DOI: 10.1017/s0022112079001592. On the interpretation of dynamic contact angles in capillaries

On the interpretation of dynamic contact angles in capillaries

10.1017/s0022112079001592

Crossref journal-article

Cambridge University Press (CUP)

Journal of Fluid Mechanics (56)

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.

Bibliography

Kafka, F. Y., & Dussan, E. B. (1979). On the interpretation of dynamic contact angles in capillaries. Journal of Fluid Mechanics, 95(3), 539â565.

Authors 2

Fred Y. Kafka (first)
E. B. Dussan (additional)

References 26 Referenced 76

Rose, W. & Heins, R. W. 1962 Moving interfaces and contact angle rate-dependence.J. Colloid Interface Sci. 17,39. (10.1016/0095-8522(62)90074-0)
Hocking, L. M. 1976 A moving fluid interface on a rough surface.J. Fluid Mech. 76,801. (10.1017/S0022112076000906)
West, G. D. 1911–1912 On resistance to the motion of a thread of mercury in a glass tube.Proc. Roy. Soc. A86,20. (10.1098/rspa.1911.0076)
Abramowitz, M. & Stegun, I. 1964 Handbook of Mathematical Functions.Washington:National Bureau of Standards.
Washburn, E. W. 1921 The dynamics of capillary flow.Physical Rev. 17,243. (10.1103/PhysRev.17.273)
Huh, C. & Scriven, L. E. 1971 Hydrodynamic model of steady movement of a solid/liquid/ fluid contact line.J. Colloid Interface Sci. 35,85. (10.1016/0021-9797(71)90188-3)
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. (10.1017/S0022112077000123)
Dussan V., E. B. 1976 The moving contact line: the slip boundary condition.J. Fluid Mech. 77,665. (10.1017/S0022112076002838)
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. (10.1017/S0022112074001261)
Elliott, G. E. P. & Riddiford, A. C. 1967 Dynamic contact angles. I. The effect of impressed motion.J. Colloid Interface Sci. 23,389. (10.1016/0021-9797(67)90183-X)
Hoffman, R. 1975 A study of the advancing interface I. Interface shape in liquid-gas systems.J. Colloid Interface Sci. 50,228. (10.1016/0021-9797(75)90225-8)
Greenspan, H. P. 1978 On the motion of a small viscous droplet that wets a surface.J. Fluid Mech. 84,125. (10.1017/S0022112078000075)
Yarnold, G. D. 1938 The motion of a mercury index in a capillary tube.Proc. Phys. Soc. London 50,540. (10.1088/0959-5309/50/4/307)
Dussan, V. , E. B. 1977 Immiscible liquid displacement in a capillary tube: the moving contact line.A.I.Ch.E.J. 23,131. (10.1002/aic.690230122)
Hansen, R. J. & Toong, T. Y. 1971b Dynamic contact angle and its relationship to forces of hydrodynamic origin.J. Colloid Interface Sci. 37,196. (10.1016/0021-9797(71)90280-3)
Yoo, J. Y. & Joseph, D. D. 1978 Stokes flow in a trench between concentric cylinders.SIAM J. Appl. Math. 32. (10.1137/0134022)
Blake, T. D. 1968 Ph.D. thesis,Department of Physical Chemistry, University of Bristol, England.
Huh, C. & Mason, S. G. 1977 The steady movement of a liquid meniscus in a capillary tube.J. Fluid Mech. 81,401. (10.1017/S0022112077002134)
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. (10.1016/0021-9797(71)90014-2)
Wagner, M. H. 1975 Developing flow in circular conduits: transition from plug flow to pipe flow.J. Fluid Mech. 72,257. (10.1017/S0022112075003333)
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.
Dussan V., E. B. 1979 On the spreading of liquids on solid surfaces: static and dynamic contact lines.Ann. Rev. Fluid Mech. 11,371. (10.1146/annurev.fl.11.010179.002103)
Jiang, T. S. , Oh, S. G. & Slattery, J. C. 1978 Correlation for dynamic contact angles.J. Colloid Interface Sci. In press.
Blake, T. D. & Haynes ,1969 Kinetics of liquid/liquid displacement.J. Colloid Interface Sci. 3,421. (10.1016/0021-9797(69)90411-1)
Smith, R. C. T. 1952 The bending of a semi-infinite stip.Australian J. Sci. Res. A5,227. (10.1071/CH9520227)
Batchelor, G. K. 1970 An Introduction to Fluid Dynamics .Cambridge University Press.

Dates

Type	When
Created	19 years, 4 months ago (April 19, 2006, 10:11 a.m.)
Deposited	2 months, 2 weeks ago (June 20, 2025, 10:09 p.m.)
Indexed	1 month, 1 week ago (July 25, 2025, 5:56 a.m.)
Issued	45 years, 8 months ago (Dec. 11, 1979)
Published	45 years, 8 months ago (Dec. 11, 1979)
Published Online	19 years, 4 months ago (April 19, 2006)
Published Print	45 years, 8 months ago (Dec. 11, 1979)

Funders 0

None

BibTeX

@article{Kafka_1979, title={On the interpretation of dynamic contact angles in capillaries}, volume={95}, ISSN={1469-7645}, url={http://dx.doi.org/10.1017/s0022112079001592}, DOI={10.1017/s0022112079001592}, number={3}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press (CUP)}, author={Kafka, Fred Y. and Dussan, E. B.}, year={1979}, month=dec, pages={539–565} }

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