Dependence Of Contact Angle Research Articles

Numerical Simulation of Thin Film Breakup on Nonwettable Surfaces

When a continuous film flows on a nonwettable substrate surface, it may break up, with the consequent formation of a dry-patch. The actual shape of the resulting water layer is of great interest in several engineering applications, from in-flight icing simulation to finned dehumidifier behavior modeling. Here, a 2D numerical solver for the prediction of film flow behavior is presented. The effect of the contact line is introduced via the disjoining pressure terms, and both gravity and shear are included in the formulation.The code is validated with literature experimental data for the case of a stationary dry-patch on an inclined plane. Detailed numerical results are compared with literature simplified model prediction. Numerical simulation are then performed in order to predict the threshold value of the film thickness allowing for film breakup and to analyze the dependence of the dynamic contact angle on film velocity and position along the contact line. Those informations will be useful in order to efficiently predict more complex configuration involving multiple breakups on arbitrarily curved substrate surfaces (as those involved in in-flight icing phenomena on aircraft).

An experimental and computational study of size-dependent contact-angle of dewetted metal nanodroplets below its melting temperature

Decorating 1D nanostructures (e.g., wires and tubes) with metal nanoparticles serves as a hierarchical approach to integrate the functionalities of metal oxides, semiconductors, and metals. This paper examines a simple and low-temperature approach to self-assembling gold nanoparticles (Au-np)—a common catalytic material—onto silicon nanowires (SiNWs). A conformal ultra-thin film (i.e., <15 nm thick) is deposited onto SiNWs and thermally dewetted, forming nanoparticles in the 6–70 nm range. Two parameters of its morphology are dependent upon dewetting conditions: particle size and particle contact angle. Using transmission electron microscopy imaging, it is found that annealing temperature profile has a strong effect on the particle size. Additionally, the contact angle is found to be dependent on particle size and temperature even below the eutectic temperature of the Au-Si alloy. Molecular dynamics simulations were performed to investigate potential explanations for such experimental observation. In this temperature regime, the simulations reveal the formation of an amorphous phase at the interface between the catalyst and SiNW that is sensitive to temperature. This amorphous layer increases the adhesion energy at the interface and explains the contact angle dependence on temperature.

Effect of Wettability on Micro- and Nanostructure Surface Using Sessile Droplet Contact Angle for Heat Transfer Application

This experimental investigation studied the variation in the dynamic contact angle measured on copper surface roughened by emery with grit size of 320, 600, 1000, 1500 and 2000 and titanium oxide nanoparticle-coated nanostructure with thickness of 250, 500, 750 and 1000 nm on copper substrates by e-beam evaporation process using deionized water as liquid with the help of macroscopic contact angle meter. In case of emery-roughened copper, advancing contact angle increases with the increase in emery grit size. For nanoparticle-coated surface, initially with the increase in coating thickness from 250 up to 750 nm, advancing contact angle increases; after that, further increasing in coating thickness to 1000 nm, advancing contact angle diminishes. Generally, the contact angle was found to vary from 30° to 60° for deionized water droplet for the nanoparticle-coated surface having different thickness. The surfaces are characterized with respect to morphology and topography to know the particle size and shape and particle distribution pattern and surface roughness with the help of AFM and FEG-SEM. The theoretical analysis is also carried out to determine the dependency of contact angle and roughness on the nanoparticle-coated titanium oxide thin-film surface. This formulation qualitatively showed a similar trend with experimental results.

Kinetics of gravity‐driven slug flow in partially wettable capillaries of varying cross section

AbstractA mathematical model for slug (finite liquid volume) motion in not‐fully‐wettable capillary tubes with sinusoidally varying cross‐sectional areas was developed. The model, based on the Navier‐Stokes equation, accounts for the full viscous terms due to nonuniform geometry, the inertial term, the slug's front and rear meniscus hysteresis effect, and dependence of contact angle on flow velocity (dynamic contact angle). The model includes a velocity‐dependent film that is left behind the advancing slug, reducing its mass. The model was successfully verified experimentally by recording slug movement in uniform and sinusoidal capillary tubes with a gray‐scale high‐speed camera. Simulation showed that tube nonuniformity has a substantial effect on slug flow pattern: in a uniform tube it is monotonic and depends mainly on the slug's momentary mass/length; an undulating tube radius results in nonmonotonic flow characteristics. The static nonzero contact angle varies locally in nonuniform tubes owing to the additional effect of wall slope. Moreover, the nonuniform cross‐sectional area induces slug acceleration, deceleration, blockage, and metastable‐equilibrium locations. Increasing contact angle further amplifies the geometry effect on slug propagation. The developed model provides a modified means of emulating slug flow in differently wettable porous media for intermittent inlet water supply (e.g., raindrops on the soil surface).

Experimental and simulation study of carbon dioxide, brine, and muscovite surface interactions

Capture and subsequent geologic storage of CO2 in deep brine reservoirs plays a significant role in plans to reduce atmospheric carbon emission and resulting global climate change. Subsurface injection of CO2 is also used industrially in enhanced oil and natural gas recovery operations to increase the amount of hydrocarbon that can be economically recovered from a geologic reservoir. The interaction of CO2 and brine species with mineral surfaces controls the ultimate fate of injected CO2 at the nanoscale via surface chemistry, at the pore-scale via capillary trapping, and at the field-scale via relative permeability. High resolution micro X-ray CT scanning, optical contact angle measurements, and large scale molecular dynamics simulations were used to investigate the behavior of supercritical CO2 and aqueous fluids on basal surfaces of muscovite, a common phyllosilicate mineral. Experimental results demonstrate partial wetting by the aqueous phase and a dependence of contact angle upon aqueous phase brine composition. This contrasts with simulation results, which predict that supercritical CO2 forms a non-wetting droplet, separated from direct interaction with the muscovite surface by distinct layers of water and charged species. Simulations with trace amounts of acetate or acetic acid added to the CO2/water/mineral system were used to investigate the potential effect of contamination with small organic molecules. While the observed contact angle was not significantly altered, these simulations demonstrate the influence of pH on species partitioning, with acetic acid molecules partitioning to the CO2/water interface and acetate ions adsorbing to the mineral surface. Similar simulations using hexanoate displayed a greater surfactant effect and significantly increased wetting by the CO2 phase, suggesting that small concentrations of secondary species or contaminants can significantly influence macroscopic wetting behavior.

Dominance of Dispersion Interactions and Entropy over Electrostatics in Determining the Wettability and Friction of Two-Dimensional MoS2 Surfaces.

The existence of partially ionic bonds in molybdenum disulfide (MoS2), as opposed to covalent bonds in graphene, suggests that polar (electrostatic) interactions should influence the interfacial behavior of two-dimensional MoS2 surfaces. In this work, using molecular dynamics simulations, we show that electrostatic interactions play a negligible role in determining not only the equilibrium contact angle on the MoS2 basal plane, which depends solely on the total interaction energy between the surface and the liquid, but also the friction coefficient and the slip length, which depend on the spatial variations in the interaction energy. While the former is found to result from the exponential decay of the electric potential above the MoS2 surface, the latter results from the trilayered sandwich structure of the MoS2 monolayer, which causes the spatial variations in dispersion interactions in the lateral direction to dominate over those in electrostatic interactions in the lateral direction. Further, we show that the nonpolarity of MoS2 is specific to the two-dimensional basal plane of MoS2 and that other planes (e.g., the zigzag plane) in MoS2 are polar with respect to interactions with water, thereby illustrating the role of edge effects, which could be important in systems involving vacancies or nanopores in MoS2. Finally, we simulate the temperature dependence of the water contact angle on MoS2 to show that the inclusion of entropy, which has been neglected in recent mean-field theories, is essential in determining the wettability of MoS2. Our findings reveal that the basal planes in graphene and MoS2 are unexpectedly similar in terms of their interfacial behavior.

Numerical Investigation of a Dependence of the Dynamic Contact Angle on the Contact Point Velocity in a Problem of the Convective Fluid Flow

Received 07.12.2015, received in revised form 09.02.2016, accepted 20.06.2016 A two-dimensional problem of the fluid flows with a dynamic contact angle is studied in the case of an uniformly moving contact point. Mathematical modeling of the flows is carried out with the help of the Oberbeck-Boussinesq approximation of the Navier-Stokes equations. On the thermocapillary free boundary the kinematic, dynamic conditions and the heat exchange condition of third order are fulfilled. The slip conditions (conditions of proportionality of the tangential stresses to the difference of the tangential velocities of liquid and wall) are prescribed on the solid boundaries of the channel supporting by constant temperature. The dependence of the dynamic contact angle on the contact point velocity is investigated numerically. The results demonstrate the contact angle behavior and the different flow characteristics with respect to the various values of the contact point velocity, friction coefficients, gravity acceleration and an intensity of the thermal boundary regimes.

Phase-field modeling of interfacial dynamics in emulsion flows: Nonequilibrium surface tension

A weakly nonlocal phase-field model is used to define the surface tension in liquid binary mixtures in terms of the composition gradient in the interfacial region so that, at equilibrium, it depends linearly on the characteristic length that defines the interfacial width. Contrary to previous works suggesting that the surface tension in a phase-field model is fixed, we define the surface tension for a curved interface and far-from-equilibrium conditions as the integral of the free energy excess (i.e., above the thermodynamic component of the free energy) across the interface profile in a direction parallel to the composition gradient. Consequently, the nonequilibrium surface tension can be widely different from its equilibrium value under dynamic conditions, while it reduces to its thermodynamic value for a flat interface at local equilibrium. In nonequilibrium conditions, the surface tension changes with time: during mixing, it decreases as the inverse square root of time, while in the linear regime of spinodal decomposition, it increases exponentially to its equilibrium value, as nonlinear effects saturate the exponential growth. In addition, since temperature gradients modify the steepness of the concentration profile in the interfacial region, they induce gradients in the nonequilibrium surface tension, leading to the Marangoni thermocapillary migration of an isolated drop. Similarly, Marangoni stresses are induced in a composition gradient, leading to diffusiophoresis. We also review results on the nonequilibrium surface tension for a wall-bound pendant drop near detachment, which help to explain a discrepancy between our numerically determined static contact angle dependence of the critical Bond number and its sharp-interface counterpart from a static stability analysis of equilibrium shapes after numerical integration of the Young-Laplace equation. Finally, we present new results from phase-field simulations of the motion of an isolated droplet down an incline in gravity, showing that dynamic contact angle hysteresis can be explained in terms of the nonequilibrium surface tension.

Pressure and Temperature Dependence of Contact Angles for CO2/Water/Silica Systems Predicted by Molecular Dynamics Simulations

Wettability controls the capillary behavior of injected CO2, including capillary entry pressure, relative permeability, and residual fluid saturation, and it is one of the most active topics in geologic carbon sequestration (GCS). However, the large uncertainty of water contact angle (CA) data and its pressure, temperature, and salinity dependence in the literature limit our understanding on wettability. Molecular dynamics (MD) simulations have been performed to investigate the pressure (P) and temperature (T) dependence of water CAs on the silica surface. Three typical molecular surface models for silica, namely, Q2, crystalline Q3, and amorphous Q3, were selected, and simulations were conducted at wide pressure (2.8–32.6 MPa) and temperature (318–383 K) conditions. The results show that P and T dependence of water CAs on silica surfaces is controlled by surface functional groups. These findings provide new information to help with the better understanding of wettability alteration under different GCS co...

Thickness dependence of surface energy and contact angle of water droplets on ultrathin MoS2 films.

We have performed a systematic density functional study of surface energy of MoS2 films as a function of thickness from one to twelve layers with the consideration of van der Waals (vdW) interactions using the vdW-DF and DFT-D2 methods. Both vdW schemes show that the surface energy will increase with the increase of the number of atomic layers and converge to a constant value at about six layers. Based on the calculated surface energies, we further analyze the surface contact angle of water droplets on the MoS2 film surface using Young's equation as a function of thickness in comparison with experiments, from which the water-MoS2 interfacial energy is derived to be independent of MoS2 thickness. Our calculations indicate that the vdW interactions between the MoS2 layers play an important role in determining surface energy, and results in the thickness dependence of the contact angle of water droplets on the MoS2 film surface. Our results explain well the recent wetting experiment [Nano Lett., 2014, 14(8), 4314], and will be useful for future studies of physical and chemical properties of ultrathin MoS2 films.

接触線の過渡運動時における動的接触角の決定機構

Estimation of the contact angle on a moving contact line is one of the important factors for the prediction of the liquid surface geometry contacting with solid. In this study the dynamic contact angle on an accelerating vertical glass rod is investigated both experimentally and numerically to elucidate the effect of the acceleration of the contact line. The experiment was held by using ethylene-glycol and its aqueous solution as test fluid. The measured contact angle in the transient state clearly deviated from that for the steady state, depending on the acceleration of the rod. Numerical simulation shows that the acceleration and the gravity terms in the momentum equation, which are relatively remarkable in macroscopic scale, are not responsible for such deviation in the contact angle. Rather, the dependence of the microscopic contact angle on the acceleration, estimated with the viscous bending model, should be the primary factor on the deviation of the contact angle.

Moving contact line dynamics: from diffuse to sharp interfaces

We reconcile two scaling laws that have been proposed in the literature for the slip length associated with a moving contact line in diffuse interface models, by demonstrating each to apply in a different regime of the ratio of the microscopic interfacial width $l$ and the macroscopic diffusive length $l_{D}=(M{\it\eta})^{1/2}$, where ${\it\eta}$ is the fluid viscosity and $M$ the mobility governing intermolecular diffusion. For small $l_{D}/l$ we find a diffuse interface regime in which the slip length scales as ${\it\xi}\sim (l_{D}l)^{1/2}$. For larger $l_{D}/l>1$ we find a sharp interface regime in which the slip length depends only on the diffusive length, ${\it\xi}\sim l_{D}\sim (M{\it\eta})^{1/2}$, and therefore only on the macroscopic variables ${\it\eta}$ and $M$, independent of the microscopic interfacial width $l$. We also give evidence that modifying the microscopic interfacial terms in the model’s free energy functional appears to affect the value of the slip length only in the diffuse interface regime, consistent with the slip length depending only on macroscopic variables in the sharp interface regime. Finally, we demonstrate the dependence of the dynamic contact angle on the capillary number to be in excellent agreement with the theoretical prediction of Cox (J. Fluid Mech., vol. 168, 1986, p. 169), provided we allow the slip length to be rescaled by a dimensionless prefactor. This prefactor appears to converge to unity in the sharp interface limit, but is smaller in the diffuse interface limit. The excellent agreement of results obtained using three independent numerical methods, across several decades of the relevant dimensionless variables, demonstrates our findings to be free of numerical artefacts.

Water Contact Angle Dependence with Hydroxyl Functional Groups on Silica Surfaces under CO2 Sequestration Conditions.

Functional groups on silica surfaces under CO2 sequestration conditions are complex due to reactions among supercritical CO2, brine and silica. Molecular dynamics simulations have been performed to investigate the effects of hydroxyl functional groups on wettability. It has been found that wettability shows a strong dependence on functional groups on silica surfaces: silanol number density, space distribution, and deprotonation/protonation degree. For neutral silica surfaces with crystalline structure (Q(3), Q(3)/Q(4), Q(4)), as silanol number density decreases, contact angle increases from 33.5° to 146.7° at 10.5 MPa and 318 K. When Q(3) surface changes to an amorphous structure, water contact angle increases 20°. Water contact angle decreases about 12° when 9% of silanol groups on Q(3) surface are deprotonated. When the deprotonation degree increases to 50%, water contact angle decreases to 0. The dependence of wettability on silica surface functional groups was used to analyze contact angle measurement ambiguity in literature. The composition of silica surfaces is complicated under CO2 sequestration conditions, the results found in this study may help to better understand wettability of CO2/brine/silica system.

Buoyancy-driven detachment of a wall-bound pendant drop: interface shape at pinchoff and nonequilibrium surface tension.

We present numerical results from phase-field simulations of the buoyancy-driven detachment of an isolated, wall-bound pendant emulsion droplet acted upon by surface tension and wall-normal buoyancy forces alone. Our theoretical approach follows a diffuse-interface model for partially miscible binary mixtures which has been extended to include the influence of static contact angles other than 90^{∘}, based on a Hermite interpolation formulation of the Cahn boundary condition as first proposed by Jacqmin [J. Fluid Mech. 402, 57 (2000)JFLSA70022-112010.1017/S0022112099006874]. In a previous work, this model has been successfully employed for simulating triphase contact line problems in stable emulsions with nearly immiscible components, and, in particular, applied to the determination of critical Bond numbers for buoyancy-driven detachment as a function of static contact angle. Herein, the shapes of interfaces at pinchoff are investigated as a function of static contact angle and distance to the critical condition. Furthermore, we show numerical results on the nonequilibrium surface tension that help to explain the discrepancy between our numerically determined static contact angle dependence of the critical Bond number and its sharp-interface counterpart based on a static stability analysis of equilibrium shapes after numerical integration of the Young-Laplace equation. Finally, we show the influence of static contact angle and distance to the critical condition on the temporal evolution of the minimum neck radius in the necking regime of drop detachment.

Dynamic contact angle and three-phase contact line of water drop on copper surface

Nowadays there is a lack of experimental data describing the physical process of drop spreading on a solid metal surface for developing wetting and spreading theory. The experimental data obtained by using the high speed video-recording will allow to identify unknown previously spreading modes as well as the change of the dynamic contact angle and the three-phase contact line. The purpose of the work is to determine the effect of the drop growth rate and the copper substrate surface roughness on the dynamic contact angle and the three-phase contact line speed at distilled water drop spreading. Shadow and Schlieren methods are used to obtain experimental data. Three drop spreading modes on the rough surfaces were identified. Time dependences of the dynamic contact angle and contact line speed were obtained. Experimental results can be used for assessing the validity of the developed mathematical models of wetting and spreading processes in the field of micro- and nanoelectronics, ink jet printing, thin-film coatings, spray cooling, and optoelectronics.

3D computation of an incipient motion of a sessile drop on a rigid surface with contact angle hysteresis

Contact line phenomena govern a large number of multiphase flows. A reliable description of the contact line dynamics is therefore essential for prediction of such flows. Well-known difficulties of computation of the wetting phenomena include the mesh dependence of the results caused by flow singularity near the contact line and accurate estimation of its propagating velocity. The present study deals with the computational problem arising from the discontinuity in the dependence of the dynamic contact angle on the propagation velocity, associated with the contact angle hysteresis. The numerical simulations are performed using the volume of fluid method. The boundary conditions in the neighborhood of the contact line are switched depending on the value of the computed current local contact angle between a propagating contact line and a pinning condition. The method is applied to the simulation of the deformation and incipient motion of a shedding drop. The model is validated by comparison of the numerical predictions with experimental data.

Hydrogen-Bond Heterogeneity Boosts Hydrophobicity of Solid Interfaces.

Experimental and theoretical studies suggest that the hydrophobicity of chemically heterogeneous surfaces may present important nonlinearities as a function of composition. In this article, this issue is systematically explored using molecular simulations. The hydrophobicity is characterized by computing the contact angle of water on flat interfaces and the desorption pressure of water from cylindrical nanopores. The studied interfaces are binary mixtures of hydrophilic and hydrophobic sites, with and without the ability to form hydrogen bonds with water, intercalated at different scales. Water is described with the mW coarse-grained potential, where hydrogen-bonds are modeled in the absence of explicit hydrogen atoms, via a three-body term that favors tetrahedral coordination. We found that the combination of particles exhibiting the same kind of coordination with water gives rise to a linear dependence of contact angle with respect to composition, in agreement with the Cassie model. However, when only the hydrophilic component can form hydrogen bonds, unprecedented deviations from linearity are observed, increasing the contact angle and the vapor pressure above their values in the purely hydrophobic interface. In particular, the maximum enhancement is seen when a 35% of hydrogen bonding molecules is randomly scattered on a hydrophobic background. This effect is very sensitive to the heterogeneity length-scale, being significantly attenuated when the hydrophilic domains reach a size of 2 nm. The observed behavior may be qualitatively rationalized via a simple modification of the Cassie model, by assuming a different microrugosity for hydrogen bonding and non-hydrogen bonding interfaces.

Connection of Intrinsic Wettability and Surface Topography with the Apparent Wetting Behavior and Adhesion Properties

The need for connecting the intrinsic material wettability with surface geometry, adhesion to liquids, and the apparent wettability is of primary importance when aiming to design advanced functional materials. Here, by solving the Young−Laplace equation, augmented with a Derjaguin pressure, we tackle the necessity for implementing the Young angle boundary condition at the contact line, and thus we are able to compute multiple and reconfigurable three-phase contact lines in equilibrium. Using the finite element method and special parameter continuation techniques, we highlight the highly nonlinear dependence of the apparent contact angle on the Young angle, which quantifies the material wettability. By computing equilibrium shapes of entire droplets, we find multiple Cassie and Wenzel type states in certain wettability regimes. We, for the first time, find a material wettability regime where Cassie, Wenzel, and partially impregnated states are (meta)stable. The energy barriers for transitions between these states are computed, and their dependence on certain surface geometric features is shown. The “rose petal effect” as well as the “lotus effect” are illuminated through free and adhesion energy computations, and certain geometries are suggested that favor one state or the other.

Dependency of Contact Angle on Water Content and Drying Time in the Moisture Range Below Wilting Point

Many researchers have found an arc-shaped curve for the apparent contact angle α vs. the equilibrium water content θ, with the highest values for α at moisture close to the wilting point and lower values under wetter and drier conditions. We hypothesized that measured α(θ) relationships are not in equilibrium in the drier moisture range and that α increases with drying time after reaching constant θ. A laboratory experiment with two water-repellent soil materials was conducted for moisture conditions from field capacity to oven dry at 40°C. The 40°C treatments were repeated with drying times of 1 h to 4 wk. Contact angles were determined using the molarity of an ethanol droplet test. Although the θ of oven-dried samples was constant after 1 wk, α slightly decreased with time for both materials, even after 4 wk of drying. Therefore, the hypothesis that states an increasing α with drying time at constant θ should be reconsidered.

Dynamic contact angle measurements on superhydrophobic surfaces

In this paper, the dynamic advancing and receding contact angles of a series of aqueous solutions were measured on a number of hydrophobic and superhydrophobic surfaces using a modified Wilhelmy plate technique. Superhydrophobic surfaces are hydrophobic surfaces with micron or nanometer sized surface roughness. These surfaces have very large static advancing contact angles and little static contact angle hysteresis. In this study, the dynamic advancing and dynamic receding contact angles on superhydrophobic surfaces were measured as a function of plate velocity and capillary number. The dynamic contact angles measured on a smooth hydrophobic Teflon surface were found to obey the scaling with capillary number predicted by the Cox-Voinov-Tanner law, θD3 ∝ Ca. The response of the dynamic contact angle on the superhydrophobic surfaces, however, did not follow the same scaling law. The advancing contact angle was found to remain constant at θA = 160∘, independent of capillary number. The dynamic receding contact angle measurements on superhydrophobic surfaces were found to decrease with increasing capillary number; however, the presence of slip on the superhydrophobic surface was found to result in a shift in the onset of dynamic contact angle variation to larger capillary numbers. In addition, a much weaker dependence of the dynamic contact angle on capillary number was observed for some of the superhydrophobic surfaces tested.