A new experimental method for determining liquid density and surface tension
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I.
INTRODUCTION
T H E R E are several methods for measuring the density
of liquids, among which the method based on the Archimedes principle is one of the most effective, especially for the system with a high melting point, due to its manipulative ease and accuracy. In Bockris and co-workers t~'z] have pointed out that when using this method to high-temperature melts, the effect of surface tension on the measurement is not easily excluded for it can cause considerable errors. In order to decrease this effect, several efforts have been made in the past two decades. Detailed reviews have been given by Iida et al., |31 Crawley, t41 and Veazey and Roe. tS~These methods include the modified method, [6-9J the bisinker (or double bob) method, t6'~~ and the couple weighing method. ]16,t71 All of these are devoted to eliminating the effect of surface tension on the measurement as much as possible. However, some problems are still encountered. The modified method needs accurate data of surface tension of melts and the contact angle between melts and bob, which sometimes are not available. The bisinker method requires twice weighing with two different size bobs with identical neck diameters (Figure l(a), ~b~ = ~bz). If the masses of two bobs are designated as Gl and G2, the following formula can be used to calculate density: (G2 - W2) - (G1 -- W1)
m =
V2- V~
[1]
where Pe represents the liquid density of melt, and W~ and W2, and V~ and V2 denote the weights and volumes, respectively, of two bobs after immersion in liquid in twice experiments. The differences, (G~ - W0 and (G2 W2), in fact, represent the buoyancy exerting on two bobs. The accuracy of this method depends on the neck di-
KUO-CHIH CHOU, Professor, Department of Chemistry, and Director, on leave from Thermodynamics and Phase Diagram Lab, University of Science and Technology Beijing, is with the Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139. JIAN-HONG HU, Graduate Student, is with the Department of Chemistry, University of Science and Technology Beijing, Beijing, People's Republic of China. Manuscript submitted July 3, 1989. METALLURGICAL TRANSACTIONS B
ameters of the two bobs which are required to be identical. However, this requirement is difficult to accurately satisfy in bob processing, especially for ceramic bob processing. The couple weighing method II6,171 was developed recently and was designed with a principle similar to the bisinker method mentioned above; however, it combines two bobs into one (Figure l(b)) and measures twice in two different immersed depths of bob where the identical neck diameter is also required. Hence, the measurement error is almost the same as in the bisinker method. In summary it may be seen from the above analysis that reducing the effect of surface tension on the measured density is still a topic in the Archimedes method. This will be discussed in the remainder of the paper.
II. A GENERAL THEORETICAL ANALYSIS OF THE ARCHIMEDES METHOD Assuming that there are two different bobs (Figur
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