Stefan Karpitschka

Droplets move over viscoelastic substrates by surfing a ridge

Liquid drops on soft solids generate strong deformations below the contact line, resulting from a balance of capillary and elastic forces. The movement of these drops may cause strong, potentially singular dissipation in the soft solid. Here we show that a drop on a soft substrate moves by surfing a ridge: the initially flat solid surface is deformed into a sharp ridge whose orientation angle depends on the contact line velocity. We measure this angle for water on a silicone gel and develop a theory based on the substrate rheology. We quantitatively recover the dynamic contact angle and provide a mechanism for stick–slip motion when a drop is forced strongly: the contact line depins and slides down the wetting ridge, forming a new one after a transient. We anticipate that our theory will have implications in problems such as self-organization of cell tissues or the design of capillarity-based microrheometers.

Quantitative experimental study on the transition between fast and delayed coalescence of sessile droplets with different but completely miscible liquids

Quantitative experimental data on the coalescence behavior of sessile droplets with different but completely miscible liquids are presented. The liquids consist of various aqueous mixtures of different nonvolatile diols and carbon acids with surface tensions ranging from 33 to 68 mN/m, contact angles between 9 degrees and 20 degrees, and viscosities from 1 to 12 cP. Two distinctly different coalescence behaviors, a delayed and a fast regime, are found. The transition between the two behaviors is remarkably sharp. It is found that the coalescence mode depends predominantly on the differences in the surface tensions of the two droplets. If the surface tension difference exceeds approximately 3 mN/m, the coalescence is delayed. If it is less, droplet fusion occurs fast. Within the investigated parameter space, the transition seems independent from droplet size, absolute values of the surface tensions, and viscosity. Certain aspects of the experimental findings are explained with the simple hydrodynamic model presented in a recent publication.

Noncoalescence of Sessile Drops from Different but Miscible Liquids: Hydrodynamic Analysis of the Twin Drop Contour as a Self-Stabilizing Traveling Wave

Capillarity always favors drop fusion. Nevertheless, sessile drops from different but completely miscible liquids often do not fuse instantaneously upon contact. Rather, intermediate noncoalescence is observed. Two separate drop bodies, connected by a thin liquid neck, move over the substrate. Supported by new experimental data, a thin film hydrodynamic analysis of this state is presented. Presumably advective and diffusive volume fluxes in the neck region establish a localized and temporarily stable surface tension gradient. This induces a local surface (Marangoni) flow that stabilizes a traveling wave, i.e., the observed moving twin drop configuration. The theoretical predictions are in excellent agreement with the experimental findings.

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.

Sharp transition between coalescence and non-coalescence of sessile drops

Unexpectedly, under certain conditions, sessile drops from different but completely miscible liquids do not always coalesce instantaneously upon contact: the drop bodies remain separated in a temporary state of non-coalescence , connected through a thin liquid bridge. Here we investigate the transition between the states of instantaneous coalescence and temporary non-coalescence. Experiments reveal that it is barely influenced by viscosities and absolute surface tensions. The main system control parameters for the transition are the arithmetic means of the three-phase angles,

Delayed coalescence of droplets with miscible liquids: Lubrication and phase field theories

\overline{\Theta }_{a}

Coalescence and noncoalescence of sessile drops: impact of surface forces.

, and the surface tension differences

The evaporation behavior of sessile droplets from aqueous saline solutions

\Delta \gamma

Lubrication of soft viscoelastic solids

between the two liquids. These relevant parameters can be combined into a single system parameter, a specific Marangoni number

Reaction hysteresis of the CO + O --> CO2 reaction on palladium(111).

\widetilde{M}=3\Delta \gamma /(2\overline{\gamma }\overline{\Theta }_{a}^2)