Measurement of Surface Tension, Viscosity, and Density at High Temperatures by Free-Fall Drop Oscillation
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INTRODUCTION
PROPERTIES of materials at high temperature are required for precise numerical modeling and to control many industrial processes. Although there have been different methods proposed in the literature for measuring thermophysical properties of liquids,[1,2] most of them are not applicable at high temperatures. For instance, the application of the popular methods for surface tension measurement (e.g., the sessile drop method) is limited not only because of the need for a container with a higher melting point to hold the molten sample but also because of the extremely high reactivity of melts with contaminations at high temperatures. As a result, in case of high melting point metals, refractories, and ceramics, containerless methods are preferred. Among the containerless methods, drop oscillation is one technique to study liquid surface rheology. This method has the advantage of noncontact measurement and requires relatively small amounts of test samples.[3] Heating materials with a high melting point, such as metals, refractories, and ceramics, is one of the challenges for the measurements of physical properties in the molten state. Since heating by pure conduction (i.e., physical contact) is not possible in containerless methods, the selection of heating sources is limited to laser beams,[4,5] electromagnetic fields,[6] induction heating,[7] or thermal plasmas.[8] There are a number of variations for the drop oscillation method; the oscillation of a drop may be studied through either a forced levitation or in a freefall.[9,10] Levitation is usually the result of an external force field applied to compensate for the gravitational acceleration. In addition to experiments under terrestrial ALA MORADIAN, Postdoctoral Fellow, and JAVAD MOSTAGHIMI, Professor, are with the Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON M5S 3G8, Canada. Contact e-mail: [email protected] Manuscript submitted August 8, 2007. Article published online March 11, 2008. 280—VOLUME 39B, APRIL 2008
conditions, levitation may be obtained in a costly microgravity environment.[11] An electromagnetic field,[12,13] acoustic force,[3] aerodynamic force,[6,14] electrostatic force,[15] or a hybrid force (such as combined electrostatic-aerodynamic field[16]) is commonly used to levitate the liquid. The relation between the surface tension and the resonance frequency of oscillation for a spherical drop was first investigated by Rayleigh.[17] The natural frequency of the oscillation for a known mass of liquid can be used to calculate surface tension based on the modes of oscillation. However, in certain cases of using levitation methods, as a consequence of inherent asymmetry of the levitation devices, there can be more than one distinct peak in the frequency spectrum of oscillations (Rayleigh frequency). In such cases, one of the peaks should be considered, while the others are discarded. For the first time, Lamb[18] and Chandrasekhar[19] included the effect of viscosity in the analysis of drop oscillation.
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