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General exotic capillary tubes

Published online by Cambridge University Press:  17 December 2019

Fei Zhang Open the ORCID record for Fei Zhang [Opens in a new window]  and
Xinping Zhou Open the ORCID record for Xinping Zhou [Opens in a new window]
Fei Zhang
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, PR China
Xinping Zhou*
Affiliation:
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China
*
†Email address for correspondence: [email protected]
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Abstract

The general exotic capillary tube is a non-uniform capillary tube which permits an entire continuum of equilibrium menisci if applying a pressure $p=-\unicode[STIX]{x1D700}z$ at the tube inlet. The shapes of general exotic capillary tubes under positive and negative loads are determined mathematically. Lowering the pressure at the tube inlet slightly from the value $p=-\unicode[STIX]{x1D700}z$ causes the tube to completely drain out, while raising the pressure slightly forces the tube to fill up, which implies that the general exotic capillary tube is sensitive to pressure. The general exotic capillary tube is also related to meniscus stability. It is found that the boundary parameters $\unicode[STIX]{x1D712}_{1}$ of general exotic cylinders with arbitrary contact angle are equal to the critical values $\unicode[STIX]{x1D712}_{1}^{\ast }$ for determining the meniscus stability. Then, a convenient alternative to solving the Jacobi equation for determining $\unicode[STIX]{x1D712}_{1}^{\ast }$ is proposed based on the ‘exotic’ property.

JFM classification

Interfacial Flows (free surface): Capillary flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 885 , 25 February 2020 , A1
Copyright
© 2019 Cambridge University Press

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References

Bostwick, J. B. & Steen, P. H. 2015 Stability of constrained capillary surfaces. Annu. Rev. Fluid Mech. 47, 539–568.CrossRefGoogle Scholar
Boucher, E. A. & Evans, M. J. B. 1975 Pendent drop profiles and related capillary phenomena. Proc. R. Soc. Lond. A 346, 349–374.CrossRefGoogle Scholar
Brakke, K. A. 1992 The surface evolver. Exp. Math. 1, 141–165.CrossRefGoogle Scholar
Callahan, M., Concus, P. & Finn, R. 1991 Energy minimizing capillary surfaces for exotic containers. In Computing Optimal Geometries (ed. Taylor, J. E.), pp. 13–15. AMS.Google Scholar
Concus, P. & Finn, R. 1989 Instability of certain capillary surfaces. Manuscr. Math. 63, 209–213.CrossRefGoogle Scholar
Concus, P. & Finn, R. 1991 Exotic containers for capillary surfaces. J. Fluid Mech. 224, 383–394.CrossRefGoogle Scholar
Concus, P., Finn, R. & Weislogel, M. 1992 Drop-tower experiments for capillary surfaces in an exotic container. AIAA J. 30, 134–137.CrossRefGoogle Scholar
Concus, P., Finn, R. & Weislogel, M. 1999 Capillary surfaces in an exotic container: results from space experiments. J. Fluid Mech. 394, 119–135.CrossRefGoogle Scholar
Finn, R. 1986 Equilibrium Capillary Surfaces. Springer.CrossRefGoogle Scholar
Finn, R. 1988 Non uniqueness and uniqueness of capillary surfaces. Manuscr. Math. 61, 347–372.CrossRefGoogle Scholar
Gillette, R. D. & Dyson, D. C. 1972 Stability of axisymmetric liquid–fluid interfaces towards general disturbances. Chem. Engng J. 3, 196–199.CrossRefGoogle Scholar
Gulliver, R. & Hildebrandt, S. 1986 Boundary configurations spanning continua of minimal surfaces. Manuscr. Math. 54, 323–347.CrossRefGoogle Scholar
Huh, C. & Scriven, L. E. 1969 Shapes of axisymmetric fluid interfaces of unbounded extent. J. Colloid Interface Sci. 30, 323–337.CrossRefGoogle Scholar
Kravchenko, V. V. & Porter, R. M. 2010 Spectral parameter power series for Sturm–Liouville problems. Math. Meth. Appl. Sci. 33 (4), 459–468.Google Scholar
Lawrence, J. D. 2013 A Catalog of Special Plane Curves. Courier Corporation.Google Scholar
Myshkis, A. D., Babskii, V. G., Kopachevskii, N. D., Slobozhanin, L. A., Tyuptsov, A. D. & Wadhwa, R. S. 1987 Low-Gravity Fluid Mechanics. Springer.CrossRefGoogle Scholar
Russo, M. J. & Steen, P. H. 1986 Instability of rotund capillary bridges to general disturbances: experiment and theory. J. Colloid Interface Sci. 113, 154–163.CrossRefGoogle Scholar
Siegel, D. 1980 Height estimates for capillary surfaces. Pacific J. Math. 88, 471–515.CrossRefGoogle Scholar
Slobozhanin, L. A. & Alexander, J. I. D. 2003 Stability diagrams for disconnected capillary surfaces. Phys. Fluids 15, 3532–3545.CrossRefGoogle Scholar
Slobozhanin, L. A., Alexander, J. I. D. & Resnick, A. H. 1997 Bifurcation of the equilibrium states of a weightless liquid bridge. Phys. Fluids 9, 1893–1905.CrossRefGoogle Scholar
Tsori, Y. 2006 Discontinuous liquid rise in capillaries with varying cross-sections. Langmuir 22, 8860–8863.CrossRefGoogle ScholarPubMed
Wang, C. Y. & Cheng, P. 1996 A multiphase mixture model for multiphase, multicomponent transport in capillary porous media – I. Model development. Intl J. Heat Mass Transfer 39, 3607–3618.CrossRefGoogle Scholar
Wente, H. C. 1999 Stability analysis for exotic containers. Dyn. Contin. Discrete Impuls. Syst. 5, 151–158.Google Scholar
Wente, H. C. 2011 Exotic capillary tubes. J. Math. Fluid Mech. 13, 355–370.CrossRefGoogle Scholar
Young, T. III 1805 An essay on the cohesion of fluids. Phil. Trans. R. Soc. Lond. 95, 65–87.Google Scholar
Zhang, F. & Zhou, X. 2020 Capillary surfaces in and around exotic cylinders with application to stability analysis. J. Fluid Mech. 882, A28.CrossRefGoogle Scholar