breakage and agglomeration and two different laminar kernels for zero-gravity conditions. The simulations covered a wide range of scenarios and results are presented as a bell and histogram shapes for number density and particle percentage distribution, respectively.