Dimensionless Analysis and Numerical Modeling of Rebalancing Phenomena During Levitation

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ELECTROMAGNETIC levitation (EML) is a contactless process which avoids contamination from the crucible and is very useful in producing high-purity materials. The non-crucible technique can provide the ability of massive undercooling, and has immense significance to materials science research.[1,2] In material science, EML experiments were proposed to observe unique phenomena including solidification front speed, nucleation statistics, and phase selection and morphology directly by using high-speed cameras and other additional equipments.[3] Surface properties of materials including specific heat, emissivity, thermal expansion, mass density, thermal diffusivity, electrical resistivity, thermal conductivity, surface tension, and viscosity were measured by recording the deformation and oscillation frequency of levitated droplets.[4,5] In addition, nanomaterials were manipulated with modified EML systems like Electromagnetic Levitational Gas Condensation (ELGC) and Flow Levitated (FL) system.[6,7] In materials physics, fundamental research related to reactions between different gas-fluid systems were investigated by LEI GAO, Ph.D. Candidate, is with the Faculty of Metallurgical and Energy Engineering, State Key Laboratory of Complex NonFerrous Metal Resources Clean Utilization, Kunming University of Science and Technology, 650093, Kunming, China, and also Visiting Student with the Department of Materials Science and Engineering, Process Metallurgy and Modeling Group (PM2G), University of Toronto, Toronto, ON, M5S 3E4, Canada. ZHE SHI, Professor, is with the Faculty of Metallurgical and Energy Engineering, State Key Laboratory of Complex Non-Ferrous Metal Resources Clean Utilization, Kunming University of Science and Technology. DONGHUI LI, Research Associate, ALEXANDER MCLEAN, Professor, and KINNOR CHATTOPADHYAY, Assistant Professor, are with the Department of Materials Science and Engineering, Process Metallurgy and Modeling group (PM2G), University of Toronto. Contact E-mail: kinnor. [email protected] Manuscript submitted December 13, 2015. Article published online February 18, 2016. METALLURGICAL AND MATERIALS TRANSACTIONS B

EML as well. EML experiments were set up to investigate the equilibrium reactions ([N] fi N2) in the gas-liquid systems at high temperatures.[8,9] The solubility of nitrogen in liquid iron, chromium, nickel, cobalt, vanadium, and iron alloys was investigated under various pressures, and temperature ranges without crucible contamination. This contactless method was also used to investigate alloy refinement on gas-liquid interface at high temperatures.[10,11] All these valuable research had different EML system designs, and presented a requirement for stable levitation systems.[12] Since the levitation process is opaque and complicated, the most effective way to investigate the levitated droplet is numerical modeling. With logical assumptions and virtual physical models, numerical modeling provides the direct prediction of the levitation process and already proved to be helpful.[13] To the autho