Abstract.

In the present work we report crack patterns formed in aqueous Laponite^® gel in a rectangular box, while exposed to a uniform static electric field. The crack pattern shows a very interesting tree-like geometry extending from the positive to the negative electrode. At the positive electrode a large number of cracks appear at first and merge with each other in stages thus forming tree-like fractal structures. These structures are reminiscent of the Bethe lattice or Cayley tree. The “trees” divide the system into peds of varying size, with numerous smaller ones on the positively charged end, gradually increasing in size, and decreasing in number towards the negative end. If the cumulative distribution of the number of peds exceeding a certain area in size, is plotted against that area, a power-law relation is obtained. This implies a scale-invariant fractal character of the pattern. For a given system size, the exponent of the power-law has a nearly constant value for different applied voltages. We present an experimental study demonstrating this behaviour and discuss how it compares with similar distributions of river-basin areas and viscous fingers in a Hele-Shaw cell.

Graphical abstract

中文翻译：

---

Laponite®层中的分支裂纹模式在电场下干燥：幂律和标度scalin的证据>。

摘要。

在目前的工作我们报告形成的Laponite水性裂纹图案^®凝胶在矩形盒中，同时暴露于均匀的静电场中。裂纹图案显示出非常有趣的树状几何形状，从正电极延伸到负电极。在正电极处，首先出现大量裂纹，然后彼此分阶段合并，从而形成树状的分形结构。这些结构让人联想到Bethe格子或Cayley树。“树”将系统分成大小不同的小节，在带正电的一端有许多较小的小节，大小逐渐增大，而向负数减小。如果相对于该面积绘制超过一定面积的脚踏板数的累积分布，则获得幂律关系。这意味着图案的尺度不变的分形特征。对于给定的系统大小，对于不同的施加电压，幂律的指数具有几乎恒定的值。我们提供了一个实验研究来证明这种行为，并讨论了它如何与Hele-Shaw单元中的流域和粘性手指的相似分布进行比较。

图形概要