Prediction of positive and negative elastic dilatancy in 2D and 3D liquid foams

¹  Matière et Systèmes Complexes, Université Paris Diderot - Paris 7, CNRS, UMR 7057, Bâtiment Condorcet Case courrier 7056, F-75205 Paris cedex 13, France, EU
²  Centre de Recherche Paul Pascal, CNRS, UPR 8641, Université de Bordeaux 1 - 115 Av. Schweitzer, F-33600 Pessac, France, EU
³  Department of Endocrinology, Institute of Functional Genomics, CNRS, UMR 5203, INSERM U661, Universities of Montpellier 1 and 2 - 141 rue de la Cardonille, F-34094 Montpellier cedex 05, France, EU

Corresponding author: cyprien.gay@univ-paris-diderot.fr

Received: 26 September 2009
Accepted: 26 April 2010

Abstract

Liquid foams have been observed to behave like immersed granular materials in at least one respect: deformation tends to raise their liquid contents, a phenomenon called dilatancy. While experimental observations evidenced the effect of a continuous deformation rate (dynamic dilatancy), we present a geometrical interpretation of both main contributions to elastic dilatancy (during elastic deformation) in foams squeezed between two solid plates (2D GG foams), which contain pseudo Plateau borders along the plates, and in 3D foams. The positive contribution is related to the increase in total Plateau border length while the negative contribution reflects the increase in total surface area of the foam. In 2D, we show that the negative dilatancy predicted by Weaire and Hutzler (Philos. Mag., 83 (2003) 2747) at very low liquid fractions is specific to ideal 2D foams (with no glass plates). In 3D, we predict that dilatancy should be positive at low liquid fractions (below 1%) and negative at moderate liquid fractions (above 4%).