Department of Physics, Emory University, Atlanta, Georgia 30322, USA.
Phys Rev E. 2019 Jan;99(1-1):012802. doi: 10.1103/PhysRevE.99.012802.
Polygonal desiccation crack patterns are commonly observed in natural systems. Despite their quotidian nature, it is unclear whether similar crack patterns which span orders of magnitude in length scales share the same underlying physics. In thin films, the characteristic length of polygonal cracks is known to monotonically increase with the film thickness; however, existing theories that consider the mechanical, thermodynamic, hydrodynamic, and statistical properties of cracking often lead to contradictory predictions. Here we experimentally investigate polygonal cracks in drying suspensions of micron-sized particles by varying film thickness, boundary adhesion, packing fraction, and solvent. Although polygonal cracks were observed in most systems above a critical film thickness, in cornstarch-water mixtures, multiscale crack patterns were observed due to two distinct desiccation mechanisms. Large-scale, primary polygons initially form due to capillary-induced film shrinkage, whereas small-scale, secondary polygons appear later due to the deswelling of the hygroscopic particles. In addition, we find that the characteristic area of the polygonal cracks, A_{p}, obeys a universal power law, A_{p}=αh^{4/3}, where h is the film thickness. By quantitatively linking α with the material properties during crack formation, we provide a robust framework for understanding multiscale polygonal crack patterns from microscopic to geologic scales.
多边形干燥裂纹模式在自然系统中很常见。尽管它们很常见，但目前尚不清楚跨越长度尺度数量级的类似裂纹模式是否具有相同的潜在物理性质。在薄膜中，多边形裂纹的特征长度已知会随着薄膜厚度单调增加；然而，现有的考虑裂纹的力学、热力学、流体力学和统计特性的理论往往会导致相互矛盾的预测。在这里，我们通过改变薄膜厚度、边界附着力、堆积分数和溶剂来实验研究干燥悬浮液中微米级颗粒的多边形裂纹。尽管在高于临界薄膜厚度的大多数系统中观察到了多边形裂纹，但在玉米淀粉-水混合物中，由于两种不同的干燥机制，观察到了多尺度裂纹模式。大尺度的初始多边形最初是由于毛细作用引起的薄膜收缩形成的，而小尺度的二次多边形则是由于吸湿颗粒的溶胀而出现的。此外，我们发现多边形裂纹的特征面积 A_{p} 遵循普适幂律，A_{p}=αh^{4/3}，其中 h 是薄膜厚度。通过在裂纹形成过程中定量地将 α 与材料性质联系起来，我们为从微观到地质尺度理解多尺度多边形裂纹模式提供了一个强大的框架。
