Session M36: Drops: Wall-bound

Corner wetting during the vapor-liquid-solid growth of faceted nanowires

We consider the corner wetting of liquid drops in the context of vapor-liquid-solid growth of nanowires. Specifically, we construct numerical solutions for the equilibrium shape of a liquid drop on top of a faceted nanowire by solving the Laplace-Young equation with a free boundary determined by mixed boundary conditions. A key result for nanowire growth is that for a range of contact angles there is no equilibrium drop shape that completely wets the corner of the faceted nanowire. Based on our numerical solutions we determine the scaling behavior for the singular surface behavior near corners of the nanowire in terms of the Young contact angle and drop volume.   

Measuring static and dynamic contact angles using a liquid needle.

The optical determination of static and advancing contact angle is made on drops applied or extended, respectively, onto a substrate through the use of thin solid needles. Although this method has been used extensively, this method of dosing can be time consuming, cumbersome and if not meticulously performed can lead to erroneous contact angle results. Herein, we present an alternative way of applying drops onto substrates using a small liquid jet, which is produced by a liquid pressure dosing system acting as a ``liquid needle.'' A comparative static contact angle study on 14 different surfaces with two different liquids were performed utilizing two different ways of dosing: the conventional solid and a novel liquid needle based technique. We found, for all but one sample, that the obtained results were highly comparable. Observed differences can be explained by the characteristics of either way of dosing. In addition, we used the liquid pressure based dosing system for optical advancing contact angle measurement on two different samples. The liquid needle based method facilitates the expansion of a drop from 0.1 to 22 $\mu $L within less than 1.2 seconds, which provided constant contact angle versus drop base diameter curves. The obtained results were highly comparable with dynamic Wilhelmy contact angle measurements.   

Static 2D solutions for the profiles of liquids on rigid substrates, including the special case of droplets with finite-length precursor films

We present analytical solutions for the shape of static bidimensional profiles of a liquid resting on a substrate under partial-wetting conditions imposed by means of a two-term disjoining–conjoining pressure. In contrast with previous works where we studied the shape of droplets surrounded by infinite precursor films [Gomba, J. M. {\&} Homsy, G. M \textit{Langmuir} 25, 5684 (2009)], [Gomba, J. M. {\&} Perazzo, C. A \textit{Phys. Rev. E} 86, 056310 (2012)], [Mac Intyre, J. R. {\&} Gomba, J. M. {\&} Perazzo, C. A \textit{J. Eng. Math.}, in press (2016)], here we do not impose restrictions on the shape of the profile. We show that for quite general disjoining–conjoining pressure, the free surface can adopt only 5 non–trivial static patterns. In particular we find solutions when the height goes to zero which describe satisfactorily the profile of a finite amount of fluid deposited on a substrate. Interestingly, one of the solutions represents the shape of a droplet surrounded by a finite length precursor film. We make a parametric study and identify the regions where each solution can be found. We compare the solutions with the corresponding ones obtained by more complete models (where the hypothesis of the lubrication approximation is not strictly valid) and with axisymmetric s   

Effects of induced vibration modes on droplet sliding phenomena

An analytical and experimental investigation has been undertaken to understand the effects of induced vibration modes on droplet sliding phenomena. A mathematical model has been postulated which is capable of estimating accurately droplet sliding angles when using hydrophobic and hydrophilic surfaces. The model, which takes into account equilibrium contact angle, contact angle hysteresis, and droplet volume, has been validated using experimental data. The model has been modified to be able to estimate droplet sliding angle when different modes of vibrations are imposed on the surfaces. Experimental results to date reveal that when resonance modes of vibrations are imposed, the droplet sliding angles decrease considerably. The results also indicate that the modified model can be used effectively to relate imposed resonance frequencies to the critical sliding angle of droplets.   

Capillary adhesion forces between flexible fibers

We consider the capillary adhesion produced by a drop placed between two elastic fibers. We measure the force exerted by the drop as we vary the inter-fiber distance, and report two types of wet adhesion: a weak capillary adhesion, where a liquid drop bridges the fibers, and a strong elastocapillary adhesion where the liquid is spread between two collapsed fibers. The weak adhesion is characterized by a force that increases linearly with the liquid length. With flexible fibers, the force exerted by the drop can induce deformation and rapid collapse, or zipping, of the fibers. This zipping results in a sudden increase of the wetted length and a force that departs from the linear evolution. As the inter-fiber distance is subsequently increased, the liquid length decreases while the fibers deformation increases, and the force actually reaches a plateau, i.e. remains constant until unzipping, or detachment of the fibers occurs. We measure the value of this plateau, i.e. the maximal adhesion force, as we vary the drop volume and the fibers elasticity. We also show that flexibility extends capillary adhesion to inter-fiber distances impossible to reach with rigid fibers, while keeping a constant pull-out force characteristic of the elastocapillary coupling.   

Molecular dynamics analysis of a equilibrium nanoscale droplet on a solid surface with periodic roughness

Molecular dynamics simulations of the equilibrium wetting behavior of hemi-cylindrical argon droplets on solid surfaces with a periodic roughness were carried out. The rough solid surface is located at the bottom of the calculation cell with periodic boundary conditions in surface lateral directions and mirror boundary condition at the top boundary. Similar to on a smooth surface, the change of the cosine of the droplet contact angle was linearly correlated to the potential well depth of the inter-atomic interaction between liquid and solid on a surface with a short roughness period while the correlation was deviated on one with a long roughness period. To further investigate this feature, solid-liquid, solid-vapor interfacial free energies per unit projected area of solid surface were evaluated by using the thermodynamic integration method in independent quasi-one-dimensional simulation systems with a liquid-solid interface or vapor-solid interface on various rough solid surfaces at a constant pressure. The cosine of the apparent contact angles estimated from the density profile of the droplet systems corresponded well with ones calculated from Young's equation using the interfacial energies evaluated in the quasi-one dimensional systems.   

Shapes of randomly placed droplets

Surface characterization is essential for many industrial applications. Surface defects result in a range of contact angles, which lead to Contact Angle Hysteresis (CAH). We use shapes of randomly shaped drops on surfaces to study the family of shapes that may result from CAH. We image the triple line from these drops and extract additional information related to local contact angles as well as curvatures from these images. We perform a generalized extreme value analysis (GEV) on this microscopic contact angle data. From this analysis, we predict a range for extreme contact angles that are possible for a sessile drop. We have also measured the macroscopic advancing and receding contact angles using a Goniometer. From the extreme values of the contact line curvature, we estimate the pinning stress distribution responsible for the random shapes. It is seen that this range follows the same trend as the macroscopic CAH measured using a Goniometer, and can be used as a method of characterizing the surface.   

Three dimensional force balance of asymmetric droplets

An equilibrium contact angle of a droplet is determined by a horizontal force balance among vapor, liquid, and solid, which is known as Young's law. Conventional wetting law is valid only for axis-symmetric droplets, whereas real droplets are often asymmetric. Here we show that three-dimensional geometry must be considered for a force balance for asymmetric droplets. By visualizing asymmetric droplets placed on a free-standing membrane in air with X-ray microscopy, we are able to identify that force balances in one side and in other side control pinning behaviors during evaporation of droplets. We find that X-ray microscopy is powerful for realizing the three-dimensional force balance, which would be essential in interpretation and manipulation of wetting, spreading, and drying dynamics for asymmetric droplets.   

Nanodrop contact angles from molecular dynamics simulations

The contact angle between three phases being in thermodynamic equilibrium is highly sensitive to the nature of the intermolecular forces as well as to various fluctuation effects. Determining the Young contact angle of a sessile drop sitting on a substrate from molecular dynamics (MD) simulations is a highly non-trivial task. Most commonly employed methods for finding droplet contact angles from MD simulation data either require large numbers of particles or are system-dependent. We propose a systematic geometry based methodology for extracting the contact angle from simulated sessile droplets by analysing an appropriately coarse-grained density field. To demonstrate the method, we consider Lennard-Jones (LJ) and SPC/E water nanodroplets of different sizes sitting on planar LJ walls. Our results are in good agreement with Young contact angle values computed employing test-area perturbation method.   

Footprint Geometry and Sessile Drop Resonance

How does a sessile drop resonate if its footprint is square (square drop)? In this talk, we discuss the two distinct families of observed modes in our experiments. One family (spherical modes) is identified with the natural modes of capillary spherical caps, and the other (grid modes) with Faraday waves on a square bath (square Faraday waves). A square drop exhibits grid or spherical modes depending on its volume, and the two families of modes arise depending on how wavenumber selection of footprint geometry and capillarity compete. For square drops, a dominant effect of footprint constraint leads to grid modes which are constrained response; otherwise the drops exhibit spherical modes, the characteristic of sessile drops on flat plates.