Droplets Sit and Slide Anisotropically on Soft, Stretched Substrates

Complexity in Wetting Dynamics

The spreading dynamics of a droplet of pure liquid deposited on a rigid, nonsoluble substrate has been extensively investigated. In a purely hydrodynamic description, the dynamics of the contact line is determined by a balance between the energy associated with the capillary driving force and the energy dissipated by the viscous shear in the liquid. This balance is expressed by the Cox-Voinov law, which relates the spreading velocity to the contact angle. More recently, complex situations have been examined in which dissipation and/or the driving force may be strongly modified, leading to sometimes spectacular changes in wetting dynamics. We review recent examples of effects at the origin of deviations from the hydrodynamic model, which may involve physical or chemical modifications of the substrate or of the wetting liquid, occurring at scales ranging from the molecular to the mesoscopic.

Morphology and stability of droplets sliding on soft viscoelastic substrates

We show that energy dissipation partition between a liquid and a solid controls the shape and stability of droplets sliding on viscoelastic gels. When both phases dissipate energy equally, droplet dynamics is similar to that on rigid solids. When the solid is the major contributor to dissipation, we observe an apparent contact angle hysteresis of viscoelastic origin. We find excellent agreement between our data and a non-linear model of the wetting of gels of our own that also indicates the presence of significant slip. Our work opens general questions on the dynamics of curved contact lines on compliant substrates.

Nanoscale Elasto-Capillarity in the Graphene-Water System under Tension: Revisiting the Assumption of a Constant Wetting Angle

Wetting highly compliant surfaces can cause them to deform. Atomically thin materials, such as graphene, can have exceptionally small bending rigidities, leading to elasto-capillary lengths of a few nanometers. Using large-scale molecular dynamics (MD), we have studied the wetting and deformation of graphene due to nanometer-sized water droplets, focusing on the wetting angle near the vesicle transition. Recent continuum theories for wetting of flexible membranes reproduce our MD results qualitatively well. However, we find that when the curvature is large at the triple-phase contact line, the wetting angle increases with decreasing tension. This is in contrast to existing macroscopic theories but can be amended by allowing for a variable wetting angle.

Diameter-Optimum Spreading for the Impinging of Water Nanodroplets on Solid Surfaces

The impinging of water nanodroplets on solid surfaces is crucial to many nanotechnologies. Through large-scale molecular dynamics simulations, the size effect on the spreading of water nanodroplets after impinging on hydrophilic, graphite, and hydrophobic surfaces under low impinging velocities has been systematically studied. The spreading rates of nanodroplets first increase and then decrease and gradually become constant with the increase of nanodroplet diameter. The nanodroplets with the diameters of 17-19 nm possess the highest spreading rates because of the combined effect of the strongest interfacial interaction and the strongest surface interaction within water molecules. The highest water molecule densities, hydrogen bond numbers, and dielectric constants of interface and surface layers mainly contribute to the lowest interface work of adhesion and surface tension values at optimal diameters. These results unveil the nonmonotonic characteristics of spreading velocity, interface work of adhesion and surface tension with nanodroplet diameter for nanodroplets on solid surfaces.

Moving wetting ridges on ultrasoft gels

The surface mechanics of soft solids are important in many natural and technological applications. In this context, static and dynamic wetting of soft polymer gels has emerged as a versatile model system. Recent experimental observations have sparked controversial discussions of the underlying theoretical description, ranging from concentrated elastic forces over strain-dependent solid surface tensions to poroelastic deformations or the capillary extraction of liquid components in the gel. Here we present measurements of the shapes of moving wetting ridges with high spatiotemporal resolution, combining distinct wetting phases (water, FC-70, air) on different ultrasoft PDMS gels (∼100Pa). Comparing our experimental results to the asymptotic behavior of linear viscoelastocapillary theory in the vicinity of the ridge, we separate reliable measurements from potential resolution artifacts. Remarkably, we find that the commonly used elastocapillary scaling fails to collapse the ridge shapes, but, for small normal forces, yields a viable prediction of the dynamic ridge angles. We demonstrate that neither of the debated theoretical models delivers a quantitative description, while the capillary extraction of an oil skirt appears to be the most promising.

Influence of the Atmosphere on the Wettability of Polymer Brushes

Polymer brushes, i.e., end-tethered polymer chains on substrates, are sensitive to adaptation, e.g., swelling, adsorption, and reorientation of the surface molecules. This adaptation can originate from a contacting liquid or atmosphere for partially wetted substrates. The macroscopic contact angle of the aqueous drop can depend on both adaptation mechanisms. We analyze how the atmosphere around an aqueous droplet determines the resulting contact angle of the wetting droplet on polymer brush surfaces. Poly(N-isopropylacrylamide) (PNiPAAm)-based brushes are used due to their exceptional sensitivity to solvation and liquid mixture composition. We develop a method that reliably measures wetting properties when the drop and the surrounding atmosphere are not in equilibrium, e.g., when evaporation and condensation tend to contaminate the liquid of the drop and the atmosphere. For this purpose, we use a coaxial needle in the droplet, which continuously exchanges the wetting liquid, and in addition, we constantly exchange the almost saturated atmosphere. Depending on the wetting history, PNiPAAm can be prepared in two states, state A with a large water contact angle (∼65°) and state B with a small water contact angle (∼25°). With the coaxial needle, we can demonstrate that the water contact angle of a sample in state B significantly increases by ∼30° when a water-free atmosphere is almost saturated with ethanol, compared to an ethanol-free atmosphere at 50% relative humidity. For a sample in state A, the relative humidity has little influence on the water contact angle.

Curvature Adjustable Liquid Transport on Anisotropic Microstructured Elastic Film

Directional liquid transport is expected via adjusting chemical components, surface morphology, and external stimuli and is critical for practical applications. Although many studies have been conducted, there are still challenges to achieving real-time transformation of liquid transport direction on the material surface. Herein, we demonstrate a strategy to achieve curvature responsive anisotropic wetting on the elastic film with V-shaped prism microarray (VPM) microstructure, which can be used to control the direction of liquid transport. The results reveal that the curvature change of an elastic film can adjust the arrangement of V-shaped prisms on the elastic film. Correspondingly, the liquid wetting trend will change and even the moving direction reverses with varying arrangements of the V-shaped prisms on the elastic film. Meanwhile, surface hydrophobicity of the VPM elastic film also affects the liquid wetting trend and even shows the opposite transport direction of the liquid, which is up to the water wetting state on the VPM elastic film. Based on these results, the VPM elastic film can serve as a valve to control the liquid transport direction and is promising in the application of liquid directional harvest, chemical reaction, microfluidic, etc.

Direct force measurement of microscopic droplets pulled along soft surfaces

When a droplet is placed on a soft surface, surface tension deforms the substrate, creating a capillary ridge. We study how the motion of the ridge dissipates energy in microscopic droplets. Using a micropipette based method, we are able to simultaneously image and measure forces on a microscopic droplet moving at a constant speed along a soft film supported on a rigid substrate. Changing the thickness of the thin film tunes the effective stiffness of the substrate. Thus we can control the ridge size without altering the surface chemistry. We find that the dissipation depends strongly on the film thickness, decreasing monotonically as effective stiffness increases. This monotonic trend is beyond the realm of small deformation theory, but can be explained with a simple scaling analysis.

Elastic deformation of soft substrates occurs upon wetting, yet it is challenging to follow its dynamics at a microscale. Khattak et al. show that the force required to pull a droplet along a soft surface decreases monotonically as the film thickness decreases and explain the phenomenon using a scaling analysis.

The role of crosslinking density in surface stress and surface energy of soft solids

Surface stress and surface energy are two fundamental parameters that determine the surface properties of any material. While it is commonly believed that the surface stress and surface energy of liquids are identical, the relationship between the two parameters in soft polymeric gels remains debatable. In this work, we measured the surface stress and surface energy of soft silicone gels with varying weight ratios of crosslinkers in soft wetting experiments. Above a critical density, k₀, the surface stress was found to increase significantly with crosslinking density while the surface energy remained unchanged. In this regime, we can estimate a non-zero surface elastic modulus that also increases with the ratio of crosslinkers. By comparing the surface mechanics of the soft gels with their bulk rheology, the surface properties near the critical density k₀ were found to be closely related to the underlying percolation transition of the polymer networks.

Elasticity-to-Capillarity Transition in Soft Substrate Deformation

Whereas capillarity controls fluid dynamics at submillimeter scale and elasticity determines the mechanics of rigid solids, their coupling governs elastocapillary deformations on soft solids. Here, we directly probed the deformations on soft substrates induced by sessile nanodroplets. The wetting ridge created around the contact line and the dimple formed underneath the nanodroplet were imaged with a high spatial resolution using atomic force microscopy. The ridge height nonmonotonically depends on the substrate stiffness, and the dimple depth nonlinearly depends on the droplet size. The capillarity of the substrate overcomes the elasticity of the substrate in dominating the deformations when the elastocapillary length is approximately larger than the droplet contact radius, showing an experimental observation of the elasticity-to-capillarity transition. This study provides an experimental approach to investigate nanoscale elastocapillarity, and the insights have the potential to kick-off future work on the fundamentals of solid mechanics.

Gradient-dynamics model for liquid drops on elastic substrates

The wetting of soft elastic substrates exhibits many features that have no counterpart on rigid surfaces. Modelling the detailed elastocapillary interactions is challenging, and has so far been limited to single contact lines or single drops. Here we propose a reduced long-wave model that captures the main qualitative features of statics and dynamics of soft wetting, but which can be applied to ensembles of droplets. The model has the form of a gradient dynamics on an underlying free energy that reflects capillarity, wettability and compressional elasticity. With the model we first recover the double transition in the equilibrium contact angles that occurs when increasing substrate softness from ideally rigid towards very soft (i.e., liquid). Second, the spreading of single drops of partially and completely wetting liquids is considered showing that known dependencies of the dynamic contact angle on contact line velocity are well reproduced. Finally, we go beyond the single droplet picture and consider the coarsening for a two-drop system as well as for a large ensemble of drops. It is shown that the dominant coarsening mode changes with substrate softness in a nontrivial way.