Contact angle hysteresis at the nanoscale: a molecular dynamics simulation study

Molecular Simulation Study on the Wettability of a Surface Texturized with Hierarchical Pillars

By using molecular dynamics simulation, we investigate the wettability of a surface texturized with a periodic array of hierarchical pillars. By varying the height and spacing of the minor pillars on top of major pillars, we investigate the wetting transition from the Cassie-Baxter (CB) to Wenzel (WZ) states. We uncover the molecular structures and free energies of the transition and meta-stable states existing between the CB and WZ states. The relatively tall and dense minor pillars greatly enhance the hydrophobicity of a pillared surface, in that, the CB-to-WZ transition requires an increased activation energy and the contact angle of a water droplet on such a surface is significantly larger.

Contact Line Friction and Dynamic Contact Angles of a Capillary Bridge between Superhydrophobic Nanostructured Surfaces

The Cassie-Baxter state of wetting explains a large equilibrium contact angle and the slippery dynamics of a water droplet on a superhydrophobic rough surface. It also causes a contact angle hysteresis (CAH) which cannot be fully described by dynamic wetting theories including the molecular kinetic theory (MKT). We analyze the contact line dynamics on a superhydrophobic surface in the framework of the MKT. Multi-body dissipative particle dynamics simulations of a capillary bridge confined between two rough surfaces under steady shear are performed. We find that, in addition to the contact line friction force from the MKT, an additional friction force contribution is needed on rough surface, which is almost constant at all contact line velocities. Thus, it is directly related to the CAH. The CAH originates not only from contact line pinning but also from the shear flow due to the strong friction in the central region of the liquid-solid interface away from the contact line. The analysis of the particle flow inside the capillary bridge shows that liquid particles trapped in the grooves of the surface texture actually move with the same velocity as the surface, and exert strong additional friction to other liquid particles. This work extends the MKT to rough surfaces, as well as to elucidate the origin of the CAH of a capillary bridge. The finding would help to better understand also other situations of dynamic wetting on superhydrophobic surfaces.

Nanoscale Wetting of Crystalline Cellulose

Cellulose possesses considerable potential for a wide range of sustainable applications. Nanocellulose-based material properties are primarily dependent on the structural surface characteristics of its crystalline planes. Experimental measurements of the affinity of crystalline nanocellulose surfaces with water are scarce and challenging to obtain. Therefore, the relative hydrophilicity of different cellulose allomorphs crystalline planes is often inferred from qualitative assessments of their surface and the exposition of polar groups to the solvent. This work investigates the relative hydrophilicity of cellulose surfaces using molecular dynamics simulations. The behavior of a water droplet laid on different crystal planes was used to determine their relative hydrophilicity. The water molecules fully spread onto highly hydrophilic surfaces. However, a water droplet placed on less hydrophilic surfaces equilibrates as an oblate spheroidal cap allowing the measurement of a contact angle. The results indicate that the Iα (010), Iα (11̅0), Iβ (010), and Iβ (110) faces, as well as the faces of human-made celluloses II and III_I (100), (11̅0), (010), and (110) are all highly hydrophilic. They all have a contact angle value inferior to 11°. Not unexpectedly, the Iα (001) and Iβ (100) surfaces are less hydrophilic with contact angles of 48 and 34°, respectively. However, the Iβ (11̅0) plane, often referred to as a hydrophilic surface, forms a contact angle of about 32°. The results are rationalized in terms of structure, exposure of hydroxyl groups to the solvent, and degree of cellulose-cellulose versus cellulose-water hydrogen bonds on each face. The simulations also show that the surface oxidation degree tunes the surface hydrophilicity in a nonlinear manner due to cooperative effects involving water-cellulose interactions. Our study helps us to understand how the degree of hydrophilicity of cellulose emerges from specific structural features of each crystalline surface.

Size dependent influence of contact line pinning on wetting of nano-textured/patterned silica surfaces

Wetting behavior on a heterogeneous surface undergoes contact angle hysteresis as the droplet stabilized at a metastable state with a contact angle significantly different from its equilibrium value due to contact line pinning. However, there is a lack of consensus on how to calculate the influence of pinning forces. In general, the pinning effect can be characterized as (i) microscopic behavior when a droplet is pinned and the contact angle increases/decreases as the droplet volume increases/decreases and (ii) macroscopic behavior as the pinning effects decrease and ultimately, disappear with the increase of the droplet size. The current work studied both behaviors using molecular dynamics (MD) simulation with more than 300 different size water droplets on silica surfaces with three different patterns across two different wetting conditions. Results showed that the contact angle increases linearly with increasing droplet volume through the microscopic behavior, while the droplet is pinned on top of a certain number of patterns. When we normalized the droplet size with the corresponding pattern size, we observed a "wetting similarity" that linear microscopic contact angle variations over different size heterogeneities continuously line up. This shows that the pinning force remains constant and the resulting pinning effects are scalable by the size ratio between the droplet and pattern, independent of the size-scale. The slope of these microscopic linear variations decreases with an increase in the droplet size as observed through the macroscopic behavior. We further found a universal behavior in the variation of the corresponding pinning forces, independent of the wetting condition. In macroscopic behavior, pinning effects become negligible and the contact angle reaches the equilibrium value of the corresponding surface when the diameter of the free-standing droplet is approximately equal to 24 times the size of the surface structure. We found that the pinning effect is scalable with the droplet volume, not the size of the droplet base.

A Volume-Corrected Wenzel Model

The Wenzel model, commonly used for predicting the equilibrium contact angle (CA) of drops which penetrate the asperities of a rough surface, does not account for the liquid volume stored in the asperities. Interestingly, many previous experimental and molecular dynamics studies have noted discrepancies between observed CAs and those predicted by the Wenzel model because of this neglected liquid volume. Here, we apply a thermodynamic model to wetting of periodically patterned surfaces to derive a volume-corrected Wenzel equation in the limit of small pattern wavelength (compared to drop size). We show that the corrected equilibrium CA is smaller than that predicted by the Wenzel equation and that the reduction in CA can be significant when the liquid volume within the asperities becomes non-negligible compared to the total droplet volume. In such cases, the corrected CAs agree reasonably well with experimental observations and results of molecular dynamics simulations reported in previous studies.

Effect of substrate wettability and flexibility on the initial stage of water vapor condensation

Understanding the mechanisms of controlling vapor condensation on surfaces is of significant importance in many fields. Despite many efforts made in the investigation of vapor condensation, few studies concern the condensation on flexible substrates, especially in microscale. In this paper, the condensation of high temperature water vapor on substrate with various flexibilities and wettabilities is investigated using molecular dynamics simulation. The results indicate that when substrates with the same flexibility vary from hydrophobic to hydrophilic, the condensation rate increases and the condensation mode changes from no-condensation to dropwise condensation, incomplete filmwise condensation and filmwise condensation, and meanwhile, the heat exchange between the water vapor and the substrate becomes more efficient; when substrates with the same wettability vary from rigid to flexible, the nucleation density, the condensation rate and the heat exchange efficiency increase significantly. In particular, the condensation modes on rigid and flexible substrates with the same wettability are generally the same except for the substrates with εwater-Cu = 0.4 kcal mol-1; and the critical values of substrate spring constant for the condensation mode transition are about 80-100 kcal mol-1 Å-2 when εwater-Cu = 0.4 kcal mol-1. Therefore, changing the flexibility of the substrate is proposed as a new way to control the condensation mode at the initial stage of water vapor condensation to meet design requirements.

The Impact of the Electric Field on Surface Condensation of Water Vapor: Insight from Molecular Dynamics Simulation

In this study, molecular dynamics simulations were carried out to study the coupling effect of electric field strength and surface wettability on the condensation process of water vapor. Our results show that an electric field can rotate water molecules upward and restrict condensation. Formed clusters are stretched to become columns above the threshold strength of the field, causing the condensation rate to drop quickly. The enhancement of surface attraction force boosts the rearrangement of water molecules adjacent to the surface and exaggerates the threshold value for shape transformation. In addition, the contact area between clusters and the surface increases with increasing amounts of surface attraction force, which raises the condensation efficiency. Thus, the condensation rate of water vapor on a surface under an electric field is determined by competition between intermolecular forces from the electric field and the surface.

Dynamic Contact Angles and Mechanisms of Motion of Water Droplets Moving on Nanopillared Superhydrophobic Surfaces: A Molecular Dynamics Simulation Study

In this work, we investigate the dynamic advancing and receding contact angles, and the mechanisms of motion of water droplets moving across nanopillared superhydrophobic surfaces using molecular-dynamics simulation. We obtain equilibrium Cassie states of droplets on nanopillared surfaces with different pillar heights, groove widths, and intrinsic contact angles. We quantitatively evaluate the dynamic advancing and receding contact angles along the advancing direction of an applied body force, and find that they depend on the roughness parameters and the applied body force in a predictable way. The maximum dynamic advancing contact angle is 180°, and the minimum dynamic advancing contact angle is close to the static contact angle. On the receding side, the maximum dynamic receding contact angle is as large as 180°, while the minimum dynamic receding contact angle is close to the intrinsic contact angle of smooth surface. Interestingly, water droplets exhibit a "rolling" mechanism as they move across the surface, which is confirmed by movies of interfacial water molecules, as well as droplet velocity profiles.

Analyzing the Molecular Kinetics of Water Spreading on Hydrophobic Surfaces via Molecular Dynamics Simulation

In this paper, we report molecular kinetic analyses of water spreading on hydrophobic surfaces via molecular dynamics simulation. The hydrophobic surfaces are composed of amorphous polytetrafluoroethylene (PTFE) with a static contact angle of ~112.4° for water. On the basis of the molecular kinetic theory (MKT), the influences of both viscous damping and solid-liquid retarding were analyzed in evaluating contact line friction, which characterizes the frictional force on the contact line. The unit displacement length on PTFE was estimated to be ~0.621 nm and is ~4 times as long as the bond length of C-C backbone. The static friction coefficient was found to be ~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${10}^{-3}$$\end{document}10−3 Pa·s, which is on the same order of magnitude as the dynamic viscosity of water, and increases with the droplet size. A nondimensional number defined by the ratio of the standard deviation of wetting velocity to the characteristic wetting velocity was put forward to signify the strength of the inherent contact line fluctuation and unveil the mechanism of enhanced energy dissipation in nanoscale, whereas such effect would become insignificant in macroscale. Moreover, regarding a liquid droplet on hydrophobic or superhydrophobic surfaces, an approximate solution to the base radius development was derived by an asymptotic expansion approach.

Pore-scale simulation of wettability and interfacial tension effects on flooding process for enhanced oil recovery

For enhanced oil recovery (EOR) applications, the oil/water flow characteristics during the flooding process was numerically investigated with the volume-of-fluid method at the pore scale. A two-dimensional pore throat-body connecting structure was established, and four scenarios were simulated in this paper. For oil-saturated pores, the wettability effect on the flooding process was studied; for oil-unsaturated pores, three effects were modelled to investigate the oil/water phase flow behaviors, namely the wettability effect, the interfacial tension (IFT) effect, and the combined wettability/IFT effect. The results show that oil saturated pores with the water-wet state can lead to 25-40% more oil recovery than with the oil-wet state, and the remaining oil mainly stays in the near wall region of the pore bodies for oil-wet saturated pores. For oil-unsaturated pores, the wettability effects on the flooding process can help oil to detach from the pore walls. By decreasing the oil/water interfacial tension and altering the wettability from oil-wet to water-wet state, the remaining oil recovery rate can be enhanced successfully. The wettability-IFT combined effect shows better EOR potential compared with decreasing the interfacial tension alone under the oil-wet condition. The simulation results in this work are consistent with previous experimental and molecular dynamics simulation conclusions. The combination effect of the IFT reducation and wettability alteration can become an important recovery mechanism in future studies for nanoparticles, surfactant, and nanoparticle-surfactant hybrid flooding process.

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.

Nanoscale View of Dewetting and Coating on Partially Wetted Solids

There remain significant gaps in our ability to predict dewetting and wetting despite the extensive study over the past century. An important reason is the absence of nanoscopic knowledge about the processes near the moving contact line. This experimental study for the first time obtained the liquid morphology within 10 nm of the contact line, which was receding at low speed (U < 50 nm/s). The results put an end to long-standing debate about the microscopic contact angle, which turned out to be varying with the speed as opposed to the constant-angle assumption that has been frequently employed in modeling. Moreover, a residual film of nanometer thickness ubiquitously remained on the solid after the receding contact line passed. This microscopic residual film modified the solid surface and thus made dewetting far from a simple reverse of wetting. A complete scenario for dewetting and coating is provided.

Molecular origin of contact line stick-slip motion during droplet evaporation

Understanding and controlling the motion of the contact line is of critical importance for surface science studies as well as many industrial engineering applications. In this work, we elucidate the molecular origin of contact line stick-slip motion during the evaporation of liquid droplets on flexible nano-pillared surfaces using molecular dynamics simulations. We demonstrate that the evaporation-induced stick-slip motion of the contact line is a consequence of competition between pinning and depinning forces. Furthermore, the tangential force exerted by the pillared substrate on the contact line was observed to have a sawtooth-like oscillation. Our analysis also establishes that variations in the pinning force are accomplished through the self-adaptation of solid-liquid intermolecular distances, especially for liquid molecules sitting directly on top of the solid pillar. Consistent with our theoretical analysis, molecular dynamics simulations also show that the maximum pinning force is quantitatively related to both solid-liquid adhesion strength and liquid-vapor surface tension. These observations provide a fundamental understanding of contact line stick-slip motion on pillared substrates and also give insight into the microscopic interpretations of contact angle hysteresis, wetting transitions and dynamic spreading.

Lattice Boltzmann modeling of contact angle and its hysteresis in two-phase flow with large viscosity difference

Contact angle hysteresis is an important physical phenomenon omnipresent in nature and various industrial processes, but its effects are not considered in many existing multiphase flow simulations due to modeling complexity. In this work, a multiphase lattice Boltzmann method (LBM) is developed to simulate the contact-line dynamics with consideration of the contact angle hysteresis for a broad range of kinematic viscosity ratios. In this method, the immiscible two-phase flow is described by a color-fluid model, in which the multiple-relaxation-time collision operator is adopted to increase numerical stability and suppress unphysical spurious currents at the contact line. The contact angle hysteresis is introduced using the strategy proposed by Ding and Spelt [Ding and Spelt, J. Fluid Mech. 599, 341 (2008)JFLSA70022-112010.1017/S0022112008000190], and the geometrical wetting boundary condition is enforced to obtain the desired contact angle. This method is first validated by simulations of static contact angle and dynamic capillary intrusion process on ideal (smooth) surfaces. It is then used to simulate the dynamic behavior of a droplet on a nonideal (inhomogeneous) surface subject to a simple shear flow. When the droplet remains pinned on the surface due to hysteresis, the steady interface shapes of the droplet quantitatively agree well with the previous numerical results. Four typical motion modes of contact points, as observed in a recent study, are qualitatively reproduced with varying advancing and receding contact angles. The viscosity ratio is found to have a notable impact on the droplet deformation, breakup, and hysteresis behavior. Finally, this method is extended to simulate the droplet breakup in a microfluidic T junction, with one half of the wall surface ideal and the other half nonideal. Due to the contact angle hysteresis, the droplet asymmetrically breaks up into two daughter droplets with the smaller one in the nonideal branch channel, and the behavior of daughter droplets is significantly different in both branch channels. Also, it is found that the contact angle hysteresis is strengthened with decreasing the viscosity ratio, leading to an earlier droplet breakup and a decrease in the maximum length that the droplet can reach before the breakup. These simulation results manifest that the present multiphase LBM can be a useful substitute to Ba et al. [Phys. Rev. E 88, 043306 (2013)PLEEE81539-375510.1103/PhysRevE.88.043306] for modeling the contact angle hysteresis, and it can be easily implemented with higher computational efficiency.

Identifying Differences and Similarities in Static and Dynamic Contact Angles between Nanoscale and Microscale Textured Surfaces Using Molecular Dynamics Simulations

We quantify some of the effects of patterned nanoscale surface texture on static contact angles, dynamic contact angles, and dynamic contact angle hysteresis using molecular dynamics simulations of a moving Lennard-Jones droplet in contact with a solid surface. We observe static contact angles that change with the introduction of surface texture in a manner consistent with theoretical and experimental expectations. However, we find that the introduction of nanoscale surface texture at the length scale of 5-10 times the fluid particle size does not affect dynamic contact angle hysteresis even though it changes both the advancing and receding contact angles significantly. This result differs significantly from microscale experimental results where dynamic contact angle hysteresis decreases with the addition of surface texture due to an increase in the receding contact angle. Instead, we find that molecular-kinetic theory, previously applied only to nonpatterned surfaces, accurately describes dynamic contact angle and dynamic contact angle hysteresis behavior as a function of terminal fluid velocity. Therefore, at length scales of tens of nanometers, the kinetic phenomena such as contact line pinning observed at larger scales become insignificant in comparison to the effects of molecular fluctuations for moving droplets, even though the static properties are essentially scale-invariant. These findings may have implications for the design of highly hierarchical structures with particular wetting properties. We also find that quantitatively determining the trends observed in this article requires the careful selection of system and analysis parameters in order to achieve sufficient accuracy and precision in calculated contact angles. Therefore, we provide a detailed description of our two-surface, circular-fit approach to calculating static and dynamic contact angles on surfaces with nanoscale texturing.

Functional map of biological and biomimetic materials with hierarchical surface structures

The properties and functions of both biological and artificial materials with hierarchical surface structures are reviewed to establish the functional map of various hierarchical surface structures.

Wetting on physically patterned solid surfaces: the relevance of molecular dynamics simulations to macroscopic systems

We used molecular dynamics (MD) simulations to study the wetting of Lennard-Jones cylindrical droplets on surfaces patterned with grooves. By scaling the surface topography parameters with the droplet size, we find that the preferred wetting modes and contact angles become independent of the droplet size. This result is in agreement with a mathematical model for the droplet free energy at small Bond numbers for which the effects of gravity are negligible. The MD contact angles for various wetting modes are in good agreement with those predicted by the mathematical model. We construct phase diagrams of the dependence of the wetting modes observed in the MD simulations on the topography of the surface. Depending on the topographical parameters characterizing the surface, multiple wetting modes can be observed, as is also seen experimentally. Thus, our studies indicate that MD simulations can yield insight into the large-length-scale behavior of droplets on patterned surfaces.

Dynamics of nanoscale droplets on moving surfaces

We use molecular dynamics (MD) simulations to investigate the dynamic wetting of nanoscale water droplets on moving surfaces. The density and hydrogen bonding profiles along the direction normal to the surface are reported, and the width of the water depletion layer is evaluated first for droplets on three different static surfaces: silicon, graphite, and a fictitious superhydrophobic surface. The advancing and receding contact angles, and contact angle hysteresis, are then measured as a function of capillary number on smooth moving silicon and graphite surfaces. Our results for the silicon surface show that molecular displacements at the contact line are influenced greatly by interactions with the solid surface and partly by viscous dissipation effects induced through the movement of the surface. For the graphite surface, however, both the advancing and receding contact angles values are close to the static contact angle value and are independent of the capillary number; i.e., viscous dissipation effects are negligible. This finding is in contrast with the wetting dynamics of macroscale water droplets, which show significant dependence on the capillary number.