Universal Scaling of Polygonal Desiccation Crack Patterns

TL;DR

This study reveals a universal power law governing polygonal crack areas in drying films, linking microscopic and geologic scales, and clarifies the mechanisms behind multi-scale crack pattern formation.

Contribution

It introduces a universal power law for polygonal crack areas and explains multi-scale crack patterns through distinct desiccation mechanisms in drying suspensions.

Findings

Polygonal crack area follows a universal power law with film thickness.

Multi-scale crack patterns arise from two distinct desiccation mechanisms.

Quantitative link between material properties and crack pattern characteristics.

Abstract

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, multi-scale 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, $A_p=\alpha h^{4/3}$, where $h$ is the film thickness. By quantitatively linking $\alpha$ with the material properties during crack formation, we provide a robust framework for understanding multi-scale polygonal crack patterns from microscopic to geologic scales.