Stratifications of cellular patterns

Physical Review E, 1999

Foams have unique rheological properties that range from solid-like to fluid-like. We study twodimensional non-coarsening foams of different disorder under shear in a Monte Carlo simulation, using a driven large-Q Potts model. Simulations of periodic shear on an ordered foam show several different response regimes. At small strain amplitudes, bubbles deform and recover their shapes elastically, and the macroscopic response is that of a linear elastic cellular material. For increasing strain amplitude, the energy-strain curve starts to exhibit hysteresis before any topological rearrangements occur, indicating a macroscopic viscoelastic response. When the applied strain amplitude exceeds a critical value, the yield strain, topological rearrangements (T1 events) occur, the foam starts to flow, and we observe macroscopic irreversibility. We find that the dynamics of topological rearrangements depend sensitively on the structural disorder. Structural disorder decreases the yield strain; sufficiently high disorder changes the macroscopic response of a foam from a viscoelastic solid to a viscoelastic fluid. This wide-ranging dynamical response and the associated history effects of foams result from avalanche-like T1 events. The spatio-temporal statistics of T1 events T1 do not display long-range correlations for ordered foams or at low shear rates, consistent with experimental observations. As the shear rate or structural disorder increases, the topological events become more correlated and their power spectra change from that of white noise toward 1/f noise. Intriguingly, the power spectra of the total stored energy also exhibit this 1/f trend.

Physical review letters, 2014

Geometrical frustration arises when a local order cannot propagate throughout the space because of geometrical constraints. This phenomenon plays a major role in many systems leading to disordered ground-state configurations. Here, we report a theoretical and experimental study on the behavior of buckling-induced geometrically frustrated triangular cellular structures. To our surprise, we find that buckling induces complex ordered patterns which can be tuned by controlling the porosity of the structures. Our analysis reveals that the connected geometry of the cellular structure plays a crucial role in the generation of ordered states in this frustrated system.

Journal of Fluid Mechanics, 2014

T1 topological rearrangement, i.e. switching of neighbouring bubbles in a liquid foam, is the elementary process of foam dynamics, and it involves film disappearance and generation. It has been studied extensively as it is crucial in foam rheology or foam collapse. T1 dynamics depends mainly on the surfactants used to generate the foam, and several models taking into account surface viscosity and/or elasticity have been proposed. By performing experiments in a cubic assembly of films, we go a step forward in this global analysis and investigate experimentally the mechanism of formation of the new film. In particular, the flow velocity field is probed by particle tracking and the film thickness is measured by light absorption and interferometric measurements. Two limit behaviours for the film are reported: it may (i) undergo an homogeneous extension, or (ii) resist elongation and remain at rest, new film being created from liquid exchange with connecting meniscus. Both T1 dynamics an...

Journal of Physics: Condensed Matter, 1999

This paper investigates the evolution of defects in two-dimensional (2D) wet foams by using the dynamic bubble simulation approach. Two defect types are considered: a single large bubble, and a cluster of small bubbles inserted in an otherwise monodisperse hexagonal lattice. In the case of a single large defect bubble, the disorder of the cluster associated with the defect is seen to increase and peak before returning to a state having a degree of order different from that of the disordered foam scaling state. This long-timescale behaviour agrees with recent 2D wet-foam experiments yet disagrees with the majority of existing simulations on dry foam. The inclusion of a finite liquid content in the present simulations is identified as a possible reason for the improved predictions. In the case of a defect of small bubbles, coarsening trends observed in experiments are reproduced. Unlike the case for a single large bubble defect, no peak was observed in the disorder of the bubble cluster.

Physics Letters A, 2008

The European Physical Journal E, 2001

The "staircase" (2,1,1) foam structure in an ordered foam under expansion in a cylindrical tube and the structural transition to the "bamboo" (1,1,0) structure are studied experimentally, analytically, and numerically using the Surface Evolver minimization program. An analytical expression of the oblique interface in the (2,1,1) structure, a minimal surface, but curved by stretching of the foam, is given as a classic example of singular perturbation (boundary layer) theory. The structural transition from staircase structure to bamboo structure takes place at a considerable dilation. The transition is not due to an edge length tending to zero continuously with dilation, but results from the equilibrium (2,1,1) solution losing its stability due to a saddle node bifurcation.

The European Physical Journal E - Soft Matter, 2003

Experiments on a small cluster of bubbles in a nominally two-dimensional foam show an instability in which a topological change forces one of the bubbles to be ejected to the outside of the cluster at a point where this is not predicted by a two-dimensional model of a foam. This is interpreted in terms of the energy of the initial and ejected states and of the finite liquid content of the experimental system. A description of the distribution of liquid in various experimental set-ups suggests that the exact response may depend critically upon the type of system used. This is demonstrated experimentally with reference to small clusters of bubbles undergoing a single topological change.

Physical Chemistry Chemical Physics, 2009

The physical properties of many multiphase systems are determined by coarsening phenomena. From raindrops to polycrystal grains and foams, the formation and stability of these systems continuously evolve towards lower-energy configurations through events such as coalescence, Ostwald ripening and drainage. Here we propose a procedure to identify and characterise key topological transformations of coarsening phenomena using a physically-based fluid dynamic framework. In situ, real-time foaming processes of a polymeric matrix reinforced with two morphologically different nanofillers, carbon nanotubes and graphene sheets were observed by synchrotron X-ray radioscopy. We obtained detailed information on the evolution of the growth patterns and coarsening events. Filled samples showed differences in both trend and speed compared with the unfilled sample. Furthermore, we found different dominating coarsening phenomena due to the wetting nature of carbon nanoparticles. Our procedure can be extended to sequences of any type of 2D projection or 3D images and to other multiphase systems.

Physical Review Letters, 1999

We propose a particular percolation model for the coalescence of 2-dimensional dry foams. Growth takes place by successive wall ruptures according to a probability proportional to the length of interface between two cells. We show that there exists a critical time t c where the systems undergo a phase transition. Analyses of the fluctuations of the order parameter and of Binder's cumulant suggest that this transition is first order. [S0031-9007(99)08936-X]

Advanced Engineering Materials, 2009

In this paper we characterize foams and tetrahedral structures in a unified way, by a simplified representation of both that conserves the system's topology. The paper presents a workflow for an automated characterization of the topology of the void space, using a partition of the void space into polyhedral cells connected by windows. This characterization serves as the basic input for the Edwards entropic formalism that deals with the statistical characterization of configurational disorder in granular aggregates and argued to work for foams. The Edwards formalism is introduced and simplified expectation-values are calculated.