Abstract
We consider a coexistence of two axisymmetric liquid bridges LB i and LB m of two immiscible liquids i and m which are immersed in a third liquid (or gas) e and trapped between two smooth solid bodies with axisymmetric surfaces S 1, S 2 and free contact lines. Evolution of liquid bridges allows two different configurations of LB i and LB m with multiple (five or three) interfaces of non-smooth shape. We formulate a variational problem with volume constraints and present its governing equations supplemented by boundary conditions. We find a universal relationship between curvature of the interfaces and discuss the Neumann triangle relations at the singular curve where all liquids meet together.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Fel L.G., Rubinstein B.Y.: Stability of axisymmetric liquid bridges. Z. Angew. Math. Phys. 66, 3447–3471 (2015)
Finn R.: The contact angle in capillarity. Phys. Fluids 18, 047102 (2006)
http://www.kruss.de/services/education-theory/substance-data/liquids/
Gelfand I.M., Fomin S.V.: Calculus of Variations. Prentice-Hall, Inc, Englewood Cliffs (1963)
Marchand A., Das S., Snoeijer J.H., Andreotti B.: Contact angles on a soft solid: from Young’s law to Neumann’s law. Phys. Rev. Lett. 109, 236101 (2012)
Morgan F.: Geometric Measure Theory: A Beginner’s Guide, 4th Edition. Academic Press, New York (2009)
Roman B., Bico J.: Elasto-capillarity: deforming an elastic structure with a liquid droplet. J. Phys.: Condens. Matter 22, 493101 (2010)
Rowlinson J.S., Widom B.: Molecular Theory of Capillarity. Clarendon Press, Oxford (1982)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fel, L.G., Rubinstein, B.Y. & Ratner, V. Multiple liquid bridges with non-smooth interfaces. Z. Angew. Math. Phys. 67, 107 (2016). https://doi.org/10.1007/s00033-016-0702-7
Received:
Revised:
Published:
DOI: https://doi.org/10.1007/s00033-016-0702-7