Viscous froth lens
Viscous froth lens
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DOI：
10.1103/physreve.74.051403
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发表时间：
2006-11-01
影响因子：
2.4
通讯作者：
Grassia, P.
中科院分区：
文献类型：
--
作者：
Green, T. E.;Bramley, A.;Grassia, P.
泡沫结构的微尺度模型传统上包括气泡压力和与气泡膜曲率相关的表面张力之间的平衡。特别是，流动泡沫微观流变学模型假设这种平衡是在一些外部施加的运动的作用下保持的。然而，最近，泡沫结构的动态模型已被提出，粘性泡沫模型，它平衡了气泡压力和表面张力的净效应粘性耗散力：这允许描述快速流动的泡沫。这篇文章研究了粘性泡沫模型在应用于具有特别简单几何形状的范例问题时的行为：即二维气泡“透镜。“该透镜由一个通道组成，该通道部分地被气泡（称为“透镜气泡”）填充，该气泡接触一个通道壁。另外的膜（称为“跨越膜”）连接到该气泡，跨越与相对通道壁的距离。这个简单的结构可以通过在跨膜上施加压力来运动和变形，从而产生丰富的动力学行为。透镜结构沿通道沿着稳定传播的解可由粘性泡沫模型计算。微扰的解决方案中得到的限制透镜结构与弱施加的压力，而数值解可用于较高的压力。这些稳定传播的解决方案表明，小透镜移动速度比大的，而小和大的透镜气泡是相当抵抗变形，至少在弱的反压力。随着所施加的背压增大，具有小透镜泡的结构保持相对刚性，而具有大透镜泡的结构变得更加柔顺。然而，甚至进一步增加所施加的背压，临界压力似乎存在的稳态结构失去稳定性和非稳态数值模拟表明，它打破了拓扑变换的路线。
Microscale models of foam structure traditionally incorporate a balance between bubble pressures and surface tension forces associated with curvature of bubble films. In particular, models for flowing foam microrheology have assumed this balance is maintained under the action of some externally imposed motion. Recently, however, a dynamic model for foam structure has been proposed, the viscous froth model, which balances the net effect of bubble pressures and surface tension to viscous dissipation forces: this permits the description of fast-flowing foam. This contribution examines the behavior of the viscous froth model when applied to a paradigm problem with a particularly simple geometry: namely, a two-dimensional bubble "lens." The lens consists of a channel partly filled by a bubble (known as the "lens bubble") which contacts one channel wall. An additional film (known as the "spanning film") connects to this bubble spanning the distance from the opposite channel wall. This simple structure can be set in motion and deformed out of equilibrium by applying a pressure across the spanning film: a rich dynamical behavior results. Solutions for the lens structure steadily propagating along the channel can be computed by the viscous froth model. Perturbation solutions are obtained in the limit of a lens structure with weak applied pressures, while numerical solutions are available for higher pressures. These steadily propagating solutions suggest that small lenses move faster than large ones, while both small and large lens bubbles are quite resistant to deformation, at least for weak applied back pressures. As the applied back pressure grows, the structure with the small lens bubble remains relatively stiff, while that with the large lens bubble becomes much more compliant. However, with even further increases in the applied back pressure, a critical pressure appears to exist for which the steady-state structure loses stability and unsteady-state numerical simulations show it breaks up by route of a topological transformation.