https://doi.org/10.1140/epje/i2004-10133-x
Regular Articles
Foams in contact with solid boundaries: Equilibrium conditions and conformal invariance
LPTM, Université de Cergy-Pontoise, 95302, Cergy-Pontoise, France
* e-mail: mancini@ptm.u-cergy.fr
** e-mail: oguey@ptm.u-cergy.fr
Received:
4
November
2004
Accepted:
22
March
2005
Published online:
6
May
2005
A liquid foam in contact with a solid surface forms a two-dimensional foam on the surface. We derive the equilibrium equations for this 2D foam when the solid surface is curved and smooth, generalising the standard case of flat Hele-Shaw cells. The equilibrium conditions at the vertices in 2D, at the edges in 3D, are invariant by conformal transformations. Regarding the films, conformal invariance only holds with restrictions, which we explicit for 3D and flat 2D foams. Considering foams confined in thin interstices between two non-parallel plates, normal incidence and Laplace’s law lead to an approximate equation relating the plate profile to the conformal map. Solutions are given for the logarithm and power laws in the case of constant pressure. The paper concludes on a comparison with available experimental data.
PACS: 82.70.Rr Aerosols and foams – / 82.70.Kj Emulsions and suspensions – / 68.03.Hj Gas-liquid and vacuum-liquid interfaces: Structure, measurements and simulations –
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2005
