Drying-induced stresses in poroelastic drops on rigid substrates

Abstract

We develop a theory for drying-induced stresses in sessile, poroelastic drops undergoing evaporation on rigid surfaces. Using a lubrication-like approximation, the governing equations of three-dimensional nonlinear poroelasticity are reduced to a single thin-film equation for the drop thickness. We find that the drop experiences compressive elastic stresses but the overall in-plane stress is tensile due to a negative fluid pressure. The mechanical response of the drop is strongly dictated by the initial profile of the solid skeleton, which controls the in-plane deformation, the dominant components of elastic stress, and sets a limit on the depth of delamination that can potentially occur. Our theory suggests that the alignment of desiccation fractures in colloidal drops is selected by the shape of the drop at the point of gelation. We propose that the emergence of three distinct fracture patterns in dried blood drops is a consequence of a non-monotonic drop profile at gelation. Finally, we show that depletion fronts, which separate wet and dry solid, invade the drop from the contact line and localise the generation of mechancial stress during drying.