Luuk A. Lubbers

Drops on soft solids: free energy and double transition of contact angles

The equilibrium shape of liquid drops on elastic substrates is determined by minimizing elastic and capillary free energies, focusing on thick incompressible substrates. The problem is governed by three length scales: the size of the drop R, the molecular size a and the ratio of surface tension to elastic modulus γ/E. We show that the contact angles undergo two transitions upon changing the substrate from rigid to soft. The microscopic wetting angles deviate from Young’s law when γ/(Ea)≫1, while the apparent macroscopic angle only changes in the very soft limit γ/(ER)≫1. The elastic deformations are worked out for the simplifying case where the solid surface energy is assumed to be constant. The total free energy turns out to be lower on softer substrates, consistent with recent experiments.

Discontinuous buckling of wide beams and metabeams

We uncover how nonlinearities dramatically alter the buckling of elastic beams. First, we show experimentally that sufficiently wide ordinary elastic beams and specifically designed metabeams-beams made from a mechanical metamaterial-exhibit discontinuous buckling, an unstable form of buckling where the postbuckling stiffness is negative. Then we use simulations to uncover the crucial role of nonlinearities, and show that beams made from increasingly nonlinear materials exhibit an increasingly negative postbuckling slope. Finally, we demonstrate that for sufficiently strong nonlinearity, we can observe discontinuous buckling for metabeams as slender as 1% numerically and 5% experimentally.

Liquid drops attract or repel by the inverted Cheerios effect

Significance The Cheerios effect is the attraction of solid particles floating on liquids, mediated by surface tension forces. We demonstrate experimentally that a similar interaction can also occur for the inverse case, liquid particles on the surface of solids, provided that the solid is sufficiently soft. Remarkably, depending on the thickness of the solid layer, the interaction can be either purely attractive or become repulsive. A theoretical model, in excellent agreement with the experimental data, shows that the interaction requires both elasticity and capillarity. Interactions between objects on soft substrates could play an important role in phenomena of cell–cell interaction and cell adhesion to biological tissues, and be exploited to engineer soft smart surfaces for controlled drop coalescence and colloidal assembly. Solid particles floating at a liquid interface exhibit a long-ranged attraction mediated by surface tension. In the absence of bulk elasticity, this is the dominant lateral interaction of mechanical origin. Here, we show that an analogous long-range interaction occurs between adjacent droplets on solid substrates, which crucially relies on a combination of capillarity and bulk elasticity. We experimentally observe the interaction between droplets on soft gels and provide a theoretical framework that quantitatively predicts the interaction force between the droplets. Remarkably, we find that, although on thick substrates the interaction is purely attractive and leads to drop–drop coalescence, for relatively thin substrates a short-range repulsion occurs, which prevents the two drops from coming into direct contact. This versatile interaction is the liquid-on-solid analog of the “Cheerios effect.” The effect will strongly influence the condensation and coarsening of drops on soft polymer films, and has potential implications for colloidal assembly and mechanobiology.