Young Contact Angle Research Articles

The effect of pillar surface fraction and pillar height on contact angles using molecular dynamics

Predicting hydrophobicity is very important in manufacturing products with self-cleaning properties. This study focuses on the effect of graphite surfaces with pillars of different surface fractions and heights on the contact angles of a nano-sized water droplet. This study used molecular dynamics simulations to investigate the hydrophobic properties of water droplets on the nano-scale. The contact angles were calculated and averaged over time for each case. Results showed the droplets in either the Wenzel state or the Cassie state. In general, as the pillar height increases the static contact angle increases to a certain point when the pillar height no longer has a significant effect on the contact angle. Over all, the smaller the pillar surface fraction the larger the change in the contact angle as the pillar height increased. As pillar surface fractions decreased from 36%, simulated contact angles undershot Cassie predictions at increasing amounts due to part of the water droplet sagging below the pillar tops. Graphite displayed anisotropic characteristics due to its layered structure which caused the contact angles to increase as surface roughness increased even though its Young contact angle was less than 90 degrees.

Contact angles of rotating sessile droplets

The paper proposes a general framework allowing the analysis of wetting problems in the situation where a sessile drop is placed on a rotating substrate. Wetting of ideal, rough and chemically heterogeneous surfaces by sessile rotating droplets is treated. The effect of the line tension is considered. The problem of wetting is discussed in the framework of a variational approach. It is demonstrated that the Young, Wenzel and Cassie equilibrium contact angles are independent of the rotation of a substrate as well as external fields.

Droplet Detachment by Air Flow for Microstructured Superhydrophobic Surfaces

Quantitative correlation between critical air velocity and roughness of microstructured surface has still not been established systematically until the present; the dynamics of water droplet detachment by air flow from micropillar-like superhydrophobic surfaces is investigated by combining experiments and simulation comparisons. Experimental evidence demonstrates that the onset of water droplet detachment from horizontal micropillar-like superhydrophobic surfaces under air flow always starts with detachment of the rear contact lines of the droplets from the pillar tops, which exhibits a similar dynamic mechanism for water droplet motion under a gravity field. On the basis of theoretical analysis and numerical simulation, an explicit analytical model is proposed for investigating the detaching mechanism, in which the critical air velocity can be fully determined by several intrinsic parameters: water-solid interface area fraction, droplet volume, and Young's contact angle. This model gives predictions of the critical detachment velocity of air flow that agree well with the experimental measurements.

Synergistic effects of geometry, inertia, and dynamic contact angle on wetting and dewetting of capillaries of varying cross sections

Understanding the role of geometry, inertia, and dynamic contact angle on wetting and dewetting of capillary tubes has theoretical and practical aspects alike. The specific and synergistic effects of these factors were studied theoretically using a mathematical model that includes inertial and dynamic contact angle terms. After validating the model for capillaries of uniform cross section, the model was extended to capillaries with sinusoidal modulations of the radius, since in practice, capillaries rarely have uniform cross-sections. The height of the meniscus during wetting and dewetting was significantly affected by the relations between the local slope of the capillary surface and the Young contact angle. Non-dimensional variables were defined using viscous effects and gravity as the scaling parameters. Simulations using the dimensionless model showed that the inertial and dynamic contact angle terms can be neglected for narrow capillaries of uniform cross-section but not for uniform, wide cross-section capillaries. Moreover, nonuniformity in cross-sectional area induced hysteresis, deceleration, blocking, and metastable equilibrium locations. An increase in contact angle further amplified the effect of geometry on wetting and dewetting processes. These results enable characterization and modeling of fluid retention and flow in porous structures that inherently consist of capillaries of varying cross section.

Apparent-contact-angle model at partial wetting and evaporation: Impact of surface forces

This theoretical and numerical study deals with evaporation of a fluid wedge in contact with its pure vapor. The model describes a regime where the continuous wetting film is absent and the actual line of the triple gas-liquid-solid contact appears. A constant temperature higher than the saturation temperature is imposed at the solid substrate. The fluid flow is solved in the lubrication approximation. The introduction of the surface forces in the case of the partial wetting is discussed. The apparent contact angle (the gas-liquid interface slope far from the contact line) is studied numerically as a function of the substrate superheating, contact line velocity, and parameters related to the solid-fluid interaction (Young and microscopic contact angles, Hamaker constant, etc.). The dependence of the apparent contact angle on the substrate temperature is in agreement with existing approaches. For water, the apparent contact angle may be 20° larger than the Young contact angle for 1 K superheating. The effect of the surface forces on the apparent contact angle is found to be weak.

Enabling efficient energy barrier computations of wetting transitions on geometrically patterned surfaces.

Proper roughness design is important in realizing surfaces with fully tunable wetting properties. Engineering surface roughness boils down to an energy barrier optimization problem, in which the geometric features of roughness serve as the optimization parameters. Computations of energy barriers, separating admissible equilibrium wetting states on patterned surfaces, have been demonstrated utilizing fine-scale simulators (e.g., lattice-Boltzmann for mesoscale and molecular dynamics for microscale simulations), however with substantial computational requirements. Here, by solving an augmented Young–Laplace equation with a disjoining pressure term, we demonstrate accurate and efficient computations of equilibrium shapes of entire millimeter sized droplets on patterned surfaces. In particular, by adopting a natural parameterization of the Young–Laplace equation along the liquid/air and liquid/solid interfaces, the tedious implementation of the Young's contact angle boundary condition at multiple three phase contact lines is bypassed. We, thus, enable the computation of wetting transition energy barriers, separating the well-known Cassie–Baxter and Wenzel states, as well as intermediate states, but with negligible computational cost. We demonstrate the method's efficiency by computing the equilibrium of droplets on stripe-patterned surfaces, and compare the results with mesoscopic lattice Boltzmann simulations. Our computationally efficient continuum-level analysis can be readily applied to patterned surfaces with increased and unstructured geometric complexity, and straightforwardly coupled with shape optimizers towards the design of surfaces with desirable wetting behavior.

Nanocomposites of high-density polyethylene with amorphous calcium phosphate: in vitro biomineralization and cytocompatibility of human mesenchymal stem cells

Polyethylene is widely used as a component of implants in medicine. Composites made of high-density polyethylene (HDPE) containing different amounts of amorphous calcium phosphate nanoparticles were investigated concerning their in vitro biomedical performance. The nanoparticles were produced by flame spray synthesis and extruded with HDPE, the latter complying with Food and Drug Administration regulations. Mechanical properties such as Young's modulus and contact angle as well as in vitro biomineralization of the nanocomposites hot-pressed into thin films were evaluated. The deposition of a hydroxyapatite layer occurred upon immersion in simulated body fluid. Additionally, a cell culture study with human mesenchymal stem cells for six weeks allowed a primary assessment of the cytocompatibility. Viability assays (alamarBlue and lactate dehydrogenase detection) proved the absence of cytotoxic effects of the scaffolds. Microscopic images after hematoxylin and eosin staining confirmed typical growth and morphology. A preliminary experiment analyzed the alkaline phosphatase activity after two weeks. These findings motivate further investigations on bioactive HDPE in bone tissue engineering.

Modulation of surface wettability of superhydrophobic substrates using Si nanowire arrays and capillary-force-induced nanocohesion

We describe a new scalable method to fabricate large-area hybrid superhydrophobic surfaces with selective adhesion properties on silicon (Si) nanowire array substrates by exploiting liquid-medium-dependent capillary-force-induced nanocohesion. Gold (Au) nanoparticles were deposited on Si by glancing angle deposition followed by metal-assisted chemical etching of Si to form Si nanowire arrays. The surfaces were dried in either deionized (DI) water, 2-propanol or methanol to vary the capillary forces exerted on the Si nanowires during the drying process in order to tune the extent of clustering of nanowires and hence the adhesion properties of the resulting superhydrophobic surfaces. Here, we exploit the combined effects of surface tension and Young's contact angle to modulate the degree of clustering of the Si nanowires during capillary-force-induced nanocohesion. These surfaces were chemically modified and rendered hydrophobic by fluorosilane deposition. Drying in DI water resulted in small clusters of nanowires which produce a low-hysteresis superhydrophobic surface that mimics a lotus leaf. Drying in methanol resulted in large nanowire clusters that lead to a high-hysteresis superhydrophobic surface. Further, we demonstrate the ability to fabricate both small and large nanowire clusters by controlling the drying of the nanowire arrays in order to selectively define and modulate adhesion of water on the same superhydrophobic substrate. The simplicity of our process to tune surface wettability on single substrates paves the way for future applications in lab-on-chip devices and platforms for chemical and biological analyses.

A ‘conveyor belt’ model for the dynamic contact angle

The familiar Young contact angle measurement of a liquid at equilibrium on a solid is a fundamental aspect of capillary phenomena. But in the real world it is not so easy to observe it. This is due to the roughness and/or heterogeneity of real surfaces, which typically are not perfectly planar and chemically homogeneous. What can be easily detected, and in a repeatable way, are advancing and receding contact angles. In this paper, we discuss a simple model which accounts for the onset of advancing and receding contact angles measured by the Wilhelmy microbalance, one of the most powerful techniques for contact angle measurements. The model also explains the experimental observation that advancing and receding contact angles become closer to each other when the system is gently ‘shaken’, by supplying mechanical energy in an appropriate way. The model may be pedagogically useful in introducing students and teachers to aspects of capillary phenomena which are not usually discussed in basic physics courses.

Laser-Patterned Super-Hydrophobic Pure Metallic Substrates: Cassie to Wenzel Wetting Transitions

A femtosecond laser was used to create microstructures on very pure metal surfaces. The irradiated samples initially showed super-hydrophilic behavior. With time and exposure to ambient air the contact angle increased to about 160° with very low hysteresis. The surfaces supported the Cassie and Wenzel wetting states, depending on the technique used to deposit the water droplets. The created surface morphologies were idealized with a geometric model that is an assembly of densely packed cylindrical pillars with semispherical caps. Using this geometric model for calculation of the surface roughness, a theoretical Young contact angle of about 99° was calculated for all samples from the Wenzel and Cassie–Baxter equations. While the value of 99° significantly differs from the measured hydrophilic contact angles on the polished pure metallic samples, it indicates that a laser-induced surface reaction must be responsible for the evolution of contact angles to super-hydrophobic ones and that this phenomenon is independent of the type of metal.

A New Wetting Mechanism Based upon Triple Contact Line Pinning

The classical Wenzel and Cassie models fail to give a physical explanation of such phenomenon as the macroscopic contact angle actually being equal to the Young's contact angle if there is a spot (surface defect) inside the droplet. Here, we derive the expression of the macroscopic contact angle for this special substrate in use of the principle of least potential energy, and our analytical results are in good agreement with the experimental data. Our findings also suggest that it is the triple contact line (TCL) rather than the contact area that dominates the contact angle. Therefore a new model based upon the TCL pinning is developed to explain the different wetting properties of the Wenzel and Cassie models for hydrophilic and hydrophobic cases. Moreover, the new model predicts the macroscopic contact angle in a broader range accurately, which is consistent with the existing experimental findings. This study revisits the fundamentals of wetting on rough substrates. The new model derived will help to design better superhydrophobic materials and provide the prediction required to engineer novel microfluidic devices.

Quantitative Testing of Robustness on Superomniphobic Surfaces by Drop Impact

The quality of a liquid-repellent surface is quantified by both the apparent contact angle θ(0) that a sessile drop adopts on it and the value of the liquid pressure threshold the surface can withstand without being impaled by the liquid, hence maintaining a low-friction condition. We designed surfaces covered with nanowires obtained by the vapor-liquid-solid (VLS) growth technique that are able to repel most of the existing nonpolar liquids including those with very low surface tension as well as many polar liquids with moderate to high surface tension. These superomniphobic surfaces exhibit apparent contact angles ranging from 125 to 160° depending on the liquid. We tested the robustness of the surfaces against impalement by carrying out drop impact experiments. Our results show how this robustness depends on Young's contact angle θ(0) related to the surface tension of the liquid and that the orientational growth of nanowires is a favorable factor for robustness.

Profiles of Liquid Drops at the Tips of Cylindrical Fibers

In 1976, B. J. Carroll derived the equation to show that a symmetric liquid droplet sitting on a thin cylindrical fiber would acquire a bell shape at equilibrium. We have extended his derivation to describe a drop located at the top end of a vertical, cylindrical fiber. By minimizing the Gibbs free energy of the drop at the fiber tip, it was found that the drop consists of two portions, a spherical cap on the fiber tip and a full, symmetrical bell located on the fiber body adjacent to the fiber tip. The experimental verification of the predicted shapes was performed using water, ethylene glycol, and Kaydol drops on nylon cylindrical fibers. Only four parameters are required to obtain agreement between the theoretical shape and the observed shape: the drop volume, the fiber radius, the surface tension of the liquid, and the Young contact angle of the liquid on a flat surface of the same composition as the fiber.

Comparing Contact Angle Measurements and Surface Tension Assessments of Solid Surfaces

Four types of contact angles (receding, most stable, advancing, and "static") were measured by two independent laboratories for a large number of solid surfaces, spanning a large range of surface tensions. It is shown that the most stable contact angle, which is theoretically required for calculating the Young contact angle, is a practical, useful tool for wettability characterization of solid surfaces. In addition, it is shown that the experimentally measured most stable contact angle may not always be approximated by an average angle calculated from the advancing and receding contact angles. The "static" CA is shown in many cases to be very different from the most stable one. The measured contact angles were used for calculating the surface tensions of the solid samples by five methods. Meaningful differences exist among the surface tensions calculated using four previously known methods (Owens-Wendt, Wu, acid-base, and equation of state). A recently developed, Gibbsian-based correlation between interfacial tensions and individual surface tensions was used to calculate the surface tensions of the solid surfaces from the most stable contact angle of water. This calculation yielded in most cases higher values than calculated with the other four methods. On the basis of some low surface energy samples, the higher values appear to be justified.

Sliding of Water Droplets on Microstructured Hydrophobic Surfaces

Sliding behaviors of liquid droplets on solid surfaces are among the fundamental results of wettability. To remedy the lack of quantitative correlation between sliding angle and roughness of the surface, which is known to be effective at enhancing wettability, we report in this paper the observation that the onset of water droplets sliding under gravity on inclined micropillar-structured hydrophobic surfaces always starts with detachment of the rear contact lines of the droplets from the pillar tops. We also establish an explicit analytical model, based on the observed mechanism, by which the sliding angle is fully determined by the fraction of water-solid interface area, droplet volume, and Young's contact angle. This model gives predictions of sliding angles that agree well with experimental measurements.

Silicon Surface Structure-Controlled Oleophobicity

Superoleophobic surfaces display contact angles >150 degrees with liquids that have lower surface energies than does water. The design of superoleophobic surfaces requires an understanding of the effect of the geometrical shape of etched silicon surfaces on the contact angle and hysteresis observed when different liquids are brought into contact with these surfaces. This study used liquid-based metal-assisted etching and various silane treatments to create superoleophobic surfaces on a Si(111) surface. Etch conditions such as the etch time and etch solution concentration played critical roles in establishing the oleophobicity of Si(111). When compared to Young's contact angle, the apparent contact angle showed a transition from a Cassie to a Wenzel state for low-surface-energy liquids as different silane treatments were applied to the silicon surface. These results demonstrated the relationship between the re-entrant angle of etched surface structures and the contact angle transition between Cassie and Wenzel behavior on etched Si(111) surfaces.

Simulation study of the disjoining pressure profile through a three-phase contact line

Computer simulations are performed to measure the disjoining pressure profile Pi(y) across the three-phase contact line formed by a liquid-vapor interface intersecting a planar substrate wall lying in the xy plane. The method makes use of an exact expression for the disjoining pressure in terms of the density profile and the wall-fluid interaction. Pi(y) is reported for three distinct values of the wall-fluid attractive potential, representing differing levels of partial wetting by macroscopic adsorbed drops. Mechanical force-balance normal to the substrate is confirmed by direct evaluation of the required analog to Young's equation. For the model system under study, the disjoining pressure profiles are well-fitted by inverted Gaussians. The fitted results are used with an extension (to large values of Young's contact angle theta) of the interface Hamiltonian theory of Indekeu, thereby enabling us to report the line tension tau(theta).

A new model to estimate the Young contact angle from contact angle hysteresis measurements

Beyond the linear model of Schulze et al. [ J. Adhes. Sci. Technol. 3 (1) (1989) 39–48], a more comprehensive model for predicting the Young contact angle of rough and chemically homogeneous surfaces from contact angle hysteresis measurements is proposed. This new model incorporates the barrier effect, described by Shuttleworth and Bailey, and the Wenzel model as well. Both the linear and nonlinear models were evaluated using a thermoplastic polyether-based elastomer and PDMS and two liquids. The elastomer surfaces were textured on purpose at differing degrees of roughness. Both models provided similar values of Young angle, although the nonlinear model also provided information about the distribution of practical metastable configurations around the most stable equilibrium configuration. Despite the linear model showed slightly better goodness-of-fit and minor uncertainties in its parameters, the nonlinear model is more reliable and theoretically consistent.

Effect of roughness, wettability and morphology of engineered titanium surfaces on osteoblast-like cell adhesion

Texturization of surfaces is usually advantageous in biomaterial engineering. However, the details of the textured surfaces can be more determining on cell adhesion and proliferation, rather than their roughness degree. Titanium is extensively used as a dental implant material in the human body. In this paper, the effect of four surface treatments on commercially pure titanium has been evaluated. These treatments were polishing (pTi); hydrofluoric acid (HF) etching (eTi); Al 2O 3 blasting (bTi); Al 2O 3 blasting + HF etching (beTi). Roughness and fractal dimensions were obtained from atomic force microscopy. Wettability was measured using water sessile drops. Morphology and surface chemical composition were analyzed with scanning electron microscopy and energy dispersive X-ray (EDX). MG-63 cell cultures were performed at different times (180 min, 24 h, 48 h, 72 h). Lowest roughness was found in pTi samples followed by eTi, bTi and beTi samples. Etching generated surfaces with the highest fractal dimension and negative skewness. Young contact angles were similar except for pTi and bTi surfaces. Silicon and aluminum traces were found in pTi and bTi samples, respectively. Cell adhesion (≤24 h) was greater on bTi and beTi surfaces. After 48 h, cell proliferation, mediated by specific morphologies, was improved in eTi samples followed by beTi surfaces. For the same surface chemistry, cell growth was driven by topography features.

Tunable Open-Channel Microfluidics on Soft Poly(dimethylsiloxane) (PDMS) Substrates with Sinusoidal Grooves

On soft poly(dimethylsiloxane) (PDMS) substrates with 1D sinusoidal wrinkle patterns, we study the anisotropic wetting behavior and fluidic transport as a function of surface energy and groove geometry. On grooved substrates with a contact angle greater than 90 degrees , liquids form dropletlike morphology, and its contact angle in the direction perpendicular to the grooves is larger than that parallel to the grooves. This wetting anisotropy, for a fixed Young's contact angle, is found to increase when the grooves become deeper. On substrates with a contact angle smaller than 90 degrees and deep grooves (aspect ratio >/=0.3), liquids form filament-like morphology. When the groove depth is further increased by compressing the PDMS film beyond a threshold value, which depends on the surface wettability, fluid starts imbibing the grooves spontaneously. The dynamics of the liquid imbibition of grooves is studied, and a square-law dependence between the length of the liquid filament and time is found, which obeys Washburn's law. Using a simple model based on force balance, we find that the capillary force is mainly responsible for groove filling in sinusoidal grooves.