Microscopic Contact Angle Research Articles

Wear behavior of plasma and HVOF sprayed WC-12Co + 6% ETFE coatings on AA2024-T6 aluminum alloy

In this study, WC-12Co + 6% ethylene trifluoroethylene (ETFE) coatings were formed on the surface of an AA2024-T6 aluminum alloy using both plasma spray and high velocity oxygen fuel (HVOF) processes. The characterization of the coatings was made by microscopic examinations, thickness, porosity, contact angle and hardness measurements and X-ray diffraction (XRD) analysis. The coefficient of friction and wear resistance of coatings were obtained using a reciprocating wear tester by rubbing a 10 mm diameter Al 2O 3 ball on the coatings in dry and acid environments. It was observed that the WC-12Co + 6% ETFE coating sprayed using HVOF method exhibited higher hardness and contact angle, better tribological performance and higher amount of retained WC when compared to the plasma sprayed WC-12Co + 6% ETFE coating. The wear resistance of the HVOF sprayed WC-12Co + 6% ETFE coating tested in acid environment was almost one and a half times bigger than that of dry sliding condition, but the plasma sprayed WC-12Co + 6% ETFE coating tested in acid environment showed a lower wear resistance when compared to the result of the experiment performed on dry sliding condition.

Superheating of liquid xenon in metal tubes

The method of measuring the lifetime has been used to investigate the kinetics of spontaneous boiling-up of superheated xenon in copper tubes. In experiments the temperature dependence of the mean lifetime has been determined at pressures of 1.48 and 1.98 MPa. The data obtained have been compared with homogeneous nucleation theory. It has been found that experimental values of the attainable superheating temperature and the derivative (partial differential ln J/partial differential T)p are systematically lower than their theoretical values. A description of experimental data in the framework of heterogeneous nucleation theory has shown that for the agreement of theory and experiment with the use of a macroscopic model of nucleation on a smooth surface it is necessary to take the value of the equilibrium contact angle theta0 equal to 70 degrees, which is not a characteristic for a xenon-metal system. Taking into account the contribution of the energy of the three-phase contact solid wall-liquid-gas in a microscopic nucleation model makes it possible to reconcile heterogeneous nucleation theory and experimental data at a contact angle theta0 close to zero, with the linear tension taken equal to -6 x 10(-12) J/m and the microscopic contact angle theta* approximately 57 degrees. The number of weakened sites, on which bubbles may form, is always smaller than the number of molecules adjacent to the solid wall.

T0501-2-3 ナノスケールステップにおける微視的接触角の分子動力学解析(マイクロ・ナノスケールの熱流体現象(2))

Microscopic contact angle on a moving contact line traveling over a step with a height of 0.3〜1.2 nm is investigated with molecular dynamics simulation. The simulations were made with a Couette flow geometry where two immiscible fluids are sheared between two parallel plates, one of which is equipped with step-structured surface. The contact lines strongly tend to be captured (pinned) at the edge of the convex step and the minimum contact angle observed at the moment of the depinning of the contact line is dependent on the height of the steps. An analytical model for the estimation of the relation between the minimum contact angle and the step height is developed. By taking account into the deviation between the normal and tangential components of the pressure distribution near the interface, the model reproduces well the increase of the minimum contact angle with the decrement in the step height.

A Model for Estimating the Dynamic Contact Angle with Molecular Dynamics Simulation

The microscopic configuration of fluid interface near the wetting or dewetting front (i.e., moving contact line) is of significant interest in relation to many industrial processes. In this paper we report on molecular dynamics (MD) simulations conducted for investigation of the dependence of the microscopic contact angle θ on the speed of contact line relative to the solid surface, ΔV. Our simulations were made for a Couette flow geometry where two Lennard-Jones (LJ) liquids are sheared between two solid walls moving at a speed V in opposite directions. The two liquids are immiscible and have different wall-wetting properties. The liquid configuration remains unchanged with time, since ΔV=V at all the contact lines, for V below a certain critical value. The contact angle θ measured under such steady conditions varies monotonically with ΔV. Above the critical wall speed, however, the flow at the receding contact line, where the more wetting liquid of the two is being replaced by the less wetting one, starts becoming unsteady, as ΔV remains smaller than the critical wall speed. We show that the viscous and pressure forces measured from the MD simulation results can be reproduced by the Stokes flow model of Huh and Scriven (1971) using the MD-predicted value of θ at the given ΔV. It follows that, by the aid of Qian et al.'s formulation (2003) of the stress balance at the moving contact line, and by using the MD-predicted proportionality constant between the total wall-tangential force and ΔV, this model can reproduce the MD-predicted dependence of θ on ΔV. The model predictions, furthermore, give insight into the reason why the contact line flow becomes unsteady above the critical wall speed.

Effect of oxidation on the wettability of poly(dimethylsiloxane) surfaces

The wetting of amorphous poly(dimethylsiloxane) (PDMS) surfaces by water has been studied using molecular dynamics simulations. PDMS surfaces were generated by compressing a long PDMS chain between two elastic boundaries at atmospheric pressure. Oxidation of the PDMS surface, achieved in real systems by exposure to air plasma or corona discharge, was modeled by replacing methyl groups on the PDMS chain with hydroxyl groups. Three surfaces of varying degrees of oxidation were characterized by measuring the water contact angle and the roughness. The dependence of the microscopic contact angle on drop size was measured from time averaged density profiles. The macroscopic contact angle was measured directly using a cylindrical drop of infinite length with zero contact line curvature. The measured macroscopic contact angle ranged from approximately 125 degrees on the untreated surface to 75 degrees on the most oxidized surface studied. The line tension was found to increase with increasing degree of oxidation, from a negligible value on the untreated surface to approximately 5x10(-11) J m(-1) on the most heavily oxidized surface.

Estimation of line tension and contact angle from heterogeneous nucleation experimental data

Using the classical nucleation theory corrected with line tension and experimental data of heterogeneous nucleation of n-nonane, n-propanol, and their mixture on silver particles of three different sizes, the authors were able to estimate the line tensions and the microscopic contact angles for the above mentioned systems. To do this they applied generalized Young's equation for the line tension and calculated the interfacial tensions using Li and Neumann's equation [Adv. Colloid Interface Sci. 39, 299 (1992)]. It has been found that, for both unary and binary systems, the line tension is negative and the resulting microscopic contact angle derived from experimental nucleation data is most of the time larger than the macroscopic one. This is in contrast to earlier studies where the influence of line tension has not been accounted for. The values of the three phase contact line tension obtained in this way are of the same order of magnitude as the estimations for other systems reported in literature. The line tension effect also decreases considerably the nucleation barrier.

ICONE15-10242 Molecular Dynamics Study on the Dependence of Contact Angle on the Speed of Contact Line

Wetting phenomena greatly affects boiling or condensing phenomena of liquid on the solid surface. Although the contact angle is one of the most important parameters to represent the wetting condition, the behavior of the contact angle is not understood well, especially in the dynamic condition. In this study, molecular dynamics (MD) simulations were made to investigate the dependence of microscopic contact angle on the speed of contact line, ΔV, under a condition where fluids near the wall crystallized. The results were then compared with an estimation obtained by substituting velocity distribution by Huh's theory (1971) into Qian's statement of stress balance near the contact line (2003). The estimation well reproduced the MD results on the dependence of the contact angle on ΔV. The value of ΔV in MD results is limited below a certain value; above it, contact line follows the wall motion and ΔV is suppressed below the limit. This phenomenon is also reproduced by this estimation method.

Molecular dynamics simulations of water droplets on polymer surfaces

Molecular dynamics simulations were used to study the wetting of polymer surfaces with water. Contact angles of water droplets on crystalline and two amorphous polyethylene (PE) and poly(vinyl chloride) (PVC) surfaces were extracted from atomistic simulations. Crystalline surfaces were produced by duplicating the unit cell of an experimental crystal structure, and amorphous surfaces by pressing the bulk polymer step by step at elevated temperature between two repulsive grid surfaces to a target density. Different-sized water droplets on the crystalline PE surface revealed a slightly positive line tension on the order of 10(-12)-10(-11) N, whereas droplets on crystalline PVC did not yield a definite line tension. Microscopic contact angles produced by the simple point charge (SPC) water model were mostly a few degrees smaller than those produced by the extended SPC model, which, as the model with lowest bulk energy, presents an upper boundary for contact angles. The macroscopic contact angle for the SPC model was 94 degrees on crystalline PVC and 113 degrees on crystalline PE. Amorphicity of the surface increased the water contact angle on PE but decreased it on PVC, for both water models. If the simulated contact angles on crystalline and amorphous surfaces are combined in proportion to the crystallinity of the polymer in question, simulated values in relatively good agreement with measured values are obtained.

Contact angle dynamics in droplets impacting on flat surfaces with different wetting characteristics

An experimental study is presented on contact angle dynamics during spreading/recoiling of mm-sized water droplets impacting orthogonally on various surfaces with data. Application of hydrodynamic theory indicates that in the slow stage of forced spreading the slip length and the microscopic contact angle should be contact line velocity dependent. The hydrodynamic theory performs well during kinematic (fast) spreading, in which solid/liquid interactions are weak. Application of the molecular kinetic theory yields physically reasonable molecular wetting parameters, which, however, vary with impact conditions. The results indicate that even for a single liquid there is no universal expression to relate contact angle with contact line speed. Finally, analysis of the spreading dynamics on the non-wettable surfaces shows that it conforms to the Cassie-Baxter regime (only partial liquid/solid contact is maintained). The present results offer guidance for numerical or analytical studies, which require careful attention to the implementation of boundary conditions at the moving contact line, including the need to specify the dependence of contact angle on contact line speed.

Surface Transport in Premelted Films with Application to Grain-Boundary Grooving

We present a new model of surface transport in premelted films that is applicable to a wide range of materials close to their melting points. We illustrate its use by applying it to the evolution of a grain-boundary groove in a high vapor pressure material and show that Mullins's classical equation describing transport driven by gradients in surface curvature is reproduced asymptotically. The microscopic contact angle at the groove root is found to be modified over a thin boundary layer, and the apparent contact angle is determined. An explicit transport coefficient is derived that governs the evolution rate of systems controlled by surface transport through premelted films. The transport coefficient is found to depend on temperature and diverges as the bulk melting temperature is approached.

Cylindrical Droplet on Nanofibers: A Step toward the Clam-Shell Drop Description

The existence and shape of a cylindrical (infinitely long) liquid drop on a fiber of arbitrary radius are examined using a microscopic approach based on the interaction potentials between the molecules of the system. A differential equation for the drop profile was derived by the variational minimization of the total potential energy by taking into account the structuring of the liquid near the fiber. This equation was solved by quadrature, and the existence conditions and the shape of the drop were examined as functions of the radius of the fiber, microscopic contact angle theta(0), which the actual drop profile makes with the fiber, and a certain parameter, a, which depends on the interaction potential parameters. Angle theta(0) is defined in the nanoscale range near the leading edge where the interactions between the liquid and solid are strong. It differs from the macroscopically measured wetting angle (theta(m)) that represents the extrapolation of the profile outside the range of liquid-solid interaction to the solid surface. Expressions for both theta(0) and theta(m) are established in the paper. For any given fiber radius, the range of drop existence involves two domains in the plane theta(0) - a, separated by a critical curve a = a(c)(theta(0)). In the first domain, below the curve a = a(c)(theta(0)), the drop always exists and can have any height, h(m). In the second domain, above the curve a = a(c)(theta(0)), there is an upper limit of h, h(m1), such that drops with h(m) > h(m1) cannot exist. The shape of the drop depends on whether the point (theta(0), a) on the theta(0) - a plane is far from the critical curve or near to it. In the first case, the drop profile has generally a circular shape, with the center of the circle not located on the fiber axis, whereas in the second case the shape is "quasi planar", that is, most of the drop profile lies on a circle concentric with the fiber profile. Comparing the potential energies of a cylindrical drop on a fiber and a film of uniform thickness covering the fiber and having the same volume as the drop, the energetically preferred configuration was determined for various conditions. Considering the cylindrical drop as a limiting case of a clam-shell one, and the film as a limiting case of a barrel drop, the obtained analytical results could be employed to examine the barrel-drop-clam-shell-drop transformation (roll-up transition).

Microscopic treatment of a barrel drop on fibers and nanofibers

The microscopic approach of Berim and Ruckenstein (J. Phys. Chem. B 108 (2004) 19330, 19339) regarding the shape and stability of a liquid drop on a planar bare solid surface is extended to a liquid barrel drop on the bare surface of a solid cylinder (fiber) of arbitrary radius. Assuming the interaction potentials of the liquid molecules between themselves and with the molecules of the solid of the London–van der Waals form, the potential energy of a liquid molecule with an infinitely long fiber was calculated analytically. A differential equation for the drop profile was derived by the variational minimization of the total potential energy of the drop by taking into account the structuring of the liquid near the fiber. This equation was solved in quadrature and the shape and stability of the barrel drop were analyzed as functions of the radius of the fiber and the microscopic contact angle θ 0 which the drop profile makes with the surface of the fiber. The latter angle is dependent on the fiber radius and on the microscopic parameters of the model (strength of the intermolecular interactions, densities of the liquid and solid phases, hard core radii, etc.). Expressions for the evaluation of the microcontact angle from experimentally measurable characteristics of the drop profile (height, length, volume, location of inflection point) are obtained. All drop characteristics, such as stability, shape, are functions of θ 0 and a certain parameter a which depends on the model parameters. In particular, the range of drop stability consists of three domains in the plane θ 0 – a, separated by two critical curves a = a c ( θ 0 ) and a = a c 1 ( θ 0 ) [ a c ( θ 0 ) < a c 1 ( θ 0 ) ]. In the first domain, below the curve a = a c ( θ 0 ) , the drop can have any height at its apex. In the second and third domains the values of h m are limited; in the second domain (above the curve a = a c 1 ( θ 0 ) ) there is an upper limit of h, h m 1 , and the drops with h m > h m 1 cannot exist, whereas in the third domain (between those curves) the drop can have values of h m either smaller than h m 1 or larger than h m 2 , where h m 2 > h m 1 is a second critical height. For sufficiently large fiber radii, R f ⩾ 1 μm , the critical curves almost coincide and only two domains, the first and the second, remain. The smaller the radius, the larger is the difference between the critical curves and the larger is the second domain of drop stability. The shape of the drop depends on whether the point ( θ 0 , a ) on the θ 0 – a plane is far from the critical curve or near it. In the first case the drop profile has generally a large circular part, while in the second case the shape is either almost planar or contains a long manchon that is similar to a film on the fiber.

Very Small Bubble Formation at the Solid−Water Interface

The formation of very small gas bubbles (so-called “nanobubbles”) at structured solid−water interfaces has been studied using the tapping mode atomic force microscopy (TMAFM) imaging technique. Silicon oxide wafer surfaces were prepared with different degrees of nanometer scale surface roughness and hydrophobicity. Small bubbles do not form on smooth, hydrophilic, or dehydroxylated silicon oxide wafer surfaces immersed in aqueous solutions under known levels of gas supersaturation. Randomly distributed small bubbles were observed over the whole surface of observation on methylated surfaces of controlled roughness. Bubbles formed on rough, methylated surfaces were larger and less-densely distributed than those on a smooth surface of similar hydrophobicity. The process of bubble coalescence was observed as a function of time. The macroscopic contact angle, measured with respect to the aqueous or gas phase, is very different from the microscopic contact angle detected by TMAFM and appears to be due to the influence of line tension at the pinned three-phase contact line. The latter has a value of −3 × 10-10 N and acts to stabilize the small bubbles, flattening them and thereby reducing the Laplace pressure.

Nucleation probability in binary heterogeneous nucleation of water-n-propanol vapor mixtures on insoluble and soluble nanoparticles.

Nucleation probabilities for binary heterogeneous nucleation have been measured quantitatively. Heterogeneous nucleation of binary n-propanol-water vapor mixtures on partially soluble 6.9-nm NaCl particles and on nonsoluble oxidized and nonoxidized 8-nm Ag particles at a constant nucleation temperature of 288 K (NaCl) or 285 K (Ag) has been investigated experimentally and theoretically. An expansion chamber was applied to generate supersaturated vapor mixtures. Number concentrations of particles activated to condensational growth were determined optically for various vapor phase activities at constant temperature. Nucleation probabilities have been measured as functions of the vapor phase activities for several n-propanol-water vapor mixing ratios. Beyond certain vapor phase activities a sharp onset of heterogeneous nucleation was observed both for NaCl and for Ag particles. For insoluble particle surfaces the theoretical slopes of the nucleation probability versus vapor phase activity curves were found to be somewhat steeper as compared to the experiment. On the other hand, for soluble particles the experimental slopes were found to be in satisfactory agreement with theory. The onset of the nucleation process is defined at an activity value where 50% of the particles were activated to condensational growth. Onset activities were obtained for various mixing ratios of the binary vapor mixtures. In the case of NaCl nuclei for n-propanol rich mixtures, the heterogeneous nucleation calculations based on a thermodynamically consistent version of Fletcher theory and an experimentally determined contact angle provide a reasonable approximation of the experimental data. However, it appears that the Fletcher theory is not applicable in the region of transition from n-propanol rich to water rich mixtures. Based on the Köhler theory of activation of soluble particles, a theory was formulated accounting for the presence of two condensable vapors and limited solubility of NaCl in water-propanol liquid mixtures. This approach provides a satisfactory description of the transition from activation of soluble particles to nucleation of vapors on insoluble particles. In the case of silver particles Fletcher theory with macroscopic experimental contact angles as well as with contact angle zero results in strong deviations from experimental data. A significant improvement was achieved by introducing fit contact angles, which are substantially lower than the macroscopic experimental values and may be considered as approximate values of the microscopic contact angles.

Dynamics of Partial Wetting and Dewetting of an Amorphous Fluoropolymer by Pure Liquids

We report velocity dependencies of dynamic contact angles for CCl4 and tert-butyl alcohol on the amorphous fluoropolymer AF 1600 and compare them with our previous results for octamethylcyclotetrasiloxane (OMCTS) on the same substrate. The molecules of these liquids have well-defined form and the solid surface is almost smooth and homogeneous, which enables checking the assumptions of the main theories of wetting dynamics. We find that the molecular-kinetic theory well represents the data for CCl4 in the characteristic cos ϑ/V scale but qualitatively disagrees with the experiment for tert-butyl alcohol and OMCTS at high velocities. The CCl4 data do not fulfill the requirement of the hydrodynamic theory for symmetric advancing and receding branches. For the other two systems, the hydrodynamic theory works better at high velocities, but the nonlinear initial sections of the ϑ3/V plots require consideration of the velocity dependence of the microscopic dynamic contact angle ϑc(V). This is done by the molecular-hydrodynamic theory accounting for both contact line and bulk viscous friction. This theory shows agreement with the experimental data in the entire velocity range for all systems compared. It fits the receding and advancing ϑ/V branches simultaneously, yielding unique values of the microscopic dynamic parameters λ, Ko,s, and Lc,max that do not depend on direction of the contact line motion. Only this theory describes the wetting−dewetting asymmetry observed for tert-butyl alcohol and OMCTS. However, it yields inadequately large values of λ and too small hopping frequencies Ko,s for CCl4 and tert-butyl alcohol. Such results, also reported previously, might mean that not λ and Ko,s but their combinations better serve for description of wetting dynamics. Here we analyze the characteristic molecular-kinetic velocity Vo,s = λKo,s and the coefficient of friction of a unit contact line length ξc = kT/Ko,sλ3 and find a significant difference between the studied systems.

The contact angle on an elastic substrate. 1. The role of disjoining pressure in the surface mechanics

Using the correct physical mechanism for the transmission of the surface tension stress of a free liquid interface to the substrate, viz., the disjoining pressure of the substrate/liquid/vapor system, the macroscopic and microscopic structure of three-phase contact for a liquid drop on a linearly elastic substrate is elucidated. A variational treatment which includes the elastic free energy with the surface energies is shown to yield the augmented Young–Laplace equation for the drop shape and a natural boundary condition at the microscopic contact line, which produces the important result that the microscopic contact angle is zero—a conclusion which is also valid on a rigid substrate within the confines of the Derjaguin approximation for the intersurface forces. The macroscopic contact angle—the angle that the drop appears to make at the contact line when the system is observed on length scales greater than the range of the disjoining pressure in the system—is shown to obey Young's equation with a line-tension-like correction term. The correction depends directly on the height of the substrate deformation at microscopic contact and explicit expressions for the deformation in terms of integrals over the disjoining pressure are exhibited. For typical van der Waals-type disjoining pressures the effect of the elasticity of the substrate is shown to be very large for low Young's modulus materials (hydrogels) but to be essentially negligible for typical inorganic materials with high moduli (oxides and clays).

Water Induced Dewetting of Ultrathin Polystyrene Films on Hydrophilic Surfaces

The wetting of ultrathin films of polystyrene on the hydrophilic surfaces of mica and silicon oxide was studied by atomic force microscopy. After annealing, the surfaces were covered with a homogeneous, continuous polystyrene film of roughly 1 nm thickness. On top of this film, polystyrene droplets with microscopic contact angles of 7°−16° were observed. After exposure to an oversaturated water vapor, the continuous polystyrene film disintegrates and dewets the surfaces. Polystyrene structures on silicon oxide indicate a homogeneous dewetting process starting from few nucleation sites. On mica the density of nucleation sites for water is much higher and the polystyrene dewets the surface in an inhomogeneous process. The structural changes observed imply that ultrathin polystyrene films are highly mobile in the presence of water.

Stable Drop Shapes under Disjoining Pressure: II. Multiplicity and Stability

The stability of the contact line region as affected by the disjoining pressure has been analyzed by solving the augmented Young–Laplace equation. Because of the results in Part I (Zhang, X., Neogi, P., and Ybarra, R. M., J. Colloid Interface Sci.), we have concentrated on obtaining multiple solutions for the same set of conditions. As many as five solutions were obtained: drops that end in a thin film with uniform thickness and where the film shape oscillates, drops that end with microscopic contact angles, as well as uniform thin films of two different thicknesses. The results of linear stability analysis were used to show that most cases were unstable to infinitesimal disturbances. Only two stable drop shapes for the particular disjoining pressure investigated are stable, a thin film of constant thickness and a thin drop that ends in a film of same thickness. Both multiplicity and stability have been discussed here for the first time and shed considerable light on the role of the attractive and repulsive forces.

Investigating the Interfacial Properties of Single-Liquid Nanodroplets by Atomic Force Microscopy

The interaction of a liquid with a surface is of fundamental importance to many areas of scientific research. Information on the properties of liquids at surfaces at the microscopic scale is also required to elucidate the mechanisms behind macroscopic observations. In this study, the atomic force microscope (AFM) was employed in various complementary modes of operation to investigate the properties of nanometer-scale oil droplets existing on a polystyrene surface. Force curve mapping was used to gently probe the surface of the fluid droplets, and through automated analysis of the force curves the true topography and microscopic contact angle of the droplets were extracted. The contact angle was found to be 13 ± 2°, which is in excellent agreement with values obtained from macroscopic measurements. A discrepancy between these values and contact angle values obtained from tapping mode images were attributed to deformation of the soft interface. The resultant phase contrast mechanisms in the liquid tapping m...

Effective and microscopic contact angles in thin film dynamics

We introduce and analyse a class of quasi-self-similar solutions of the thin film equation to describe the dynamics of expanding liquid films on a solid surface. Using these solutions as intermediate asymptotics profiles, we obtain a quantitative expression for the shape of the film and a relation between the speed of the contact line and the macroscopic and microscopic contact angles.