Nanodrop on a smooth solid surface with hidden roughness. Density functional theory considerations

Prediction of Contact Angles and Density Profiles of Sessile Droplets Using Classical Density Functional Theory Based on the PCP-SAFT Equation of State

This study demonstrates the capability of the density functional theory (DFT) formalism to predict contact angles and density profiles of model fluids and of real substances in good quantitative agreement with molecular simulations and experimental data. The DFT problem is written in cylindrical coordinates, and the solid-fluid interactions are defined as external potentials toward the fluid phase. Monte Carlo (MC) molecular simulations are conducted in order to assess the density profiles resulting from the Helmholtz energy functional used in the DFT formalism. Good quantitative agreement between DFT predictions and MC results for Lennard-Jones and ethane nanodroplets is observed, both for density profiles and for contact angles. That comparison suggests, first, that the Helmholtz energy functional proposed in a previous study [ Sauer , E. ; Gross , J. Ind. Eng. Chem. Res. 56 , 2017 , 4119 - 4135 ] is suitable for three-phase contact lines and, second, that Lagrange multipliers can be used to constrain the number of molecules, similar to a canonical ensemble. Experiments of sessile droplets on solid surfaces are performed to assess whether a real solid with its microscopic roughness can be described through a simple model potential. Comparison of DFT results to experimental data is done for a Teflon surface because Teflon can be regarded as a substrate exhibiting only attractive interactions of van der Waals type. It is shown that the real solid can be described as a perfectly planar solid with effective solvent-to-solid interactions, defined through a single adjustable parameter for the solid. Subsequent predictions for the contact angle of eight solvents, including polar components such as water, are found in very good agreement to experimental data using simple Berthelot-Lorentz combining rules. For the eight investigated solvents, we find mean absolute deviations of 3.77°.

Wetting hysteresis of nanodrops on nanorough surfaces

Nanodrops on smooth or patterned rough surfaces are explored by many-body dissipative particle dynamics to demonstrate the influence of surface roughness on droplet wetting. On a smooth surface, nanodrops exhibit the random motion and contact angle hysteresis is absent. The diffusivity decays as the intrinsic contact angle (θ_{Y}) decreases. On a rough surface, the contact line is pinned and the most stable contact angle (θ_{Y}^{'}) is acquired. The extent of contact angle hysteresis (Δθ) is determined by two approaches, which resemble the inflation-deflation method and inclined plane method for experiments. The hysteresis loop is acquired and both approaches yield consistent results. The influences of wettability and surface roughness on θ_{Y}^{'} and Δθ are examined. θ_{Y}^{'} deviates from that estimated by the Wenzel or Cassie-Baxter models. This consequence can be explained by the extent of impregnation, which varies with the groove position and wettability. Moreover, contact angle hysteresis depends more on the groove width than the depth.

Calculation of nanodrop profile from fluid density distribution

Two approaches are examined, which can be used to determine the drop profile from the fluid density distributions (FDDs) obtained on the basis of microscopic theories. For simplicity, only two-dimensional (cylindrical, or axisymmetrical) distributions are examined and it is assumed that the fluid is either in contact with a smooth solid or separated from the smooth solid by a lubricating liquid film. The first approach is based on the sharp-kink interface approximation in which the density of the liquid inside and the density of the vapor outside the drop are constant with the exception of the surface layer of the drop where the density is different from the above ones. In this case, the drop profile was calculated by minimizing the total potential energy of the system. The second approach is based on a nonuniform FDD obtained either by the density functional theory or molecular dynamics simulations. To determine the drop profile from such an FDD, which does not contain sharp interfaces, three procedures can be used. In the first two procedures, P1 and P2, the one-dimensional FDDs along straight lines which are parallel to the surface of the solid are extracted from the two-dimensional FDD. Each of those one-dimensional FDDs has a vapor-liquid interface at which the fluid density changes from vapor-like to liquid-like values. Procedure P1 uses the locations of the equimolar dividing surfaces for the one-dimensional FDDs as points of the drop profile. Procedure P2 is based on the assumption that the fluid density is constant on the surface of the drop, that density being selected either arbitrarily or as a fluid density at the location of the equimolar dividing surface for one of the one-dimensional FDDs employed in procedure P1. In the third procedure, P3, which is suggested for the first time in this paper, the one-dimensional FDDs are taken along the straight lines passing through a selected point inside the drop (radial line). Then, the drop profile is calculated like in procedure P1. It is shown, that procedure P3 provides a drop profile which is more reasonable than the other ones. Relationship of the discussed procedures to those used in image analysis is briefly discussed.

A nanodrop on the surface of a lubricating liquid covering a rough solid surface

A two-component fluid consisting of a lubricating fluid (LF) that covers a rough solid surface (surface decorated by periodic array of identical pillars) and a test fluid (TF) as a nanodrop over LF is considered. A horizontal external perturbative force is applied to TF and the density functional theory is used for the treatment of the system. The concepts of advancing and receding contact angles as well as of leading edges of the drop are revisited. Three different definitions of the contact angles are analyzed and the most plausible selected. The contact angles are calculated as functions of drop size and magnitude of the perturbative force. For small drops, both angles change nonmonotonously with increasing perturbative force. For larger drops, the advancing contact angle has the tendency to increase and the receding contact angle to decrease with increasing force. The sticking force which maintains the drop equilibrium in the presence of an external perturbative force is determined as function of the contact angles. It is shown that this dependence is similar to that for a drop on a rough solid surface in the absence of LF. A critical sticking force, defined as the largest value of the perturbative force for which the drop remains at equilibrium, is determined.