The influence of oscillation amplitude on liquid surface tension measurements with levitated metal droplets

Abstract

H. SODA, A. McLEAN, AND W. A. MILLER The levitation technique for measuring the surface tension ~, of liquid metals was developed recently by Lu and his coworkers. :'4 The technique differs from most of the conventional methods for measuring surface tension, in that it is a "dynamic" method based upon observations of droplets oscillating about their spherical equilibrium shape, as opposed to "static" methods involving liquids at rest. However, there are two apparent shortcomings in the results of this early work which have raised questions concerning the validity of t~he measurements obtained in this way, viz the results were usually found to be about 10 pct higher than normally accepted values s which have been obtained principally by static methods and secondly, the temperature coefficients of ), were generally found to be positive. There remains some doubt, therefore, concerning the applicability of dynamic methods in general, and of the levitation method in particular to the measurement of the surface tension of liquid metals at high temperatures. Experiments have been carried out recently by the present authors e to check the validity of the levitation method. The surface tension of copper was measured, and the values obtained for both ), and d),/dT were found to be in keeping with reliable data in the literature. The results were reported in the form YCu = 1390 - 0.43 (t- 1083) where surface tension is expressed in dynes/cm (raN/m) and temperature, t in ~ with the validity range of the equation extending from I000~ (in the supercooled region) to 1330~ During this investigation it was observed that the derived surface tension values depended strongly upon the amplitude of droplet oscillations. By varying both the levitation coil design and the generator frequency, it was found that large amplitude oscillations could be stabilized in copper droplets over the entire range of droplet mass, m, investigated (m = 0.25 to 1.3 g). By contrast, Fraser et al 2 have previously reported that small droplets of iron and nickel displayed higher oscillation amplitudes in relation to droplet radius than large droplets, and so they concluded that droplet mass controls the magnitude of oscillation amplitude. Since they found no variation of ), with m, they concluded that the amplitude effect could be ignored. During our study s with levitated copper droplets, the vibration amplitude was related to the droplet aspect ratio X, which is the ratio of the maximum droplet diameter to the minimum droplet diameter. Assuming that the droplets rotate about their spherical equilibrium figures as prelate spheroids,