Calculus of Variations and Geometric Measure Theory

M. Negri - R. Rosso

On the stability of liquid droplets with line tension

created by negri on 16 Nov 2006
modified on 13 Apr 2010


Published Paper

Inserted: 16 nov 2006
Last Updated: 13 apr 2010

Journal: Continuum Mech. Thermodyn.
Volume: 21
Pages: 173-194
Year: 2009


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 physically meaningful destabilizing modes.