Determination of surface tension from the shape oscillations of an electromagnetically levitated droplet

Abstract

In the fundamental (l=2) mode, the frequency spectrum of a magnetically levitated inviscid droplet exhibits three distinct peaks. If the modes that correspond to each of these peaks is known, the surface tension of the droplet may be calculated. In experiments that make use of this principle, there is no unambiguous method of assigning mode numbers to these peaks. The dynamics of the oscillating droplet depend on the magnetic pressure on the droplet surface. Consequently, the order of the peaks in the l=2 mode oscillations is determined by the magnetic pressure distribution. In this paper, the magnetic pressure distribution on the surface of the droplet is calculated as a function of the parameters that govern the external magnetic field. The frequencies of the droplet oscillation and its static shape deformation are also expressed in terms of these same parameters. The frequencies of oscillation are used to determine the surface tension of the liquid droplet. Finally, the magnetic pressure distribution on the droplet is shown to yield the well-known ‘‘pear-like’’ shape that is assumed by liquid metal droplets in a conical levitator.

Novel Method for Surface Tension Measurement: the Drop-Bounce Method

“…The thermophysical properties of liquid metals and their oxides, such as density, surface tension, and viscosity, are significant for industrial applications of these materials and for understanding the structure and order within these liquids. Although the high melting temperatures of liquid metals pose a challenge for contact experiments, the development of levitation technologies, such as electrostatic levitation (ESL) (Paradis et al 2001;Rhim et al 1999;Ishikawa et al 2001), electromagnetic levitation (EML) (Egry et al 1995;Bayazitoglu et al 1998;Seidel 2011;Sauerland et al 1993), and aerodynamic levitation (ADL) (Kargl et al 2015;Langstaff et al 2013;Benmore and Weber 2017;Kondo et al 2019), over the past years has facilitated measurements at high temperatures without contamination. The suitable material for a specific type of levitation technique depends on the operating principle of the levitator.…”

Thermophysical properties of a highly superheated and undercooled Ni–Si alloy melt

“…[1][2][3][4][5][6][7][8][9][10] Surface tension, which is one of the most important thermophysical properties, determines the thermodynamics and hydrodynamics of the undercooled liquid and controls many processes at the surface, including the Marangoni flow that is the dominant mechanism of convection under microgravity conditions. [1][2][3][4][5][6][7][8][9][10] Surface tension, which is one of the most important thermophysical properties, determines the thermodynamics and hydrodynamics of the undercooled liquid and controls many processes at the surface, including the Marangoni flow that is the dominant mechanism of convection under microgravity conditions.…”

Three-dimensional analysis of the steady-state shape and small-amplitude oscillation of a bubble in uniform and non-uniform electric fields

“…This frequency modification is of fundamental interest and it has been studied by many investigators. A few problems discussed in previous works include those of bubble oscillation in straining flow fields (Kang & Leal 1988), drop oscillation in electric fields (Brazier-Smith et al 1971;Feng & Beard 1990Kang 1993;Trinh, Holt & Thiessen 1996), and drop oscillation in magnetic fields (Suryanarayana & Bayazitoglu 1991;Cummings & Blackburn 1991;Bayazitoglu et al 1996). The present work is also in the same category, and we are concerned with the effects of an electric field on the oscillation frequency of a bubble in a dielectric liquid.…”