Star-triangle equivalence in soap froths

Scientific Reports

Liquid foams are classified into a dry foam and a wet foam, empirically judging from the liquid fraction or the shape of the gas bubbles. It is known that physical properties such as elasticity and diffusion are different between the dry foam and the wet foam. Nevertheless, definitions of those states have been vague and the dry-wet transition of foams has not been clarified yet. Here we show that the dry-wet transition is closely related to rearrangement of the gas bubbles, by simultaneously analysing the shape change of the bubbles and that of the entire foam in two dimensional foam. In addition, we also find a new state in quite low liquid fraction, which is named "superdry foam". Whereas the shape change of the bubbles strongly depends on the change of the liquid fraction in the superdry foam, the shape of the bubbles does not change with changing the liquid fraction in the dry foam. Our results elucidate the relationship between the transitions and the macroscopic mechanical properties.

Physical Review E, 2006

We characterize the late-time scaling state of dry, coarsening, two-dimensional froths using a detailed force-based dynamical model. We find that the slow evolution of bubbles leads to small and decreasing deviations from 120 ‫ؠ‬ angles at threefold vertices in the froth, but with a side-number dependence that is independent of time and apparently universal. We also find that a significant number of T1 side-switching processes occur for macroscopic bubbles in the scaling state, though most bubble annihilations involve foursided bubbles at microscopic scales.

Physical Review Letters, 2008

A novel thermal convection cell consisting of half a soap bubble heated at the equator is introduced to study thermal convection and the movement of isolated vortices. The soap bubble, subject to stratification, develops thermal convection at its equator. A particular feature of this cell is the emergence of isolated vortices. These vortices resemble hurricanes or cyclones and similarities between our observed structures and these natural objects are found. This is brought forth through a study of the mean square displacement of these objects showing signs of superdiffusion.

Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2013

Physical Review E, 2015

Soap bubbles are thin liquid films enclosing a fixed volume of air. Since the surface tension is typically assumed to be the only responsible for conforming the soap bubble shape, the realized bubble surfaces are always minimal area ones. Here, we consider the problem of finding the axisymmetric minimal area surface enclosing a fixed volume V and with a fixed equatorial perimeter L. It is well known that the sphere is the solution for V = L 3 /6π 2 , and this is indeed the case of a free soap bubble, for instance. Surprisingly, we show that for V < αL 3 /6π 2 , with α ≈ 0.21, such a surface cannot be the usual lens-shaped surface formed by the juxtaposition of two spherical caps, but rather a toroidal surface. Practically, a doughnut-shaped bubble is known to be ultimately unstable and, hence, it will eventually lose its axisymmetry by breaking apart in smaller bubbles. Indisputably, however, the topological transition from spherical to toroidal surfaces is mandatory here for obtaining the global solution for this axisymmetric isoperimetric problem. Our result suggests that deformed bubbles with V < αL 3 /6π 2 cannot be stable and should not exist in foams, for instance.

Europhysics Letters (EPL), 2000

PACS. 82.70.Rr -Aerosols and foams. PACS. 05.70.Ln -Nonequilibrium and irreversible thermodynamics.

Physics of Fluids, 2015

We present the results of an experimental investigation of the merger of a soap bubble with a planar soap film. When gently deposited onto a horizontal film, a bubble may interact with the underlying film in such a way as to decrease in size, leaving behind a smaller daughter bubble with approximately half the radius of its progenitor. The process repeats up to three times, with each partial coalescence event occurring over a time scale comparable to the inertial-capillary time. Our results are compared to the recent numerical simulations of Martin and Blanchette ["Simulations of surfactant e↵ects on the dynamics of coalescing drops and bubbles," Phys. Fluids 27, 012103 (2015)] and to the coalescence cascade of droplets on a fluid bath.

Physical Review E, 1996

An analysis of the shell distribution function of two-dimensional soap froth reveals a universal topological relation on the average number M(j, n) of sides per cell to the number of cells K(j, n) in the jth shell of a given center ceil with n sides. A plot of M(j, n)K(j, n) vs K(j, n) shows a slope of 5 for j = 1 and a slope of 6 for j & 2, for all samples. The results are universal for soap froths in the

Physical Review Letters, 1992

We discuss the implications of the classical Gauss-Bonnet formula to foam in two and three dimensions. For a two-dimensional foam it gives a generalization of the von Neumann law for the coarsening of foams to curved surfaces. As a consequence of this we find that the stability properties of stationary bubbles of such a froth depend on the Gaussian curvature of the surface. For three-dimensional foam we find a relation between the average Gaussian curvature of a soap film and the average number of vertices for each face.

Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2005

The energy and shape of three-dimensional clusters of equal-volume bubbles packed around a central bubble are calculated. The resulting surface areas and bubble pressures provide an improvement upon existing growth laws for three-dimensional bubble clusters. Since a bubble's growth-rate depends mostly on its number of faces, simulations of coarsening can be accelerated by considering bubble topology rather than detailed geometry. The coarsening-induced relaxation of a disordered foam towards a scaling state, in which the normalised bubble volume and face-number distributions remain invariant, can thus be characterised.