Prediction of liquid metal viscosities using an adjustable hard sphere radial distribution curve
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I.
INTRODUCTION
V I S C O S I T Y can be pictured conceptually as a measure of the resistance of one layer slipping over an adjacent layer in a continuous fluid as the result of a force applied to either layer. The slipping of adjacent planes across one another has the effect of reducing the viscosity difference between the two layers. Microscopically, the equalizing of the velocities between adjacent planes is brought about by the mixing of their respective atoms and the transport of momentum to the nearest neighbors by intermolecular forces. From an understanding of viscosity, it should be possible to gain a better understanding of the structure of liquid metals. The purpose of this work is to show that the coordination number, which is related to the empty volume fraction, can be used to modify a generalized hard sphere radial curve so that it can be used to calculate the viscosity of liquid metal elements over a wide temperature range. This procedure thus provides a method of predicting liquid metal viscosities at high temperatures, where experimental difficulties are often encountered, in addition to showing that viscosity can be related to other fundamental properties. II.
D E V E L O P M E N T OF T H E M O D E L
Viscosity calculations were made for several liquid metals by using the equation derived by Born and Green,m which was derived on the basis of the pressure tensor and is expressed as 2 (m)o,57rp2 j~ g(r) du(r) where
ANTHONY L. HINES, Vice President, is with Honda of America Manufacturing, Inc., Marysvilte, OH 43040. TSAIR-WANG CHUNG, Graduate Student Chemical Engineering Department, is with the University of Missouri-Columbia, Columbia, MO 65211. Manuscript submitted October 2, 1993. METALLURGICAL AND MATERIALS TRANSACTIONS B
m = p = K= T = g(r)
mass of an atom; atom number density; Boltzmann constant; absolute temperature; = radial distribution function; u(r) = intermolecular potential; and r = radial distance from a central atom. Their equation relates viscosity to the radial distribution function (RDF) and the intermolecular potential, which must be known or approximated.
A. Radial Distribution Function The method used in this work to obtain the RDF is based on a corresponding or similar structures approach rather than the use of experimentally determined RDFs for each element. Data gathered from several sources, most notably, Hildebrand,t21 Hildebrand and S c o t t , p] Gamertsfelder,t*l Gingrich and Heaton, tSJ Paskin, trJ and Waghome et al.,t71 were used to obtain information about existing RDFs for liquid metals. Several important points were noted. Hildebrand t21 made a comparison of molecules of different sizes by plotting g(r) against r/r where d,~ is the position of the first maximum. Hildebrand showed that the RDF curves for mercury, sodium, potassium, and gallium at a temperature just above their melting points could be superimposed, except for the height of the first peak. Waghorne et aL tT] found in their work that the K factor, which is defined as K = -
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sin 01 d.-A
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