Pressure criteria for crack formation and air invasion in drying droplets of colloidal suspensions

The drying of sessile droplets of colloidal suspensions with particle volume fraction beyond 5% leads to the formation of fracture patterns. As water evaporates, a solidification front propagates from the edge of the droplet, leaving behind a thin close-packed particle deposit that eventually covers the entire wetted area. We show that a simple mass conservation model captures the dynamics of the deposit formation across a large range of drying timescales. As the solid deposit grows, water flows radially through it to compensate for the water loss due to evaporation over the solid's surface. Flow in this porous material induces a pressure gradient leading to a large negative pore pressure, which is balanced by capillary pressure. Eventually, radial cracks form in the deposit, and subsequently air invades. Using mass conservation and Darcy's law, we show that the pressure inside the deposit controls the onset of both crack formation and air invasion. We observe two distinct regimes of air invasion which can be rationalized using a single hydrodynamic model, which further provides a criterion for the crossover between the two regimes.