Universal Scaling of Polygonal Desiccation Crack Patterns

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.

References in corpus (21)

• Patterns Formation in Drying Drops of Blood
• Development and geometry of isotropic and directional shrinkage crack patterns
• Yield stress and elastic modulus of suspensions of noncolloidal particles in yield stress fluids
• The Dynamics of Rapid Fracture: Instabilities, Nonlinearities and Length Scales
• Evolving fracture patterns: columnar joints, mud cracks, and polygonal terrain
• Spiral cracks in drying precipitates
• Dynamics of Simple Cracks
• Order and disorder in columnar joints
• Pattern formation and selection in quasi-static fracture
• Sticky Matter: Jamming and rigid cluster statistics with attractive particle interactions
• Transition in the pattern of cracks resulting from memory effects in paste
• Drying paint: from micro-scale dynamics to mechanical instabilities
• Crack patterns over uneven substrates
• Drying and cracking mechanisms in a starch slurry
• Formation of shear-bands in drying colloidal dispersions
• Origin of crack pattern in the deposition from drying colloidal suspension
• Effect of a non-volatile cosolvent on crack pattern induced by desiccation of a colloidal gel
• Morphometric analysis of polygonal cracking patterns in desiccated starch slurries
• Annular cracks in thin films of nanoparticle suspensions drying on a fiber
• Ultrasonic Attenuation and Speed of Sound of Cornstarch Suspensions
• Flow velocity-dependent transition of anisotropic crack patterns in CaCO${}_3$ pastes

Cited by in corpus (7)

• Plato's cube and the natural geometry of fragmentation
• Physics of drying complex fluid drop: flow field, pattern formation, and desiccation cracks
• Scaling Law for Cracking in Shrinkable Granular Packings
• Crack patterns of drying dense bacterial suspensions
• Universal fluctuation of polygonal crack geometry in solidified lava
• The Physics of Drying of Colloidal Dispersion: Pattern Formation and Desiccation Cracks
• Experimental investigations on the nonequilibrium dynamics of pattern formation in fluid and granular systems