Films, layers, and droplets: The effect of near-wall fluid structure on spreading dynamics

Flowerlike Spreading of Micellar Films during Emulsion Drop Evaporation

We investigated the film spreading during the evaporation of submillimeter oil-in-water emulsion droplets on a solid surface, and observed a novel phenomenon where the film follows a two-layer spreading. In combination with the instability at the film front, the spreading front acquires a flowerlike pattern. The emergence of the two-layer structure is attributed to micelles within the oil film that yield an oscillating disjoining pressure. By considering both the slipping condition and the disjoining pressure, a scaling analysis is carried out that agrees well with the observed film spreading dynamics. The film spreading follows Tanner's law initially, while it becomes faster at a later stage, where the film radius follows r∼t^{1/2} for weak slip and r∼t^{3/8} for strong slip conditions.

Binding potential and wetting behavior of binary liquid mixtures on surfaces

We present a theory for the interfacial wetting phase behavior of binary liquid mixtures on rigid solid substrates, applicable to both miscible and immiscible mixtures. In particular, we calculate the binding potential as a function of the adsorptions, i.e., the excess amounts of each of the two liquids at the substrate. The binding potential fully describes the corresponding interfacial thermodynamics. Our approach is based on classical density functional theory. Binary liquid mixtures can exhibit complex bulk phase behavior, including both liquid-liquid and vapor-liquid phase separation, depending on the nature of the interactions among all the particles of the two different liquids, the temperature, and the chemical potentials. Here we show that the interplay between the bulk phase behavior of the mixture and the properties of the interactions with the substrate gives rise to a wide variety of interfacial phase behaviors, including mixing and demixing situations. We find situations where the final state is a coexistence of up to three different phases. We determine how the liquid density profiles close to the substrate change as the interaction parameters are varied and how these determine the form of the binding potential, which in certain cases can be a multivalued function of the adsorptions. We also present profiles for sessile droplets of both miscible and immiscible binary liquids.

Surface tension of bulky colloids, capillarity under gravity, and the microscopic origin of the Kardar-Parisi-Zhang equation

Experimental measurements of the surface tension of colloidal interfaces have long been in conflict with computer simulations. In this Letter we show that the surface tension of colloids as measured by surface fluctuations picks up a gravity-dependent contribution which removes the discrepancy. The presence of this term puts a strong constraint on the structure of the interface which allows one to identify corrections to the fundamental equation of equilibrium capillarity and deduce bottom up the microscopic origin of a growth model with close relation to the Kardar-Parisi-Zhang equation.

How ice grows from premelting films and water droplets

Close to the triple point, the surface of ice is covered by a thin liquid layer (so-called quasi-liquid layer) which crucially impacts growth and melting rates. Experimental probes cannot observe the growth processes below this layer, and classical models of growth by vapor deposition do not account for the formation of premelting films. Here, we develop a mesoscopic model of liquid-film mediated ice growth, and identify the various resulting growth regimes. At low saturation, freezing proceeds by terrace spreading, but the motion of the buried solid is conveyed through the liquid to the outer liquid-vapor interface. At higher saturations water droplets condense, a large crater forms below, and freezing proceeds undetectably beneath the droplet. Our approach is a general framework that naturally models freezing close to three phase coexistence and provides a first principle theory of ice growth and melting which may prove useful in the geosciences.

Binding potentials for vapour nanobubbles on surfaces using density functional theory

We calculate density profiles of a simple model fluid in contact with a planar surface using density functional theory (DFT), in particular for the case where there is a vapour layer intruding between the wall and the bulk liquid. We apply the method of Hughes et al (2015 J. Chem. Phys. 142 074702) to calculate the density profiles for varying (specified) amounts of the vapour adsorbed at the wall. This is equivalent to varying the thickness h of the vapour at the surface. From the resulting sequence of density profiles we calculate the thermodynamic grand potential as h is varied and thereby determine the binding potential as a function of h. The binding potential obtained via this coarse-graining approach allows us to determine the disjoining pressure in the film and also to predict the shape of vapour nano-bubbles on the surface. Our microscopic DFT based approach captures information from length scales much smaller than some commonly used models in continuum mechanics.

Equilibrium Contact Angle and Adsorption Layer Properties with Surfactants

The three-phase contact line of a droplet on a smooth surface can be characterized by the Young equation. It relates the interfacial energies to the macroscopic contact angle θ_e. On the mesoscale, wettability is modeled by a film-height-dependent wetting energy f( h). Macro- and mesoscale descriptions are consistent if γ cos θ_e = γ + f( h_a), where γ and h_a are the liquid-gas interface energy and the thickness of the equilibrium liquid adsorption layer, respectively. Here, we derive a similar consistency condition for the case of a liquid covered by an insoluble surfactant. At equilibrium, the surfactant is spatially inhomogeneously distributed, implying a nontrivial dependence of θ_e on surfactant concentration. We derive macroscopic and mesoscopic descriptions of a contact line at equilibrium and show that they are consistent only if a particular dependence of the wetting energy on the surfactant concentration is imposed. This is illustrated by a simple example of dilute surfactants, for which we show excellent agreement between theory and time-dependent numerical simulations.

Influence of Salt on Supramolecular Oscillatory Structural Forces and Stratification in Micellar Freestanding Films

Freestanding films of soft matter containing micelles, nanoparticles, polyelectrolyte-surfactant complexes, bilayers, and smectic liquid crystals exhibit stratification. Stepwise thinning and coexisting thick-thin regions associated with drainage via stratification are attributed to the confinement-induced structuring and layering of supramolecular structures, which contribute supramolecular oscillatory structural forces. In freestanding micellar films, formed by a solution of an ionic surfactant above its critical micelle concentration, both interfacial adsorption and the micelle size and shape are determined by the concentration of surfactant and of added electrolytes. Although the influence of surfactant concentration on stratification has been investigated before, the influence of added salt, at concentrations typically found in water used on a daily basis, has not been investigated yet. In this contribution, we elucidate how the addition of salt affects stepwise thinning: step size, number of steps, as well as the shape and size of nanoscopic nonflat structures such as mesas in micellar foam films formed with aqueous solutions of anionic surfactant (sodium dodecyl sulfate (SDS)). The nanoscopic thickness variations and transitions are visualized and analyzed using IDIOM (Interferometry Digital Imaging Optical Microscopy) protocols with exquisite spatiotemporal resolution (thickness ∼1 nm, time <1 ms). In contrast to nanoparticle dispersions that show no influence of salt on step size, we find that the addition of salt to micellar freestanding films results in a decrease in step size as well as the number of stepwise transitions, in addition to changes in nucleation and growth of mesas, all driven by the corresponding change in supramolecular oscillatory structural forces.

Dynamical Density Functional Theory for the Evaporation of Droplets of Nanoparticle Suspension

We develop a lattice gas model for the drying of droplets of a nanoparticle suspension on a planar surface, using dynamical density functional theory (DDFT) to describe the time evolution of the solvent and nanoparticle density profiles. The DDFT assumes a diffusive dynamics but does not include the advective hydrodynamics of the solvent, so the model is relevant to highly viscous or near to equilibrium systems. Nonetheless, we see an equivalent of the coffee-ring stain effect, but in the present model it occurs for thermodynamic rather the fluid-mechanical reasons. The model incorporates the effect of phase separation and vertical density variations within the droplet and the consequence of these on the nanoparticle deposition pattern on the surface. We show how to include the effect of slip or no-slip at the surface and how this is related to the receding contact angle. We also determine how the equilibrium contact angle depends on the microscopic interaction parameters.

Nudged elastic band calculation of the binding potential for liquids at interfaces

The wetting behavior of a liquid on solid substrates is governed by the nature of the effective interaction between the liquid-gas and the solid-liquid interfaces, which is described by the binding or wetting potential g(h) which is an excess free energy per unit area that depends on the liquid film height h. Given a microscopic theory for the liquid, to determine g(h), one must calculate the free energy for liquid films of any given value of h, i.e., one needs to create and analyze out-of-equilibrium states, since at equilibrium there is a unique value of h, specified by the temperature and chemical potential of the surrounding gas. Here we introduce a Nudged Elastic Band (NEB) approach to calculate g(h) and illustrate the method by applying it in conjunction with a microscopic lattice density functional theory for the liquid. We also show that the NEB results are identical to those obtained with an established method based on using a fictitious additional potential to stabilize the non-equilibrium states. The advantages of the NEB approach are discussed.