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Axisymmetric meniscus formation: a viscous-fluid model for cones

Published online by Cambridge University Press:  20 April 2006

P. T. Squire
P. T. Squire
Affiliation:
School of Physics, University of Bath, England
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Abstract

The dynamics of the formation of the axisymmetric meniscus around a cone contacting a free liquid surface are discussed. An approximate phenomenological model is set up. In the case considered, where Re [Lt ] 1 and viscosity dominates the retarding forces, this leads to a differential equation relating the height of the circle of contact to time. Solutions are derived, involving one or more unknown parameters, which describe the time dependence of the height of the circle of contact.

Experimental data, obtained from delayed flash photographs of the meniscus profiles of silicone fluid climbing over the surface of glass cones, provide general support for the model. The agreement between the predicted and observed height as a function of time is sufficiently close to justify the model as a useful description.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 129 , April 1983 , pp. 91 - 108
Copyright
© 1983 Cambridge University Press

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References

Bashforth, F. & Adams, J. C. 1883 An Attempt to Test the Theory of Capillary Action. Cambridge University Press.
Bikerman, J. J. 1970 Physical Surfaces. Physical Chemistry vol. 20. Academic.
Catchpole, J. P. & Fulford, G. 1966 Dimensionless groups Ind. Engng Chem. 58, 46–60.Google Scholar
Dussan, V., E, B. 1979 On the spreading of liquids on solid surfaces: static and dynamic contact lines. Ann. Rev. Fluid Mech. 11, 371–400.Google Scholar
Freud, B. & Freud, B. B. 1930 A theory of the ring method for the determination of surface tension J. Am. Chem. Soc. 52, 1772–1781.Google Scholar
Hansen, R. J. & Toong, T. Y. 1971 Dynamic contact angle and its relationship to forces of hydrodynamic origin J. Colloid Interface Sci. 37, 196–207.Google Scholar
Hartland, S. & Hartley, R. W. 1976 Axisymmetric Fluid–Liquid Interfaces. Elsevier.
Huh, C. & Mason, S. G. 1977 The steady movement of a liquid meniscus in a capillary tube J. Fluid Mech. 81, 401–419.Google Scholar
Huh, C. & Scriven, L. E. 1969 Shapes of axisymmetric fluid interfaces of unbounded extent J. Colloid Interface Sci. 30, 323–337.Google Scholar
Kissling, R. L. & Gross, P. H. 1970 Capillary behaviour of viscous liquids J. Phys. Chem. 74, 318–326.Google Scholar
May, A. & Woodhull, J. C. 1948 Drag coefficients of steel spheres entering water vertically J. Appl. Phys. 19, 1109–1121.Google Scholar
Miloh, T. 1981 Wave slam on a sphere penetrating a free surface J. Engng Math. 15, 221–240.Google Scholar
Moghisi, M. & Squire, P. T. 1981 An experimental investigation of the initial force of impact on a sphere striking a liquid surface J. Fluid Mech. 108, 133–146.Google Scholar
Padday, J. F. 1976 The equilibrium and stability properties of menisci: the measurement of surface tension by exact methods. Pure Appl. Chem. 48, 485–494.Google Scholar
Shiffman, M. & Spencer, D. C. 1951 The force of impact on a cone striking a water surface Communs Pure Appl. Math. 4, 379–417.Google Scholar
Watanabe, S. 1930 Resistance of impact on a water surface. Part I – Cone Inst. Phys. Chem. Res., Tokyo Sci. Papers 226, 251–267.Google Scholar