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Pendular rings between solids: meniscus properties and capillary force

Published online by Cambridge University Press:  29 March 2006

F. M. Orr ,
L. E. Scriven  and
A. P. Rivas
F. M. Orr
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis
L. E. Scriven
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis
A. P. Rivas
Affiliation:
Facultad de Ingenieria Quimica, Universidad Pontificia Bolivariana, Medellin, Columbia
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Abstract

The Laplace–Young equation is solved for axisymmetric menisci, analytically in terms of elliptic integrals for all possible types of pendular rings and liquid bridges when the effect of gravity is negligible, numerically for selected other cases in order to assess gravity's effect. Meniscus shapes, mean curvatures, areas and enclosed volumes are reported, as are capillary forces. It is shown that capillary attraction may become capillary repulsion when wetting is imperfect. The special configurations of vanishing capillary force and of zero mean curvature are treated. The range of utility of the convenient ‘circle approximation’ is evaluated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 67 , Issue 4 , 25 February 1975 , pp. 723 - 742
Copyright
© 1975 Cambridge University Press

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References

Carman, P. C. 1953 Properties of capillary held liquids. J. Phys. Chern., 57, 56–68.Google Scholar
Clark, W. C., Haynes, J. M. & Mason, G. 1968 Liquid bridges between a sphere and a plane. Chern. Engng Sci., 23, 810–812.Google Scholar
Cross, N. L. & Picknett, R. G. 1963a Particle adhesion in the presence of a liquid film. In The Mechanism of Corrosion by Fuel Impurities (ed. H. R. Johnson & D. H. Littler), pp. 383–390. London: Butterworths.
Cross, N. L. & Picknett, R. G. 1963b The liquid layer between spheres and a plane surface. Trans. Faraduy Soc. 59, 846–855.Google Scholar
Defay, R. & Prigogine, I. 1966 In Surface. Tension and Absorption, pp. 217–227. Wiley.
Erle, M. A., Dyson, D. C. & Morrow, N. R. 1971 Liquid bridges between cylinders, in a torus, and between spheres. A.I.Ch.E.J., 17, 115–121.Google Scholar
Everett, D. H. 1967 Adsorption hysteresis. In The Solid-Gas Interface, vol. 2 (ed. E. A. Flood), pp. 1055–1113. Dekker.
Haines, W. B. 1925 A note on the cohesion developed by capillary forces in an ideal soil. J. Agric. Sci., 15, 529–543.Google Scholar
Haines, W. B. 1927 Studies in the physical properties of soils. J. Agric. Sci., 17, 264–290.Google Scholar
Heady, R. B. & Cahn, J. W. 1970 An analysis of the capillary forces in liquid-phase sintering of spherical particles. Met. Trans., 1, 185–189.Google Scholar
Howe, W. 1887 Rotations-Flächen welche bei vorgeschriebener Flächengrösse ein möglichst grosses oder kleines Volumen enthalten. Inaugural-Dissertation, Friedrich-Wilhelms-Universität zu Berlin.
Kingery, W. D. 1959 Densification during sintering in the presence of a liquid phase. J. Appl. Phys., 30, 301–306.Google Scholar
Mcfarlane, J. S. & Tabor, D. 1950 Adhesion of solids and the effect of surface films.
Mason, G. 1973 Formation of films from latices, a theoretical treatment. Brit. PolymerGoogle Scholar
Mason, G. & Clark, W. G. 1965a Liquid bridges between spheres. Chem. Engng Sci.Google Scholar
Mason, G. & Clark, W. C. 1965b Zero force liquid bridges between spherical particles.
Mayer, R. P. & Stowe, R. A. 1966 Mercury porosimetry: filling of toroidal void volume
Melrose, J. C. 1966 Model calculations for capillary condensation A.I.Ch.E. J. 12, 986–994.Google Scholar
Melrose, J. C. 1972 Chemical potential changes in capillary condensation. J. Colloid Interface Sci., 38, 312–46.Google Scholar
Morrow, N. R. 1971 The retention of connate water in hydrocarbon reservoirs. J. Can. Pet. Tech., 10, 38–46.Google Scholar
Plateau, J. 1864 The figures of equilibrium of a liquid mass. In The Annual Report of the Smithsonian Institution, pp. 338–369. Wasjomgtpm, D.C.
Pujado, P. R., Huh, C. & Scriven, L. E. 1972 On the attribution of an equation of capillarity to Young and Laplace. J. Colloid Interface Sci., 38, 662–663.Google Scholar
Rivas, A. P., Orr, F. M. & Scriven, L. E. 1975 Capillary attraction-and capillary repulsion. Latin Am. J. Chem. Engng. Appl. Chem., 5 (in press).Google Scholar
Rose, W. 1958 Volumes and surface areas of pendular rings. J. Appl. Phys., 29, 687–691.Google Scholar
Sheetz, D. P. 1965 Formation of films by drying of latex. J. Polymer Sci., 9, 3759–3773.Google Scholar
Vanderhoff, J. W., Tarkowski, H. L., Jenkins, M. C. & Bradford, E. B. 1966 Theor-etical consideration of the interfacial forces involved in the coalescence of latex particles. J. Macromolec. Chem., 1, 361–397.Google Scholar
Woodrow, J., Chilton, H. & Hawes, R. I. 1961 Forces between slurry particles due to surface tension. J. Nucl. Energy B, Reactor Tech. 2, 229–237.Google Scholar
Zimon, A. D. 1969 Adhesion of Dust and Powder. Plenum.