Pattern Formation by Fracturing in Visco-elastic Materials

在二维系统中，研究了粘弹性材料中注入流体的生长规律。以琼脂凝胶作为粘弹性材料的模型材料。注射实验中使用了填充了琼脂糖凝胶的Hele-Shaw小室。通过改变琼脂溶液中琼脂的含量，琼脂凝胶的粘弹性性质由粘性流体转变为弹性固体。在较低的AGE溶液含量(低于0.1wt%)的情况下，AGE凝胶表现为粘性流体。琼脂含量越高，琼脂凝胶的弹性越强。因此，可以通过改变AGE含量来控制模型材料的粘弹性能。在我们的实验中，空气被用作注入液体。在恒压注水条件下，通过改变注入剂含量和注水压力，进行了系统的注水成井实验。实验过程中的花样生长由CCD摄像机测量。这种模式是在外部均衡的条件下发展的。粘性流动和弹性破裂都是我们花纹生长的控制机制。粘性指进是一种众所周知的现象：将较低粘度的流体注入充满高粘度流体的Hele-Shaw单元。粘性指进的生长是一种准静态生长。在弹性固体的情况下，图案受压裂控制。水力压裂，例如火山裂缝喷发，就是典型的例子之一。在我们的系统中，观察到了一种新的模式生长。这种模式是在两种竞争机制下产生的：裂解和粘性流动。我们创造了这种新的模式，称之为粘弹性指法。得到了形态相图。在较低的注塑压力和较低的AGE含量下，粘性指进效果较好。当我们使用较高含量的琼脂凝胶时，观察到单一平面裂纹的扩展。在该范围的中间，观察到粘弹性指进。

A pattern growth of the injection fluid into visco-elastic materials was studied in two dimensional system. Ager gels were used as model materials of visco-elastic materials. A Hele-Shaw cell filled with the ager gel was used in the injection experiments. By changing ager contents of the ager solution, the visco-elastic property of the ager gel changes from one of viscous fluids to one of elastic solids. At the case of lower contents of ager solution (lower than 0.1 weight percent), ager gels behave like viscous fluids. The higher ager contents, the more elastic property ager gels will gain. Therefore, we can control visco-elastic property of model materials by changing the ager contents. Air is used as an injection fluid in our experiments. With changing the ager contents and the injection pressure, systematic pattern formation experiments were carried out under a constant injection pressure. Pattern growth during experiments was measured by CCD video camera. The pattern grows in the condition of outside equilibrium. Both viscous flow and elastic cracking are control mechanisms in our pattern growth. Viscous fingering is a well known phenomena : when a lower viscosity fluid is injected into Hele-Shaw cell filled with highly viscous fluid. The growth of viscous fingering is a quasi static growth. In the case of elastic solid, the pattern is controlled by fracturing. Hydro-fracturing, e.g.crack eruption in volcano, is one of the typical examples. In our system, a new type of pattern growth was observed. This pattern was generated under two competitive mechanisms ; cracking and viscous flow. We coined this new pattern as a visco-elastic fingering. Morphological phase diagram was obtained. At the lower injection pressure and lower ager contents, viscous fingering will appera. When we used higher contents ager gels, a single plane crack growth is observed. At the middle of the range, visco-elastic fingering is observed.