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.
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D. C. Dyson. Contact line stability at edges: Comments on Gibbs’s inequalities. Physics of Fluids, 31(2):229–232, February 1988.
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.
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.
K. A. Brakke. The Surface Evolver. Experimental Mathematics, 1:141–165, 1992. The manual and code are available at http://www.susqu.edu/facstaff/b/brakke/.
S. H. Collicott andM. M. Weislogel. Computing existence and stability of capillary surfaces using surface evolver. AIAA Journal, 42(2):289–295, February 2004.
K. A. Brakke. The Surface Evolver and the stability of liquid surfaces. Phil. trans. R. Soc. Lond, A, 354:2143–2157, 1996.
E. B. Dussan V. Hydrodynamic stability and instability of fluid systems with interfaces. Arch. Rat. Mech. Anal., 57(4):364–379, 1975.
M. M. Weislogel and H. D. Ross. Surface settling in partially filled containers upon step reduction in gravity. Technical Memorandum 103641, NASA, 1990.
D. Langbein. Capillary Surfaces: Shape-Stability-Dynamics, in Particular Under Weightlessness. Number 178 in Springer Tracts in Modern Physics. Springer, 2001. Chapter 4.
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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). https://doi.org/10.1007/BF02889516
- Contact Angle
- Contact Line
- Planar Wall
- Equilibrium Surface
- Contact Angle Hysteresis