Thesis (Ph. D.)--Carleton University, 1996. / Also available in electronic format on the Internet.

Manganese is an essential alloying element in the 2nd and 3rd generation of Advanced High Strength steels (AHSS) containing 5 to 25% manganese. A combination of excellent strength and ductility makes these grades of steel attractive for the automotive industry. To produce these steels to meet metallurgical requirements the main concern for the steelmakers is to decrease the carbon concentration as low as 0.1% while suppressing the excessive manganese losses at high temperatures. Argon Oxygen Decarburization (AOD) is a promising candidate for the refining of high manganese steels. This work has studied the kinetics of decarburization and manganese losses during the argon oxygen bubbling into a wide range of iron-manganese-carbon alloys. It was shown that decreasing the initial carbon content increased the manganese loss. In the competition between manganese and carbon for oxygen, alloys with lower initial manganese concentrations consumed a higher portion of oxygen for decarburization. This behavior was not expected by thermodynamics and the results did not support the concept of the critical carbon content either. It was demonstrated that for lower range carbon (≤0.42%) alloys, the total manganese loss can be explained by considering multiple mechanisms in parallel; oxide formation (MnO) and vapor formation (Mn (g)), and formation of Manganese mist by evaporation-condensation (Mn (l)). The evaporation-condensation mechanism was proposed with the assumption that the heat generated from MnO and CO formation increases the temperature at the surface of the bubble which facilitates the evaporation of manganese at a high vapor pressure. Consequently, manganese vapor condenses as fine droplets at the lower temperature inside the bubble. Although dilution of oxygen with argon increased the efficiency of oxygen for decarburization as expected from the mechanism of the AOD process, manganese loss did not stop completely at higher argon concentrations in the gas mixture. Therefore, the bubble and melt do not fully equilibrate with respect to Mn and C. For high carbon alloys (1%), there was excess oxygen after accounting for CO and MnO formation. According to mass balance and thermodynamic calculations, and assuming manganese loss by evaporation was negligible it was shown that oxygen was distributed amongst MnO, FeO, CO, and CO2. It was demonstrated that increasing temperature resulted in the higher manganese loss as a mist and by simple evaporation due to the increased vapor pressure and less manganese loss by oxidation. Furthermore, it was found that the rate of decarburization increased with increasing temperature due to more partitioning of oxygen to carbon than manganese. In addition, it was found that the variations of depth of lance submergence did not affect the rate of decarburization or manganese loss. This means that the reactions occur within such a short time that prolonged time after the reaction is completed does not lead to a repartitioning of the species. / Thesis / Doctor of Philosophy (PhD)

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Considerable jump and slip phenomena are observed at the non-equilibrium phase interface in microflows. Hence, accurate modelling of the liquid-vapour interface transport mechanisms that matches the observations is required, e.g. in applications such as micro/nanotechnology and micro fuel cells. In the sharp interface model, the classical Navier-Stokes-Fourier (NSF) equations can be used in the liquid and vapour phases, while the interface resistivities describe the jump and slip phenomena at the interface. However, resistivities are challenging to find from the measurements, and most of the classical kinetic theories consider them as constants. One possible approach is to determine them from a model that resolves the phase interface. In order to resolve the interface and the transport processes at and in front of the interface in high resolutions, there are two ways in general, microscopic or macroscopic. The microscopic studies are based either on molecular dynamics (MD) or kinetic models, such as the Enskog-Vlasov (EV) equation. The EV equation modifies the Boltzmann equation by considering dense gas effects, such as the interaction forces between the particles and their finite size. It can be solved by the Direct Simulation Monte Carlo (DSMC) method, which considers sample particles that stand in for thousands to hundred thousands of particles and determine most likely collisions based on interaction probabilities, but it is time-consuming and costly. Here, a closed set of 26-moment equations is numerically solved to resolve the liquid-vapour interface macroscopically while considering the dense gas and phase change effects. The 26-moment set of equations is derived by Struchtrup & Frezzotti as an approximation of the EV equation using Grad's moment method. The macroscopic moment equations resolve the phase interface in a high resolution competitive to the microscopic studies. The resolved interface visualizes the interface structure and the changes of the system variables between the two phases at the interface. The 26-moment equations are solved for a one-dimensional steady-state system for non-equilibrium evaporation/condensation process. Then, solutions are used to find the jump and slip conditions at the interface, which leads to determining the interface resistivities at different interface temperatures and non-equilibrium strengths from the Linear Irreversible Thermodynamics (LIT). The interface resistivities show their dependence on the temperature of the liquid at the interface as well as the strength of the non-equilibrium process. As a result, in further studies, similar systems can be modelled using the sharp interface method with the appropriate jump conditions at the phase interface that can be found from the determined EV interface resistivities. / Graduate

In this dissertation we study free boundary problems that model the evolution of interfaces in the presence of elasticity, such as thin film profiles and material void boundaries. These problems are characterized by the competition between the elastic bulk energy and the anisotropic surface energy. First, we consider the evolution equation with curvature regularization that models the motion of a two-dimensional thin film by evaporation-condensation on a rigid substrate. The film is strained due to the mismatch between the crystalline lattices of the two materials and anisotropy is taken into account. We present the results contained in [62] where the author establishes short time existence, uniqueness and regularity of the solution using De Giorgi’s minimizing movements to exploit the L2 -gradient flow structure of the equation. This seems to be the first analytical result for the evaporation-condensation case in the presence of elasticity. Second, we consider the relaxed energy introduced in [20] that depends on admissible pairs (E, u) of sets E and functions u defined only outside of E. For dimension three this energy appears in the study of the material voids in solids, where the pairs (E, u) are interpreted as the admissible configurations that consist of void regions E in the space and of displacements u of the atoms of the crystal. We provide the precise mathematical framework that guarantees the existence of minimal energy pairs (E, u). Then, we establish that for every minimal configuration (E, u), the function u is C 1,γ loc -regular outside an essentially closed subset of E. No hypothesis of starshapedness is assumed on the voids and all the results that are contained in [18] hold true for every dimension d ≥ 2.

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