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A fast numerical procedure for steady capillary flow in open channels

Abstract

The surface evolver (SE) algorithm is a valued numerical tool for computations of complex equilibrium interfacial phenomena. In this work, an iterative procedure is implemented such that SE can be employed to predict steady-state flows along capillary channels of arbitrary cross-section. As a demonstration, a one-dimensional stream filament flow model is solved that approximates the pressure changes inside the channel. Despite its simplicity, the precision, stability, and speed of the method affirm it as an efficient and unique design tool for a variety of capillary flow problems. The procedure is ideally suited for slender column flows such as open wedge channel flows, several of which are validated herein via parabolic flight and drop tower experiments.

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References

  1. 1

    Brakke K.A.: The surface evolver. Exp. Math. 1, 141–165 (1992)

    MATH  MathSciNet  Google Scholar 

  2. 2

    Brakke, K.A.: Surface Evolver Manual. Susquehanna University, 2.26a (2005)

  3. 3

    Collicott S.H.: Example impact of nonuniform acceleration fields on liquids in spacecraft. J. Spacecr. Rockets 44, 725–727 (2007)

    Article  Google Scholar 

  4. 4

    Walkley M.A., Gaskell P.H., Jimack P.K., Kelmanson M.A., Summers J.L.: Finite element simulation of three-dimensional free-surface flow problems. J. Sci. Comput. 24, 147–162 (2005)

    MATH  Article  MathSciNet  Google Scholar 

  5. 5

    Scholle M., Aksel N.: An exact solution of visco-capillary flow in an inclined channel. ZAMP 52, 749–769 (2001)

    MATH  Article  MathSciNet  Google Scholar 

  6. 6

    Ayyaswamy P.S., Catton I., Edwards D.K.: Capillary flow in triangular grooves. J. Appl. Mech. 4, 332–336 (1974)

    Google Scholar 

  7. 7

    Matlab. Partial differential equation toolbox. The MathWorks Inc., 7.1.0.246(R16) (2005)

  8. 8

    Weislogel M.M., Lichter S.: Capillary flow in an interior corner. J. Fluid Mech. 373, 349–378 (1998)

    MATH  Article  MathSciNet  Google Scholar 

  9. 9

    Jaekle, D.E.: Propellant management device conceptual design and analysis: Vanes. In: AIAA/SAE/ASME/ASEE 27th Joint Propulsion Conference, number AIAA 91-2172, pp. 1–13, Sacramento, CA, June (1991)

  10. 10

    Rosendahl U., Ohlhoff A., Dreyer M.E.: Choked flows in open capillary channels: theory, experiment and computations. J. Fluid Mech. 518, 187–214 (2004)

    MATH  Article  Google Scholar 

  11. 11

    Haake D., Rosendahl U., Ohlhoff A., Dreyer M.E.: Flow rate limitation in open capillary channel flows. Ann. NY Acad. Sci. 1077, 443–458 (2006)

    Article  Google Scholar 

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Correspondence to M. Dreyer.

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Dedicated to Professor Wilhelm Schneider on the occasion of his 70th birthday

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Klatte, J., Haake, D., Weislogel, M.M. et al. A fast numerical procedure for steady capillary flow in open channels. Acta Mech 201, 269–276 (2008). https://doi.org/10.1007/s00707-008-0063-1

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Keywords

  • Contact Angle
  • Contact Line
  • Wedge Angle
  • Surface Evolver
  • Capillary Channel