Vol. 2, No. 1, 2014

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Interfaces endowed with nonconstant surface energies revisited with the d'Alembert–Lagrange principle

Henri Gouin

Vol. 2 (2014), No. 1, 23–43

The equation of motion and the conditions on surfaces and edges between fluids and solids in the presence of nonconstant surface energies, as in the case of surfactants attached to fluid particles at the interfaces, are revisited under the principle of virtual work. We point out that adequate behaviors of surface concentrations may drastically modify the surface tension which naturally appears in the Laplace and the Young–Dupré equations. Thus, the principle of virtual work points out a strong difference between the two revisited concepts of surface energy and surface tension.

variational methods, capillarity, surface energy, surface tension
Physics and Astronomy Classification Scheme 2010
Primary: 02.30.Xx, 45.20.dg, 68.03.Cd, 68.35.Gy
Received: 5 November 2012
Revised: 15 March 2013
Accepted: 14 April 2013
Published: 4 December 2013

Communicated by Sergey Gavrilyuk
Henri Gouin
Aix-Marseille Université
CNRS, Centrale Marseille
M2P2 UMR 7340
  13451, Marseille