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The shape and stability of pinned rotating annular menisci

Published online by Cambridge University Press:  26 April 2006

P. D. Weidman ,
S. Krumdieck  and
P. Rouse
P. D. Weidman
Affiliation:
School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK Permanent address: Department of Mechanical Engineering, University of Colorado, Boulder CO 80309, USA.
S. Krumdieck
Affiliation:
Department of Mechanical Engineering, University of Colarado, Boulder, CO 80309, USA
P. Rouse
Affiliation:
Department of Mechanical Engineering, University of Colarado, Boulder, CO 80309, USA
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Abstract

Laboratory measurements on the instability of axisymmetric capillary surfaces pinned to the corners of annular grooves of rectangular section rotating at constant angular velocity Ω have been conducted. In stable configurations the fluid contact lines remain pinned to the corners of the groove with contact angles θ1,2 relative to the inner and outer vertical walls. Using water as the test fluid in narrow grooves of nearly constant width, the critical frequency Ωc for instability generally decreases with increasing overfill volume ΔV and mean groove radius. Numerical integration of the describing equation gives the shape of the rotating meniscus as a function of five independent parameters. In the range of contact angles θ1, 2 < π, a comparison of experimental results with numerically computed meniscus profiles suggests three mechanisms for contact line movement based on the effective static advancing (θA) and receding (θR) contact angles for liquid pinned to a sharp corner. Measurements of critical frequencies over a wide range of overfill volumes in six different grooves are in favourable agreement with composite regime diagrams for the critical static meniscus configuration. An interesting feature of this system is the existence of a range of overfill volumes inaccessible to experiments conducted by fixing the overfill volume on a stationary disk and subsequently elevating the disk rotation until contact line movement is observed. Numerical studies showing the effects of Bond number, groove curvature and contact angle hysteresis are presented.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 219 , October 1990 , pp. 25 - 50
Copyright
© 1990 Cambridge University Press

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References

Benjamin, T. B.: 1980 Theoretical problems posed by gravity–capillary waves with edge constraints. In Trends in Applications of Pure Mathematics to Mechanics, III (ed. H. Zorski), pp. 40–58. Pitman.
Benjamin, T. B. & Graham-Eagle, J. 1985 Long gravity–capillary waves with edge constraints. IMA J. Appl. Maths 35, 91.Google Scholar
Benjamin, T. B. & Scott, J. C., 1979 Gravity–capillary waves with edge constraints. J. Fluid Mech. 92, 241.Google Scholar
Coghill, W. H. & Anderson, C. O., 1923 Bureau of Mines, Tech. Paper 262.
Concus, P.: 1968 Static menisci in a vertical right circular cylinder. J. Fluid Mech. 34, 481.Google Scholar
Davis, S. H.: 1980 Moving contact lines and rivulet instabilities. Part 1. The static rivulet. J. Fluid Mech. 98, 225.Google Scholar
Dettre, R. H. & Johnson, R. E., 1965 Contact angle hysteresis. IV Contact angle measurements on heterogeneous surfaces. J. Phys. Chem. 69, 1507.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.: 1985 On the ability of drops or bubbles to stick to non-horizontal surfaces of solids. Part 2. Small drops or bubbles having contact angles of arbitrary size. J. Fluid Mech., 151, 1.Google Scholar
Finn, R.: 1986 Equilibrium Capillary Surfaces. Springer.
Goodwin, R., Rice, D. & Middleman, S., 1988 A model for the onset of motion of a sessile liquid drop on a rotating disk. J. Colloid Interface Sci. 125, 162.Google Scholar
Heckerman, D., Garrett, S., Williams, G. A. & Weidman, P. D., 1979 Surface tension restoring forces on gravity waves in narrow channels. Phys. Fluids 22, 2270.Google Scholar
Huh, C. & Scriven, L. E., 1969 Shapes of axisymmetric fluid interfaces of unbounded extent. J. Colloid Interface Sci. 30, 323.Google Scholar
Kitchener, J. A.: 1964 Foams and free liquid films. In Recent Progress in Surface Science, vol. 1, p. 51. Academic.
Michael, D. H. & Williams, P. G., 1977 The equilibrium and stability of sessile drops. Proc. R. Soc. Lond. A 354, 127.Google Scholar
Padday, J. F.: 1971 The profiles of axially symmetric menisci. Phil. Trans. R. Soc. Lond. A 269, 265.Google Scholar
Padday, J. F. & Pitt, A. R., 1973 The stability of axisymmetric menisci. Phil. Trans. R. Soc. Lond. A 275, 489.Google Scholar
Princen, H. M. & Mason, S. G., 1965 Shape of a fluid drop at the fluid-liquid interface. II. Theory for three-phase systems. J. Colloid Sci. 20, 246.Google Scholar
Rayleigh, Lord: 1879 On the instability of jets. Proc. Lond. Math. Soc. 10, 4.Google Scholar
Scott, J. C.: 1979 The preparation of clean water surfaces for fluid mechanics. In Surface Contamination: Genesis, Detection and Control, vol. 1 (ed. K. L. Mittal), p. 447. Plenum.
Scott, J. C.: 1981 The propagation of capillary–gravity waves on a clean water surface. J. Fluid Mech. 108, 127.Google Scholar
Scott, J. C. & Benjamin, T. B., 1978 Waves in narrow channels: faster capillary waves. Nature 276, 803.Google Scholar
Weidman, P. D. & Norris, J. A., 1987 Capillary gravity waves with fixed contact lines: An approximate analysis. Physicochem. Hydrodyn. 9, 393.Google Scholar