Capillary driven flow along interior corners formed by planar walls of varying wettability

  • M. M. Weislogel
  • C. L. Nardin


Closed-form analytic solutions useful for the design of capillary flows in a variety of containers possessing interior corners were recently collected and reviewed. Low-g drop tower and aircraft experiments performed at NASA to date show excellent agreement between theory and experiment for perfectly wetting fluids. The analytical expressions are general in terms of contact angle, but do not account for variations in contact angle between the various surfaces within the system. Such conditions may be desirable for capillary containment or to compute the behavior of capillary corner flows in containers consisting of different materials with widely varying wetting characteristics. A simple coordinate rotation is employed to recast the governing system of equations for flows in containers with interior corners with differing contact angles on the faces of the corner. The result is that a large number of capillary driven corner flows may be predicted with only slightly modified geometric functions dependent on corner angle and the two (or more) contact angles of the system. A numerical solution is employed to verify the new problem formulation. The benchmarked computations support the use of the existing theoretical approach to geometries with variable wettability. Simple experiments may be performed to confirm the theoretical findings. Favorable agreement between such experiments and the present theory may argue well for the extension of the analytic results to predict fluid performance in future large length scale capillary fluid systems for spacecraft as well as for small scale capillary systems on Earth.


Contact Angle Capillary Flow Planar Wall Vary Wettability Rectangular Duct 

12. References

  1. 1.
    Weislogel, M. M.: Some Analytical Tools for Fluids Management in Space: Isothermal Capillary Flows Along Interior Corners. Adv. Space Res., vol. 32, No. 2, pp. 163–170, (2003).CrossRefGoogle Scholar
  2. 2.
    Jaekle, D. E. Jr.: Propellant Management Device Conceptual Design and Analysis: Vanes. AIAA-SAE-ASME-ASEE 27th Jt. Propl. Conf., AIAA-91-2172, Sacramento, CA, (June 1991).Google Scholar
  3. 3.
    Chato, D. J., and Martin T. A.: Vented Tank Resupply Experiment-flight test results, 33rd AIAA-ASME-SAE-ASEE Joint Propulsion Conference, AIAA-97-2815, July 6–9, Seattle, (1997).Google Scholar
  4. 4.
    Weislogel, M. M., and Collicott S. H.: Analysis of Tank PMD Rewetting Following Thrust Resettling with a Post-Analysis of the Vented Tank Resupply Experiment. NASA CR-2002-211974, (October, 2002).Google Scholar
  5. 5.
    Dong M., andChatzis I.: The Imbibition and Flow of a Wetting Liquid Along the Corners of a Square Capillary Tube. J. Colloid and Int. Sci., vol. 172, pp. 278–288 (1995).CrossRefGoogle Scholar
  6. 6.
    Langbein, D., and Weislogel M. M.: Dynamics of Liquids in Edges and Corners (DYLCO): IML-2 Experiment for the BDPU. NASA TM 1998-207916 (1998).Google Scholar
  7. 7.
    Weislogel, M. M.: Capillary Flow in Containers of Polygonal Section. AIAA J., vol. 39, no. 12, pp. 2320–2326 (2001a).CrossRefGoogle Scholar
  8. 8.
    Weislogel, M., Lichter, S.: Capillary Flow in Interior Corners. J. Fluid Mech., vol. 373, pp. 349–378 (Nov. 1998).MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Romero, L. A., andYost, F. G.: Flow in an Open Channel Capillary. J. Fluid Mech., vol. 322, pp. 109–129 (1996).MATHCrossRefGoogle Scholar
  10. 10.
    Weislogel, M. M.: Capillary Flow in Interior Corners: the Infinite Column. Phys. of Fluids, vol. 13, no. 11, pp. 3101–3107 (2001).CrossRefMathSciNetGoogle Scholar
  11. 11.
    Weislogel, M. M., andLichter, S.: A Spreading Drop in an Interior Corner: Theory and Experiment. Microgravity Sci. Technol., vol. IX, no. 3, pp. 175–184 (1996).Google Scholar
  12. 12.
    Weislogel, M. M., andCollicott, S.H.: Capillary Re-Wetting of Vaned Containers: Spacecraft Tank Rewetting Following Thrust Resettling, AIAA J., Vol 42, No. 12, pp. 2551–2607, Dec. 2004.CrossRefGoogle Scholar
  13. 13.
    Weislogel, M.M.: Steady Capillary Flow Along Interior Corners. To appear as NASA technical memorandum, (2006).Google Scholar
  14. 14.
    Concus, P, andFinn, R.: On the Behavior of a Capillary Surface in a Wedge. Proc. Acad. Sci., vol 63, no. 2, pp. 292–299 (1969).MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Concus, P., andFinn, R.: Capillary Surfaces in a Wedge-Differing Contact Angles. Microgravity sci. technol., vol. VII(2), pp. 152–155 (1994).Google Scholar
  16. 16.
    Weislogel, M. M.: Capillary Flow in an Interior Corner. NASA TM 107364 (1996).Google Scholar
  17. 17.
    Ayyaswamy, P.S., Catton, I., Edwards, D.K.: Capillary Flow in Triangular Groves. ASME J. of Applied Mech., vol. 41, pp. 332–336 (1974).MATHGoogle Scholar
  18. 18.
    Ransohoff, T.C., Radke, C.J.: Laminar Flow of a Wetting Liquid along Corners of a Predominantly Gas-Occupied Noncircular Pore. J. Colloid and Int. Sci., vol. 121, No. 2, p 392 (Feb. 1988).CrossRefGoogle Scholar
  19. 19.
    White, F.: Viscous Fluid Flow. McGraw Hill, New York, Ch. 3 (1974).MATHGoogle Scholar
  20. 20.
    Nardin, C. L.: Capillary Driven Flows Along Differentially Wetted Interior Corners. To appear NASA technical memorandum, (2005).Google Scholar
  21. 21.
    de Lazzer, A., Langbein, D., Dreyer, M. &Rath, J.: Mean Curvature of Liquid Surfaces in Containers of Arbitrary Cross-Section. Microgravity Sci. Technol., vol. IX, no. 3, pp. 208–219 (1996).Google Scholar
  22. 22.
    Langbein, D.: Capillary Surfaces: Shape — Stability — Dynamics, in Particular Under Weightlessness, Springer Tracts in Modern Physics; vol. 178, Springer-Verlag 2002.Google Scholar

Copyright information

© Z-Tec Publishing 2005

Authors and Affiliations

  • M. M. Weislogel
    • 1
  • C. L. Nardin
    • 1
  1. 1.Portland State UniversityPortland

Personalised recommendations