Hysteresis and avalanches in two-dimensional foam rheology simulations

Abstract

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.

Stable small bubble clusters in two-dimensional foams

“…In this section, we will investigate to what extent the frequencies with which each distinct bubble cluster occurs is sensitive to the bubble interaction potential and the protocol used to generate the bubble clusters. Figure 12 The probabilities for the 7 distinct mechanically stable clusters of N = 4 bubbles obtained from experiments and simulations for (m, n) = (12, 6), (15,8), (20,10), and (30, 50) with JKR mixing rules for ǫij using protocol 1 with R = 10 −1 and open boundary conditions.…”

“…Stress fluctuations are often characterized by periods of increasing stress followed by sudden decreases, referred to as stress drops [15][16][17][18][19] or avalanches 20 . During flow, particle rearrangements can localize, which gives rise to shear banding [21][22][23][24][25] .…”

“…In fact, one event at a given location in the system at a given time can trigger another at a different location later in time. Theoretical descriptions of the mechanical properties of dry foams are typically formulated in terms of the activation of T1 and other topological events 7,9,12,15,17,18,[20][21][22][23]43,44 .…”

Uniaxial deformation tests of aqueous foams: rate effects and topological changes

“…For the same V, v and w the absolute value of the sliding velocity is the same. Thus, we expect reversibility of the ( ) w F curve for a given v. It should be noted that irreversibility in foam deformation is due to topological neighbour switching events as in the work of Jiang et al [12] on 2D foams. These events are absent in the deformation of a single bubble.…”

“…At higher strains topological changes occur in a foam, either locally, involving a small number of bubbles, or in avalanches which affect a large number of bubbles in succession [1,[11][12][13]. The topological changes give rise to discontinuities or jumps in the applied force, the amplitude of which depends on the number of elementary T1 topological changes in the avalanches.…”