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Within mean-field theory we study wetting of elastic substrates. Our analysis is based on a grand canonical free energy functional of the fluid number density and of the substrate displacement field. The substrate is described in terms of the linear theory of elasticity, parametrized by two Lame coefficients. The fluid contribution is of the van der Waals type. Two potentials characterize the interparticle interactions in the system. The long-ranged attraction between the fluid particles is described by a potential $w(r)$, and $v(r)$ characterizes the substrate-fluid interaction. By integrating out the elastic degrees of freedom we obtain an effective theory for the fluid number density alone. Its structure is similar to the one for wetting of an inert substrate. However, the potential $w(r)$ is replaced by an effective potential which, in addition to $w(r)$, contains a term bilinear in $v(r)$. We discuss the corresponding wetting transitions in terms of an effective interface potential $omega(ell)$, where $ell$ denotes the thickness of the wetting layer. We show that in the case of algebraically decaying interactions the elasticity of the substrate may suppress critical wetting transitions, and may even turn them first order.
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We report on the effect of intermolecular forces on the fluctuations of supported liquid films. Using an optically-induced thermal gradient, we form nanometer-thin films of wetting liquids on glass substrates, where van der Waals forces are balanced by thermocapillary forces. We show that the fluctuation dynamics of the film interface is strongly modified by intermolecular forces at lower frequencies. Data spanning three frequency decades are in excellent agreement with theoretical predictions accounting for van der Waals forces. Our results emphasize the relevance of intermolecular forces on thermal fluctuations when fluids are confined at the nanoscale.
A mean-field theory is presented which describes the basic observations of recent experiments revealing rich wetting behaviour of n-alkane/methanol mixtures at the liquid-vapour interface. The theory, qualitative and in part heuristic, is based on a microscopic lattice-gas model from which a Cahn-Landau approach is distilled. Besides the physics associated with the short-range components of the intermolecular interactions, effects of the long-range tails of the net van der Waals forces between interfaces are also taken into account. Including weak long-range forces which favour wetting in the theory does not visibly alter the critical wetting transition for the nonane/methanol mixture, in contrast with the generic expectation of first-order wetting for such systems, but in good agreement with experiment. For decane/methanol weak long-range forces bring the transition very close to the prewetting critical point, leading to an adsorption behaviour closely reminiscent of short-range tricritical wetting, observed experimentally for alkane chain length between 9.6 and 10. Finally, for undecane/methanol the transition is clearly of first order. First-order wetting is also seen in the experiment.
The understanding of sliding friction for wet, patterned surfaces from first principles is challenging. While emerging applications have sought design principles from biology, a general framework is lacking because soft interfaces experience a multiphysics coupling between solid deformation and fluid dissipation. We investigate the elastohydrodynamic sliding of >50 patterned sliding pairs comprising elastomers, thermosets, and hydrogels, and discover that texturing induces a critical transition in the macroscopic friction coefficient. This critical friction scales universally, without any fitting parameters, with the reduced elastic modulus and the pattern geometry. To capture the frictional dissipation, we separate the flow curve into two regimes and account for the contributions of shear and normal forces applied by the fluid on the patterns. Our model combines Reynolds equations and elastic deformation to provide physical insights that allow engineering of the elastohydrodynamic friction in a class of soft tribopairs using pattern geometry, material elasticity, and fluid properties.
We introduce an accurate and efficient method for characterizing surface wetting and interfacial properties, such as the contact angle made by a liquid droplet on a solid surface, and the vapor-liquid surface tension of a fluid. The method makes use of molecular simulations in conjunction with the indirect umbrella sampling technique to systematically wet the surface and estimate the corresponding free energy. To illustrate the method, we study the wetting of a family of Lennard-Jones surfaces by water. We estimate contact angles for surfaces with a wide range of attractions for water by using our method and also by using droplet shapes. Notably, as surface-water attractions are increased, our method is able to capture the transition from partial to complete wetting. Finally, the method is straightforward to implement and computationally efficient, providing accurate contact angle estimates in roughly 5 nanoseconds of simulation time.
A thin liquid film with non-zero curvature at its free surface spontaneously flows to reach a flat configuration, a process driven by Laplace pressure gradients and resisted by the liquids viscosity. Inspired by recent progresses on the dynamics of liquid droplets on soft substrates, we here study the relaxation of a viscous film supported by an elastic foundation. Experiments involve thin polymer films on elastomeric substrates, where the dynamics of the liquid-air interface is monitored using atomic force microscopy. A theoretical model that describes the coupled evolution of the solid-liquid and the liquid-air interfaces is also provided. In this soft-levelling configuration, Laplace pressure gradients not only drive the flow, but they also induce elastic deformations on the substrate that affect the flow and the shape of the liquid-air interface itself. This process represents an original example of elastocapillarity that is not mediated by the presence of a contact line. We discuss the impact of the elastic contribution on the levelling dynamics and show the departure from the classical self-similarities and power laws observed for capillary levelling on rigid substrates.
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