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 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 nonmonotonic 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 localize 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.

Directional drying of a colloidal dispersion: quantitative description with water potential measurements using water clusters in a poly(dimethylsiloxane) microfluidic chip

“…Our experimental measurements open up a number of possibilities, in particular for the quantitative description of drying-induced stresses, as the value of k plays a fundamental role in poroelastic modeling. 40,[52][53][54] In our experiments for instance, the knowledge of k enables us to estimate the water potential c, and therefore the pore pressure within the solid, a quantity related to the tensile component of the stresses during drying. 40,53,54 The data shown in the inset of Fig.…”

Time-dependent modelling of thin poroelastic films drying on deformable plates

“…For simplicity, we set the scalar permeability of the film, k(φ), to be a constant. Hennessy et al [17] showed that a porosity-dependent permeability can lead to drying fronts propagating into the bulk of the film from the contact line. These fronts separate wet and completely dry solid and hence require the porosity to become very small.…”

“…In asymptotically reducing the equations for the film, we invoke a poroelastic version of lubrication theory [11,18,22]. Furthermore, we extend our previous work on drying-induced stresses in poroelastic drops [17] by accounting for a wide range of drying regimes that are determined by the magnitude of the Péclet number. In all cases, the film model reduces to either a nonlinear ordinary differential equation or a nonlinear diffusion equation for the solvent concentration.…”

Time-dependent modelling of thin poroelastic films drying on deformable plates

“…For simplicity, we set the scalar permeability of the film, k(φ), to be a constant. Hennessy et al [29] showed that a porosity-dependent permeability can lead to drying fronts propagating into the bulk of the film from the contact line. These fronts separate wet and completely dry solid and hence require the porosity to become very small.…”

“…In asymptotically reducing the equations for the film, we invoke a poroelastic version of lubrication theory [26][27][28]. Furthermore, we extend our previous work on drying-induced stresses in poroelastic drops [29] by accounting for a wide range of drying regimes that are determined by the magnitude of the Péclet number. In all cases, the film model reduces to either a nonlinear ordinary differential equation or a nonlinear diffusion equation for the solvent concentration.…”