Surface tension of melts at high temperature has significant effects on different industrial processes. In a new containerless method for surface tension measurement, an atmospheric radio-frequency inductively coupled plasma melts metallic or ceramic rods and a high-speed charge-coupled device records the drop formation caused by melting. Pendant drops produced by the melt flow are compared with the theoretical Young–Laplace (YL) profiles. Moreover, the dynamics of the melt flow is mimicked by using numerical simulations of drop injection from a nozzle. The numerical model solves the axisymmetric Navier–Stokes equations for both the melt and the surrounding gas by using the finite volume method. Since the YL equations provide theoretical pendant drop profiles based on an inviscid quasiequilibrium condition, a detailed study of the differences between experimental, numerical, and theoretical profiles demonstrates some of the hydrodynamic effects influencing the surface tension measurement methods, which are based on drop profiles. Results from this surface tension measurement method, in addition to a discussion on the hydrodynamic effects, are presented.
Issue Section:
Technical Papers
1.
Brooks
, R. F.
, Egry
, I.
, Seetharaman
, S.
, and Grant
, D.
, 2001, “Reliable Data for High Temperature Viscosity and Surface Tension: Results From a European Project
,” High Temp. - High Press.
0018-1544, 33
(6
), pp. 631
–637
.2.
Drelich
, J.
, Fang
, C.
, and White
, C. L.
, 2003, “Measurement of Interfacial Tension in Fluid-Fluid Systems
,” in Encyclopedia of Surface and Colloid Science
, Marcel Dekker
, New York
.3.
Rusanov
, A. I.
, and Prokhorov
, V. A.
, 1996, “Interfacial Tensiometry
,” in Studies of Interface Science
, D.
Mobius
, and R.
Miller
, eds., Elsevier
, Amsterdam
.4.
Andreas
, J.
, Hauser
, A.
, and Tucker
, W. B.
, 1938, “Boundary Tension by Pendant Drops
,” J. Phys. Chem.
0022-3654, 42
, pp. 1001
–1019
.5.
Tate
, T.
, 1864, “On the Magnitude of a Drop of Liquid Formed Under Different Circumstances
,” Philos. Mag.
0031-8086, 27
, pp. 176
–180
.6.
Egry
, I.
, Lohoefer
, G.
, and Jacobs
, G.
, 1995, “Surface Tension of Liquid Metals: Results From Measurement on Ground and in Space
,” Phys. Rev. Lett.
0031-9007, 75
, pp. 4043
–4046
.7.
Allen
, B. C.
, 1972, “The Surface Tension of Liquid Metals
,” in Liquid Metals: Chemistry and Physics
, S. Z.
Beer
, ed., Marcel Dekker
, New York
, pp. 161
–212
.8.
Passerone
, A.
, and Ricci
, E.
, 1998, “High Temperature Tensiometry
,” in Drops and Bubbles in Interfacial Research
, D.
Mobius
and R.
Miller
, eds, Elsevier Science
, New York
, pp. 475
–524
.9.
Peregrine
, D. H.
, Shoker
, G.
, and Symon
, A.
, 1990, “The Bifurcation of Liquid Bridges
,” J. Fluid Mech.
0022-1120, 212
, pp. 25
–39
.10.
Zhang
, X.
, and Basaran
, O. A.
, 1995, “An Experimental Study of Dynamics of Drop Formation
,” Phys. Fluids
1070-6631, 7
, pp. 1184
–1203
.11.
Clanet
, C.
, and Lasheras
, J. C.
, 1999, “Transition From Dripping to Jetting
,” J. Fluid Mech.
0022-1120, 383
, pp. 307
–326
.12.
Rayleigh
, L.
, 1899, “Investigations in Capillarity
,” Philos. Mag.
0031-8086, 48
, pp. 321
–327
.13.
Young
, T.
, 1805, “An Essay on the Cohesion of Fluids
,” Philos. Trans. R. Soc. London
0370-2316, 95
, pp. 65
–87
.14.
Laplace
, P. S.
, 1839, “Traite de Mecanique Celeste
,” in Supplement to Book 10
, Gauthier-Villars
, Paris
.15.
Bashford
, F.
, and Adams
, J. C.
, 1883, An Attempt to Test the Theory of Capillary Action
, Cambridge University Press and Deighton Bell&Co.
, Cambridge
.16.
Maze
, C.
, and Burnet
, G.
, 1969, “A Nonlinear Regression Method for Calculating Surface Tension and Contact Angle From the Shape of a Sessile Drop
,” Surf. Sci.
0039-6028, 13
, pp. 451
–470
.17.
Maze
, C.
, and Burnet
, G.
, 1971, “Modifications of a Nonlinear Regression Technique Used to Calculate Surface Tension From Sessile Drops
,” Surf. Sci.
0039-6028, 24
, pp. 335
–342
.18.
Hartland
, S.
, and Hartley
, R. W.
, 1976, Axisymmetric Fluid-Liquid Interfaces
, Elsevier Scientific
, Amsterdam
.19.
Lahooti
, S.
, Del Rio
, O. I.
, Neumann
, A. W.
, and Cheng
, P.
, 1996, “Axisymmetric Drop Shape Analysis (ADSA)
,” in Applied Surface Thermodynamics
, A. W.
Neumann
and J. K.
Spelt
, eds., Marcel Dekker
, New York
, pp. 441
–509
.20.
Hoorfar
, M.
, and Neumann
, A. W.
, 2006, “Recent Progress in Axisymmetric Drop Shape Analysis (ADSA)
,” Adv. Colloid Interface Sci.
0001-8686, 121
(1–3
), pp. 25
–49
.21.
Harkins
, W. D.
, and Brown
, F. E.
, 1919, “The Determination of Surface Tension (Free Surface Energy) and the Weight of Falling Drop
,” J. Am. Chem. Soc.
0002-7863, 41
, pp. 499
–524
.22.
Wilkinson
, M. C.
, 1972, “Extended Use of, and Comments on, the Drop-Weight (Drop-Volume) Technique for the Determination of Surface and Interfacial Tensions
,” J. Colloid Interface Sci.
0021-9797, 40
, pp. 14
–26
.23.
Garandet
, J. P.
, Vinet
, B.
, and Gros
, P.
, 1994, “Considerations on Pendant Drop Method: A New Look at Tate’s Law and Harkins’ Correction Factor
,” J. Colloid Interface Sci.
0021-9797, 165
, pp. 351
–354
.24.
Miller
, R.
, Schano
, K.-H.
, and Hofmann
, A.
, 1994, “Hydrodynamic Effects in Measurements With the Drop Volume Technique at Small Drop Times I. Surface Tensions of Pure Liquids and Mixtures
,” Colloids Surf., A
0927-7757, 92
, pp. 189
–196
.25.
Miller
, R.
, Bree
, M.
, and Fainerman
, V. B.
, 1998, “Hydrodynamic Effects in Measurements With the Drop Volume Technique at Small Drop Times III. Surface Tensions of Viscous Liquids
,” Colloids Surf., A
0927-7757, 142
, pp. 237
–242
.26.
Montaser
, A.
, and Golightly
, D. W.
, 1992, Inductively Coupled Plasmas in Analytical Atomic Spectrometry
, 2nd ed., VCH
, New York
.27.
Moradian
, A.
, and Mostaghimi
, J.
, 2005, “High Temperature Tensiometry by a Coupled Modeling and Experimental Approach
,” Proceedings of the International Thermal Spray Conference
, Basel, Switzerland
, proceedings on DVD.28.
Moradian
, A.
, and Mostaghimi
, J.
, 2005, “High Temperature Surface Tension Measurement
,” IEEE Trans. Plasma Sci.
0093-3813, 33
(2
), pp. 410
–411
.29.
Moradian
, A.
, and Mostaghimi
, J.
, 2005, “A New Surface Tension Measurement Technique for High-Melting-Point-Materials
,” Proceedings of the International Symposium Plasma Chemistry
, Toronto, Canada
, pp. 939
–940
.30.
Vinet
, B.
, Garandet
, J. P.
, Marie
, B.
, Domergue
, L.
, and Drevet
, B.
, 2004, “Surface Tension Measurements on Industrial Alloys by the Drop-Weight Method
,” Int. J. Thermophys.
0195-928X, 25
, pp. 869
–883
.31.
Peterson
, A. W.
, Kedesdy
, H.
, Keck
, P. H.
, and Schwartz
, E.
, 1958, “Surface Tension of Titanium, Zirconium, and Hafnium
,” J. Appl. Phys.
0021-8979, 29
, pp. 213
–216
.32.
Henderson
, D. C.
, and Micale
, F. J.
, 1993, “Dynamic Surface Tension Measurement with the Drop Mass Technique
,” J. Colloid Interface Sci.
0021-9797, 158
, pp. 289
–294
.33.
Mehdi-Nejad
, V.
, 2004, “Modeling Flow and Heat Transfer in Two-Fluid Interfacial Flows with Applications to Drops and Jets
,” Ph.D. thesis, University of Toronto, Canada.34.
Youngs
, D. L.
, 1984, “An Interface Tracking Method for a 3D Eulerian Hydrodynamics Code
,” AWRE Technical Report No. 44/92/35.35.
Kothe
, D. B.
, Mjolsness
, R. C.
, and Torrey
, M. D.
, 1991, “RIPPLE: A Computer Program for Incompressible Flows with Free Surfaces
,” Technical Report LA-12007-MS.36.
Brackbill
, J. U.
, Kothe
, D. B.
, and Zamach
, C.
, 1992, “A Continuum Method for Modeling Surface Tension
,” J. Comput. Phys.
0021-9991, 100
, pp. 335
–354
.37.
Francois
, M. M.
, Cummins
, S. J.
, Dendy
, E. D.
, Kothe
, D. B.
, Sicilian
, J. M.
, and Williams
, M. W.
, 2006, “A Balanced-Force Algorithm for Continuous and Sharp Interfacial Surface Tension Models Within a Volume Tracking Framework
,” J. Comput. Phys.
0021-9991, 213
(1
), pp. 141
–173
.38.
Huh
, C.
, and Reed
, R. L.
, 1983, “A Method for Estimating Interfacial Tension and Contact Angles From Sessile and Pendant Drop Shapes
,” J. Colloid Interface Sci.
0021-9797, 91
, pp. 472
–484
.39.
Leser
, M. E.
, Acquistapace
, S.
, Cagna
, A.
, Makievski
, A. V.
, and Miller
, R.
, 2005, “Limits of Oscillation Frequencies in Drop and Bubble Shape Tensiometry
,” Colloids Surf., A
0927-7757, 261
, pp. 25
–28
.40.
Miller
, R.
, 2006, Max-Planck Institute of Colloids and Interfaces, personal communication.Copyright © 2007
by American Society of Mechanical Engineers
You do not currently have access to this content.
