Abstract

Durotaxis refers to the spontaneous motion of objects along stiffness gradients of the supporting substrate. In droplet durotaxis migration occurs down rigidity gradients towards the softer regions of the substrate due to elasto-capillary interaction. We perform experiments in the limit of very soft PDMS substrates, where the cross-linked matrix of the gel can yield under the capillary stresses exerted by the sessile droplet. We find that the droplet moves towards the softest i.e. deepest parts of the gel layer while also sinking into the gel and that droplet durotaxis is much faster when engulfment is associated with the motion. For comparison, we focus on engulfment of aqueous droplets deposited onto a substrate layer of silicone oil. On substrates with a depth gradient, we observe qualitatively similar behaviour to the sinking durotaxis case.

On deep layers, the droplet is ultimately engulfed in the oil layer. This involves rapid submersion of the droplet driven by capillary forces in the oil surface, followed by the much slower peeling of the droplet from the interface to which it is adhered. The later peeling stage is driven by a combination of geometric constraints at the apparent contact line and gravity pulling on the droplet. Gravitational effects are therefore essential to complete engulfment, even for micrometric droplets. Furthermore, the opposing effects of geometry and gravity result in the longest engulfment times for droplets of intermediate size.

Finally, if time allows, I will also briefly discuss some recent results on the fluidisation of sessile drops of elasto-viscoplastic fluids subject to vertical vibration and how such a system may be used to explore nonlinear viscoelastic effects near the yield threshold.