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On the interpretation of dynamic contact angles in capillaries

Published online by Cambridge University Press:  19 April 2006

Fred Y. Kafka  and
E. B. Dussan
Fred Y. Kafka
Affiliation:
Department of Chemical and Biochemical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19174 Present address: E. I. Du Pont De Nemairs & Company, Experimental Station-B/304, Wilmington, DE 19898.
E. B. Dussan
Affiliation:
Department of Chemical and Biochemical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19174
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Abstract

The motion of two immiscible fluids with arbitrary viscosities flowing through a capillary with an almost flat fluid-fluid interface is investigated in the limit of small capillary and Reynolds numbers. A complete description of the dynamics of the fluids is presented. It is shown that the motion of the fluid away from the moving contact line can be completely determined in terms of one material parameter, and how the capillary can be viewed as a device for measuring it. The dynamic behaviour of various contact angles, measured by others, is calculated. It is shown that they all depend on the radius of the capillary; hence, they do not represent properties of only the materials of the system.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 95 , Issue 3 , 11 December 1979 , pp. 539 - 565
Copyright
© 1979 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. 1964 Handbook of Mathematical Functions. Washington: National Bureau of Standards.
Batchelor, G. K. 1970 An Introduction to Fluid Dynamics. Cambridge University Press.
Bhattacharji, S. & Savic, P. 1965 Real and apparent non-Newtonian behaviour in viscous pipe flow of suspensions driven by a fluid piston. Proc. Heat Transfer Fluid Mech., p. 248.Google Scholar
Blake, T. D. 1968 Ph.D. thesis, Department of Physical Chemistry, University of Bristol, England.
Blake, T. D. & Haynes, 1969 Kinetics of liquid/liquid displacement. J. Colloid Interface Sci. 3, 421.Google Scholar
Dussan V., E. B. 1976 The moving contact line: the slip boundary condition. J. Fluid Mech. 77, 665.Google Scholar
Dussan, V., E. B. 1977 Immiscible liquid displacement in a capillary tube: the moving contact line. A.I.Ch.E.J. 23, 131.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.Google Scholar
Dussan V. E. B. & Davis, S. H. 1974 On the motion of a fluid-fluid interface along a solid surface. J. Fluid Mech. 65, 71.Google Scholar
Elliott, G. E. P. & Riddiford, A. C. 1967 Dynamic contact angles. I. The effect of impressed motion. J. Colloid Interface Sci. 23, 389.Google Scholar
Greenspan, H. P. 1978 On the motion of a small viscous droplet that wets a surface. J. Fluid Mech. 84, 125.Google Scholar
Hansen, R. J. & Toong, T. Y. 1971a Interface behavior as one fluid completely displaces another from a small-diameter tube. J. Colloid Interface Sci. 36, 410.Google Scholar
Hansen, R. J. & Toong, T. Y. 1971b Dynamic contact angle and its relationship to forces of hydrodynamic origin. J. Colloid Interface Sci. 37, 196.Google Scholar
Hocking, L. M. 1976 A moving fluid interface on a rough surface. J. Fluid Mech. 76, 801.Google Scholar
Hocking, L. M. 1977 A moving fluid interface. Part 2. The removal of the force singularity by a slip flow. J. Fluid Mech. 79, 209.Google Scholar
Hoffman, R. 1975 A study of the advancing interface I. Interface shape in liquid-gas systems. J. Colloid Interface Sci. 50, 228.Google Scholar
Huh, C. & Mason, S. G. 1977 The steady movement of a liquid meniscus in a capillary tube. J. Fluid Mech. 81, 401.Google Scholar
Huh, C. & Scriven, L. E. 1971 Hydrodynamic model of steady movement of a solid/liquid/ fluid contact line. J. Colloid Interface Sci. 35, 85.Google Scholar
Jiang, T. S., Oh, S. G. & Slattery, J. C. 1978 Correlation for dynamic contact angles. J. Colloid Interface Sci. In press.Google Scholar
Rose, W. & Heins, R. W. 1962 Moving interfaces and contact angle rate-dependence. J. Colloid Interface Sci. 17, 39.Google Scholar
Smith, R. C. T. 1952 The bending of a semi-infinite stip. Australian J. Sci. Res. A 5, 227.Google Scholar
Wagner, M. H. 1975 Developing flow in circular conduits: transition from plug flow to pipe flow. J. Fluid Mech. 72, 257.Google Scholar
Washburn, E. W. 1921 The dynamics of capillary flow. Physical Rev. 17, 243.Google Scholar
West, G. D. 1911–1912 On resistance to the motion of a thread of mercury in a glass tube. Proc. Roy. Soc. A 86, 20.Google Scholar
Yarnold, G. D. 1938 The motion of a mercury index in a capillary tube. Proc. Phys. Soc. London 50, 540.Google Scholar
Yoo, J. Y. & Joseph, D. D. 1978 Stokes flow in a trench between concentric cylinders. SIAM J. Appl. Math. 32.Google Scholar