Foam physics : negative line tension associated to Plateau borders

Collaboration with François Caillier, Andrzej Zywocinski and Patrick Oswald.

Introduction

Idealization of liquid foams commonly consists in considering the films as surfaces of negligible thickness, the liquid being entirely contained in curved Plateau borders of triangular section at the junctions. This limit, convenient for a theoretical study, is that of the so-called "dry foam"; the water content approaches zero and one is left with a skeleton of interconnected thin films. In two dimensions, the Decoration Theorem states that the structure of a 2D-foam of finite liquid fraction, F_L, corresponds to that of the appropriate dry skeleton (i.e. a limiting structure for zero liquid fraction in which the vertices shrink to points); in other words, from the dry limit, the increase in F_L leaves the overall foam geometry unchanged. The liquid accumulates in the Plateau borders and decorates the initial point-like vertices of the dry skeleton. In three dimensions, there is no equivalent for the Decoration Theorem. By direct observation of an annular Plateau border, we give the first experimental evidence that such a line tension plays a role in the structure of simple 3D-foams at finite liquid fraction.

Our experimental study

We measure the angles produced in the Plateau border region of "dry" soap films in a simple experimental geometry (Fig.1).

Fig.1: Experimental geometry.

In absence of line tension, the angle that three soap films make at the Plateau border are expected to be 120 degrees. In our experimental geometry (Fig.1), the angle, that the catenoidal films make between them, b* = q - a, is significantly larger than 120 degrees (Fig.2). Thus, the line tension associated to the Plateau border is negative. This result has important consequences for the theoretical description of foams approaching the dry limit.

Fig.2: Angle produced between the catenoidal films b* vs. typical size r of the Plateau border

Related publication

Observation of negative line tension from Plateau borders regions in dry soap films,
Géminard J.-C., Zywocinski A., Caillier F., and Oswald P., Phil. Mag. Lett., 84 (2004) 199-204.