|Transport of liquids on soft
substrates is critical to many biological and medical
applications, such as drug delivery systems. Yet, despite
its importance, the most basic characterization of how
liquids wet soft solids is not well understood, because, in
contrast to rigid substrates, surface tension can deform
soft solids. With regards to materials science, small
surface tension forces can be used in lieu of conventional
measurement techniques to probe the mechanical properties of
We develop models to describe the elastic response of a solid substrate from the wetting forces imparted by the liquid onto the solid. The elastocapillary length δ ∼ σ/E sets the size of the deformation. For water (σ=72mN/m) on a glass substrate (E=70GPa) δ ∼ 10-12m, justifying the neglect of elasticity in classical problems on wetting. Style et al. 2013 have used fluorescence confocal microscopy to show that droplets interacting with silicone gels (E=3 kPa), yield micron-size deformations δ ∼ 10-6m. Our model, which takes proper account of the surface energies, is able to reproduce the experimental results (upper figure).
If the substrate is sufficiently `soft', as with agarose gel (E~10Pa), the elastocapillary deformations can be of millimetric δ∼10-3m size. To put the length scales into perspective, note that to produce millimeter size deformations on a glass substrate one would have to load the substrate with the weight of 40 Mini Coopers spaced evenly along a 1mm ring. Not surpirsingly, such deformations can cause material failure in which fractures develop on the gel surface and propagate outwards from the contact-line in a starburst pattern (lower figure). The fracture process can be conveniently divided into three phases; 1) initation, 2) nucleation and 3) propagation. We study the fracture process theoretically and compare our results with experiments (K. Daniels, NCSU Physics).
Our present focus is on fundamental problems in elastocapillarity and soft fracture mechanics, as well as biological and industrial applications.