Drying-induced stresses in poroelastic drops on rigid substrates

TL;DR

This paper develops a theoretical framework for understanding drying-induced stresses in poroelastic drops on rigid substrates, revealing how initial shape and drying dynamics influence fracture patterns and stress localization.

Contribution

It introduces a simplified thin-film equation for poroelastic drops, linking initial shape to stress distribution and fracture formation during drying.

Findings

Thin drops experience compressive elastic stresses but tensile in-plane stresses.

Drop shape at gelation influences fracture pattern selection.

Depletion fronts can localize stress during drying.

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 thin drops experience compressive elastic stresses but the total in-plane stresses are tensile. The mechanical response of the drop is 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. We also show that depletion fronts, which separate wet and dry solid, can invade the drop from the contact line and localise the generation of mechanical stress during drying. Finally, the finite element method is used to explore the stress profiles in drops with large contact angles.