Foams in contact with solid boundaries : Equilibrium conditions and conformal invariance

• Published in: The European physical journal. E, Soft matter and biological physics Vol. 17; no. 2; pp. 119 - 128
• Main Authors: MAUCINI, M, OGUEY, C
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer 01-06-2005; EDP Sciences: EPJ
• Subjects: Chemistry; Colloidal state and disperse state; Condensed Matter; Emulsions. Microemulsions. Foams; Exact sciences and technology; General and physical chemistry; Physics; Soft Condensed Matter; Confinement; Liquid solid interface; Experimental data; Film; Two dimensional structure; Theoretical study; Equilibrium condition; Equilibrium equation; Solid; Liquid; Foam; Curved surface; Smooth surface; films; conformal mapping; liquid foam; solid boundary; contact; curvature
• ISSN: 1292-8941; 1292-895X
• DOI: 10.1140/epje/i2004-10133-x

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.