The density distributions and contact angles of liquid nanodrops on nanorough solid surfaces are determined on the basis of a nonlocal density functional theory. Two kinds of roughness, chemical and physical, are examined. The former considers the substrate as a sequence of two kinds of semi-infinite vertical plates of equal thicknesses but of different natures with different strengths for the liquid-solid interactions. The physical roughness involves an ordered set of pillars on a flat homogeneous surface. Both hydrophobic and hydrophilic surfaces were considered. For the chemical roughness, the contact angle which the drop makes with the flat surface increases when the strength of the liquid-solid interaction for one kind of plates decreases with respect to the fixed value of the other kind of plates. Such a behavior is in agreement with the Cassie-Baxter expression derived from macroscopic considerations. For the physical roughness on a hydrophobic surface, the contact angle which a drop makes with the plane containing the tops of the pillars increases with increasing roughness. Such a behavior is consistent with the Wenzel formula developed for macroscopic drops. For hydrophilic surfaces, as the roughness increases the contact angle first increases, in contradiction with the Wenzel formula, which predicts for hydrophilic surfaces a decrease of the contact angle with increasing roughness. However, a further increase in roughness changes nonmonotonously the contact angle, and at some roughness, the drop disappears and only a liquid film is present on the surface. It was also found that the contact angle has a periodic dependence on the volume of the drop.
The density profiles in a fluid interacting with the two identical solid walls of a closed long slit were calculated for wide ranges of the number of fluid molecules in the slit and temperature by employing a nonlocal density functional theory. Using argon as the sample fluid and considering the walls composed of solid carbon dioxide, it is shown that the density profile corresponding to the stable state of the fluid considerably changes its shape with increasing average density rho(av) of the fluid inside the slit. Temperature dependent critical values rho(sb1) and rho(sb2) of rho(av) were identified, such that for rho(sb1)
The microscopic approach of ref regarding the shape and stability of a liquid drop on a bare solid surface is extended to include the structuring of the liquid near the solid surface. It is supposed that the liquid molecules near the solid form a monolayer, which is characterized by a surface number density and short- and long-range interactions with the solid. The rest of the drop is considered as a continuous medium with only long-range interactions with the solid. Two kinds of droplets, cylindrical (two-dimensional) and axisymmetrical (three-dimensional), were examined for two types of interaction potentials similar to the London−van der Waals and the Lennard-Jones ones. The microcontact angle, θ0, that the drop profile makes with the solid surface is dependent on the microscopic parameters of the model (strength of intermolecular interactions, densities of liquid and solid phases, hard core radius, etc.), whereas in the previous continuum picture of ref , it was constant and equal to 180°. All drop characteristics, such as stability, shape, and macroscopic contact angle, become functions of θ0 and a certain parameter a dependent on the model interaction parameters. There are two domains in the plane θ0−a for the drop stability, separated by a critical curve. In the first domain, the drop can have any height, h m, at its apex and is always stable. In the second domain, h m is limited by a critical value, h c, which depends on a and θ0, and drops with h m > h c cannot exist. The drop shape depends on whether the point (θ0, a) on the θ0−a plane is far from the critical curve or near it. In the first case, the drop profile has a large circular part, while in the second case, the shape is almost planar. By extrapolating for sufficiently large drops the spherical part to the solid surface, one can obtain the macroscopic (apparent) contact angle, which is accessible experimentally. In the region near the solid surface, the tangent to the profile makes with the solid surface an angle that varies rapidly between the microcontact angle, θ0, and the macroscopic contact angle,θm.
A two-dimensional nanodrop on a vertical rough solid surface is examined using a nonlocal density functional theory in the presence of gravity. The roughness is modeled either as a chemical inhomogeneity of the solid or as a result of the decoration with pillars of a smooth homogeneous surface. From the obtained fluid density distribution, the sticking force, which opposes the drop motion along an inclined surface, and the contact angles on the lower and upper leading edges of the drop are calculated. On the basis of these results, it is shown that the macroscopically derived equation for a drop in equilibrium on an inclined surface is also applicable to nanodrops. The liquid-vapor surface tension involved in this equation was calculated for various specific cases, and the values obtained are of the same order of magnitude as those obtained in macroscopic experiments.
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