Dynamical Elastocapillary Phenomena
What happens if a localized deformation at the surface of a soft solid is forced to move? Consider, for example, a droplet that sits on top of an inclined soft solid: Capillary forces at the contact line act like a localized line force that pinches on the surface and deforms it into a sharp wetting ridge. Obviously, if the droplet slides down the soft surface, the deformation that it generates has to change over time. This causes dissipation, and it is not clear a priori what the shape of the solid will be, and which pattern the motion of the droplet will have. In my group, we investigate this problem, aiming at a fundamental understanding of cases where liquid and solid physics are strongly coupled together. In the following we give a few examples of our recent discoveries.
Previous experiments revealed that there are two distinct modes in which a contact line may move across a soft surface: one is a slow and continuous motion, that does not stop even at very small driving forces, allowing for velocities in the nanometer per second range. The other mode is a fast and irregular jumping motion, in which the velocity of the contact line fluctuates by orders of magnitude. Using the framework of linear elasticity we have calculated that, in the slow and steady mode, the wetting ridge is dragged along with the contact line, and dissipation in the solid makes it asymmetric. This asymmetry leads to a rotation of its tip, which allows to maintain a local balance between solid and liquid surface tensions [Karpitschka et al., Nature Commun. 6 (2015) 7891]. We could also shown that this must hold true in case one considers a balance of injected and dissipated power instead of local force balances [Karpitschka et al., PNAS 115 (2018) E7233]. Interestingly, very thin, soft coating layers do not follow the laws of linear viscoelasticity: The latter predicts a divergence of dissipation if the layers become thinner and thinner while keeping all other parameters constant. Experiments, however, confirm the intuitive expectation: dissipation fades as the coating thickness decreases [Khattak et al., Nature Commun. (2022)]. In the fast, jumpy mode, the moving ridge is abandoned, the contact line surfs down its advancing face, and starts forming a new ridge on the slope of the old one.
Recently, we also managed to visualize the dynamical wetting ridge shapes with high spatio-temporal resolution [van Gorcum et al., Phys. Rev. Lett. 121 (2018) 208003]. This we achieved with a little trick that gave us optical access to the ridge: instead of using a flat substrate, we made a cavity in a block of polymer gel held by a cuvette, such that the wetted surface could be observed through the (transparent) solid. With this technique, we made a very intriguing discovery: Not only the ridge rotates, but also its opening angle depends on velocity. This is unexpected because it can only originate in a change in one of the surface tensions. It turned out that this is most likely the surface tension of the solid. It is well known that the surface tension of a solid may change if the surface is stretched, an effect that does not exist for pure liquids. It does, however, have an analogy in the world of liquid surfaces, which is a surfactant-covered surface: expansion of the surface decreases coverage, and hence surface tension increases. Due to the dissipation-induced shape change of the ridge, the surface experiences a velocity-dependent stretch. However, there are indications that this is not sufficient to explain our observation: In addition to strain-dependence, the surface should follow its own, distinct rheology.
A closely related case is peeling a flexible strip off a soft, elastic adherent material. For strong adhesives, this delamination process is governed by cavitation and fibril formation, which is highly nonlinear and hard to model quantitatively. However, “weak” or rather “reversible” adhesives become increasingly important in daily applications (think about post-its, for example) because adhesion and peeling can be repeated many times. Now the adherent part of the substrate is coupled to the bending rigidity of the tape, in contrast to the case of soft wetting where solid laplace pressure was acting instead. We extended our model for that case and could provide an accurate description of the force-velocity relation of the peeling process. As in the static case, solid surface tension regularizes the crack singularity of adhesion and leads to a regular boundary condition of the soft adhesive at its contact point with the tape [Perrin et al., Soft Matter 15 (2019) 770].