Skip to main content

The shape and stability of wall-bound and wall-edge-bound drops and bubbles


The behavior of wall-bound drops and bubbles is fundamental to many natural and industrial processes. Key characteristics of such capillary systems include interface shape and stability for a variety of gravity levels and orientations. Significant solutions are in hand for axisymmetric pendent drops for a variety of uniform boundary conditions along the contact line with gravity acting normal to a planar wall. The special case of a wall-bound drop or bubble that is also pinned at an edge (i.e. a ‘wall-edge-bound’ drop) is considered here where numerical solutions are obtained for interface shape and stability as functions of drop volume, contact angle, fluid properties, and uniform gravity vector. For a semi-infinite zero-thickness planar wall (plate), a critical contact angle is identified below which wall-edge-bound drops are always stable. The critical contact angle is computed as a function of the gravity vector. The numerical procedure, which makes no account for contact angle hysteresis, predicts that such wall-edge-bound drops are unconditionally unstable for any gravity field with a component that is tangent to the wall while inwardly normal to the edge. Select experiments are conducted that support the conclusions drawn from the numerical results.

This is a preview of subscription content, access via your institution.


  1. 8

    D. C. Dyson. Contact line stability at edges: Comments on Gibbs’s inequalities. Physics of Fluids, 31(2):229–232, February 1988.

    MathSciNet  Article  Google Scholar 

  2. 9

    J. F. Oliver, C. Huh, andS. G. Mason. Resistance of spreading of liquids by sharp edges. Journal of Colloid and Interface Science, 59(3):568–581, May 1977.

    Article  Google Scholar 

  3. 10

    L. R. White. The equilibrium of a liquid drop on a nonhorizontal substrate and the Gibbs’s criteria for advance over a sharp edge. Journal of Colloid and Interface Science, 73(1):256–259, January 1980.

    Article  Google Scholar 

  4. 11

    K. A. Brakke. The Surface Evolver. Experimental Mathematics, 1:141–165, 1992. The manual and code are available at

    MathSciNet  Article  MATH  Google Scholar 

  5. 12

    S. H. Collicott andM. M. Weislogel. Computing existence and stability of capillary surfaces using surface evolver. AIAA Journal, 42(2):289–295, February 2004.

    Article  Google Scholar 

  6. 13

    K. A. Brakke. The Surface Evolver and the stability of liquid surfaces. Phil. trans. R. Soc. Lond, A, 354:2143–2157, 1996.

    MathSciNet  Article  MATH  Google Scholar 

  7. 14

    E. B. Dussan V. Hydrodynamic stability and instability of fluid systems with interfaces. Arch. Rat. Mech. Anal., 57(4):364–379, 1975.

    MathSciNet  Article  Google Scholar 

  8. 15

    M. M. Weislogel and H. D. Ross. Surface settling in partially filled containers upon step reduction in gravity. Technical Memorandum 103641, NASA, 1990.

  9. 16

    D. Langbein. Capillary Surfaces: Shape-Stability-Dynamics, in Particular Under Weightlessness. Number 178 in Springer Tracts in Modern Physics. Springer, 2001. Chapter 4.

Download references

Author information



Corresponding author

Correspondence to Mark M. Weislogel.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Chen, Y., Bacich, M., Nardin, C. et al. The shape and stability of wall-bound and wall-edge-bound drops and bubbles. Microgravity sci. Technol. 17, 14–24 (2005).

Download citation


  • Contact Angle
  • Contact Line
  • Planar Wall
  • Equilibrium Surface
  • Contact Angle Hysteresis