The dynamics of three-dimensional liquid bridges with pinned and moving contact lines

Shawn Dodds, Marcio S. Carvalho, Satish Kumar

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


Liquid bridges with moving contact lines are relevant in a variety of natural and industrial settings, ranging from printing processes to the feeding of birds. While it is often assumed that the liquid bridge is two-dimensional in nature, there are many applications where either the stretching motion or the presence of a feature on a bounding surface lead to three-dimensional effects. To investigate this we solve Stokes equations using the finite-element method for the stretching of a three-dimensional liquid bridge between two flat surfaces, one stationary and one moving. We first consider an initially cylindrical liquid bridge that is stretched using either a combination of extension and shear or extension and rotation, while keeping the contact lines pinned in place. We find that whereas a shearing motion does not alter the distribution of liquid between the two plates, rotation leads to an increase in the amount of liquid resting on the stationary plate as breakup is approached. This suggests that a relative rotation of one surface can be used to improve liquid transfer to the other surface. We then consider the extension of non-cylindrical bridges with moving contact lines. We find that dynamic wetting, characterized through a contact line friction parameter, plays a key role in preventing the contact line from deviating significantly from its original shape as breakup is approached. By adjusting the friction on both plates it is possible to drastically improve the amount of liquid transferred to one surface while maintaining the fidelity of the liquid pattern.

Original languageEnglish (US)
Pages (from-to)521-540
Number of pages20
JournalJournal of Fluid Mechanics
StatePublished - Sep 25 2012

Bibliographical note

Funding Information:
The authors would like to thank S. Roberts, R. Schunk and A. Yeckel for many fruitful discussions on FEM modelling of free surface flows in three dimensions. This work was supported by the Industrial Partnership for Research in Interfacial and Materials Engineering (IPrime) and the University of Minnesota Graduate School through a Doctoral Dissertation Fellowship to S.D.

Copyright 2012 Elsevier B.V., All rights reserved.


  • computational methods
  • contact lines
  • liquid bridges

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