Crack densification in drying colloidal suspensions

As sessile drops of aqueous colloidal suspensions dry, a close-packed particle deposit forms that grows from the edge of the drop toward the center. To compensate for evaporation over the solid’s surface, water flows radially through the deposit, generating a negative pore pressure in the deposit associated with tensile drying stresses that induce the formation of cracks. As these stresses increase during drying, existing cracks propagate and additional cracks form, until the crack density eventually saturates. We rationalize the dynamics of crack propagation and crack densification with a local energy balance between the elastic energy released by the crack, the energetic cost of fracture, and the elastic energy released by previously formed cracks. We show that the final spacing between radial cracks is proportional to the local thickness of the deposit, while the aspect ratio of the crack segments depends on the shape of the deposit.