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An external meniscus on a thin ovoidal fiber (the case of full wetting)

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Abstract

A complex shape of an external meniscus formed due to the capillary rise of a liquid along a fiber having the ovoidal profile is considered. Within the framework of the asymptotic approach and under the assumption on the complete wetting of the fiber material by the liquid, an analytical solution of the problem is derived. The particular examples of the meniscus configuration are presented in the cases in which the fiber profile has the shape of an ovoid or an ellipse.

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References

  1. A.W. Adamson and A.P. Gast, Physical Chemistry of Surfaces, Wiley, New York (1997).

    Google Scholar 

  2. D.A. White and J.A. Tallmadge, “Static Menisci on the Outside of Cylinders,” J. Fluid Mech. 23, 325 (1965).

    Article  ADS  MathSciNet  Google Scholar 

  3. M.J. Scick, Surface Characteristics of Fibers and Textiles, Marcel Dekker, New York (1977).

    Google Scholar 

  4. J.C. Maxwell, Capillary Action, Encyclopaedia Britannica (1875).

    Google Scholar 

  5. D.F. James, “The Meniscus on the Outside of a Small Circular Cylinder,” J. Fluid Mech. 63, 657 (1974).

    Article  ADS  MATH  Google Scholar 

  6. D.W. Langbein, Capillary Surfaces: Shape–Stability–Dynamics, in Particular under Weightlessness, Springer, New York (2002).

    Book  MATH  Google Scholar 

  7. L.L. Lo, “The Meniscus on a Needle–a Lesson in Matching,” J. Fluid Mech. 132, 65 (1973).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. D. Quere and J.M. di Meglio, “The Meniscus on a Fiber,” Adv. Colloid Interface Sci. 48, 141 (1994).

    Article  Google Scholar 

  9. S.Q. Zhu and D.E. Hirt, “Improving the Wettability of Deep-Groove Polypropylene Fibers by Photografting,” Textile Res. J. 79, 534 (2009).

    Article  Google Scholar 

  10. C. Duprat, C. Proti`ere, A.Y. Beebe, and H.A. Stone, “Wetting of Flexible Fibre Arrays,” Nature 482, 510 (2012).

    Article  ADS  Google Scholar 

  11. C. Pozrikidis, “Computation of Three-Dimensional Hydrostatic Menisci,” IMA J. Appl. Math. 75, 418 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  12. M.M. Alimov and K.G. Kornev, “Meniscus on a Shaped Fibre: Singularities and Hodograph Formulation,” Proc. Roy. Soc. London Ser. A 470, 20140113 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  13. R.I. Nigmatullin, Dynamics of Multiphase Media, Hemisphere Publ. Corp., New York (1990).

    MATH  Google Scholar 

  14. A. Nayfeh, Perturbation Methods, Wiley, New York (1973).

    MATH  Google Scholar 

  15. R. Courant, Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces, Interscience (1950).

    MATH  Google Scholar 

  16. M.G. Bernadiner and V.M. Entov, Hydrodynamic Theory of Anomalous Fluid Flows in Porous Media [in Russian], Nauka, Moscow (1975).

    MATH  Google Scholar 

  17. V.V. Sokolovskii, “Nonlinear Seepage Flows of Ground Waters,” Prikl. Mat. Mekh. 13, 525 (1949).

    Google Scholar 

  18. H. Lamb, Hydrodynamics, Cambridge Univ. Press, Cambridge (1932).

    MATH  Google Scholar 

  19. S.A. Khristianovich, “Motion of Underground Waters which Does not Obey the Darcy Law,” Prikl. Mat. Mekh. 4, 33 (1940).

    Google Scholar 

  20. S.A. Chaplygion, Gas Jets [in Russian], Gostekhizdat, Moscow & Leningrad (1949).

    Google Scholar 

  21. M.A. Lavrent’ev and B.V. Shabat, Methods of Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1973).

    MATH  Google Scholar 

  22. M.I. Gurevich, Theory of Jets in Ideal Fluids, Acad. Press, New York (1965).

    MATH  Google Scholar 

  23. F.D. Gakhov, Boundary Value Problems [in Russian], Fizmatgiz, Moscow (1963).

    MATH  Google Scholar 

  24. J.R. King, J.R. Ockendon, and H. Ockendon, “The Laplace–Young Equation near a Corner,” Quart. J.Mech. Appl. Math. 52, 73 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  25. M.M. Alimov and K.G. Kornev, “Singularities of Meniscus at the V-Shaped Edge,” Mech. Re. Commun. 62, 162 (2014).

    Article  Google Scholar 

  26. M.M. Alimov and K.G. Kornev, “Piercing the Water Surface with a Blade: Singularities of the Contact Line,” Phys. Fluids 28, 012102 (2016).

    Article  ADS  Google Scholar 

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Correspondence to M. M. Alimov.

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Original Russian Text © M.M. Alimov, K.G. Kornev, 2017, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2017, No. 4, pp. 97–112.

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Alimov, M.M., Kornev, K.G. An external meniscus on a thin ovoidal fiber (the case of full wetting). Fluid Dyn 52, 547–560 (2017). https://doi.org/10.1134/S0015462817040093

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  • DOI: https://doi.org/10.1134/S0015462817040093

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