Jiang Y, Swart P J, Saxena A, Asipauskas M, Glazier J A
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 May;59(5 Pt B):5819-32. doi: 10.1103/physreve.59.5819.
Foams have unique rheological properties that range from solidlike to fluidlike. We study two-dimensional noncoarsening 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 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 avalanchelike rearrangement events. The spatiotemporal statistics of rearrangement events 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.
泡沫具有从类固体到类流体的独特流变特性。我们使用驱动的大Q Potts模型，在蒙特卡罗模拟中研究了不同无序状态下二维非粗化泡沫在剪切作用下的情况。对有序泡沫进行周期性剪切的模拟显示出几种不同的响应状态。在小应变幅值下，气泡发生变形并弹性恢复其形状，宏观响应是线性弹性多孔材料的响应。随着应变幅值增大，在任何拓扑重排发生之前，能量-应变曲线开始出现滞后现象，表明存在宏观粘弹性响应。当施加的应变幅值超过临界值（屈服应变）时，拓扑重排发生，泡沫开始流动，并且我们观察到宏观不可逆性。我们发现拓扑重排的动力学敏感地依赖于结构无序。结构无序降低了屈服应变；足够高的无序度会使泡沫的宏观响应从粘弹性固体转变为粘弹性流体。泡沫这种广泛的动力学响应以及相关的历史效应源于雪崩式的重排事件。对于有序泡沫或低剪切速率，重排事件的时空统计不显示长程相关性，这与实验观察结果一致。随着剪切速率或结构无序度增加，拓扑事件变得更具相关性，其功率谱从白噪声的功率谱向1/f噪声的功率谱转变。有趣的是，总存储能量的功率谱也呈现出这种1/f趋势。
