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On the stability of liquid droplets with line tension

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Prompted by recent works on line tension effects upon the stability of liquid droplets laid on a rigid substrate, we prove existence and stability of equilibrium configurations when the substrate is either planar or spherical. For positive line tension our argument involves only set symmetrization, while for negative line tension a stability criterion is proposed which makes variational problems well-posed in the framework of sets with finite perimeter. Several applications illustrate the role of the criterion in providing a natural cutoff length that selects destabilizing modes.

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Correspondence to Matteo Negri.

Additional information

The work of M. Negri has been partially supported by INdAM through the grant “Mathematical challenges in nanomechanics at the interface between atomistic and continuum models”.

Communicated by A. DeSimone

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Negri, M., Rosso, R. On the stability of liquid droplets with line tension. Continuum Mech. Thermodyn. 21, 173–194 (2009). https://doi.org/10.1007/s00161-009-0104-6

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  • Liquid droplets
  • Line tension
  • Stability


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