  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.
