Origin of crack pattern in the deposition from drying colloidal suspension

The fracture mechanics was widely employed to explain the crack propagation in the deposition produced by drying colloidal suspension. However, more complex than conventional fracture, those cracks periodically distribute and make up a unique pattern. This still remains mysterious so far. Inspired by the concept of spinodal decomposition, here, we develop the theory to elucidate the spatial arrangement of the cracks, which indicates that the crack pattern is generated by the phase separation of colloidal clusters and water. It concludes that the crack spacing results from the wavelength of the concentration fluctuation during the phase separation, linearly growing with the increase of the deposition thickness and initial particle concentration, which is consistent with experimental results.