Stratifications of cellular patterns: hysteresis and convergence

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.

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.

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]

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.

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.

Philosophical Magazine, 2017

The software PLAT, for the simulation of two-dimensional foams, has never been fully exploited, particularly in the wet limit, where it has difficulty converging. Present computer resources have enabled us to circumvent this problem. Using a dataset of 600 000 simulations, we are able to compute the polydisperse foam excess energy all the way from the dry to the wet limit. We also present data and a simple empirical function for the number distribution of n-sided bubbles for all values of the average contact number Z. Furthermore we show that, starting from a dry foam, incremental increases in liquid fraction bring with them a steadily increasing number n of bubbles involved in rearrangements. The size distribution of these rearrangements is found to be exponential, p(n) ∼ exp (−λn), where the mean, 1/λ, increases in the wet limit.

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.

Materials Theory

Cellular patterns formed by self-organization of dislocations are a most conspicuous feature of dislocation microstructure evolution during plastic deformation. To elucidate the physical mechanisms underlying dislocation cell structure formation, we use a minimal model for the evolution of dislocation densities under load. By considering only two slip systems in a plane strain setting, we arrive at a model which is amenable to analytical stability analysis and numerical simulation. We use this model to establish analytical stability criteria for cell structures to emerge, to investigate the dynamics of the patterning process and establish the mechanism of pattern wavelength selection. This analysis demonstrates an intimate relationship between hardening and cell structure formation, which appears as an almost inevitable corollary to dislocation dominated strain hardening. Specific mechanisms such as cross slip, by contrast, turn out to be incidental to the formation of cellular patt...

Physics Letters A, 2008

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.