Microscopic Contact Angle Research Articles

Behavior of a liquid drop in a rounded corner: Different contact angles

The Concus-Finn condition, based on the local microscopic contact angle, can be used to predict discontinuous behavior of a liquid drop in an ideally sharp corner. However, since ideally sharp corners do not exist in reality, it is important to understand the effect of rounded corners on the behavior of liquid drops. In this paper, we use theoretical calculations to study the behavior of two-dimensional liquid drops in rounded corners, including the case in which the contact angles on the two sides of the corner may differ. A new discontinuous behavior was discovered in our study, which is different from the case in sharp corners. Comparing the situation in sharp corners, our study shows that the behavior of a drop in a rounded corner depends on the dimensionless volume of the drop, in addition to its dependence on the opening angle and contact angles that is covered by the Concus-Finn condition. We also use energy-minimization approach to successfully explain why this discontinuous behavior occurs in rounded corners.

Antibacterial and Corrosion Studies on Nanosecond Pulse Laser Textured 304 L Stainless Steel Surfaces

The present paper describes results of study on surface texturing of 304 L stainless steel with 1064 nm Nd:YAG laser having average power of 15 W, pulse width of 100 ns, scan rate of 20 mm/s and repetition rate of 2 kHz. Detailed surface characterization was done using microscopic techniques, XRD and water contact angle measurement. Nanosecond laser texturing generated a thin remelted layer with wavy pattern on the surface that enhanced micro roughness and hydrophobicity. XRD pattern revealed peak broadening indicating reduction in cold working effect and increase in grain size. Laser assisted texturing were successfully introduced on 304 L SS with 1064 nm wavelength and 100 ns laser pulses of energy 7.5 mJ. Electrochemical polarization studies in chloride environments and exposure to bacterial culture confirmed that this surface modification has contributed to enhanced corrosion resistance and antibacterial activity. Thus, by tailoring the wettability, surface roughness and texture; nanosecond pulsed laser texturing approach succeeded in imparting desirable properties for cooling water system materials.

A molecular-dynamics study of sliding liquid nanodrops: Dynamic contact angles and the pearling transition

HypothesisThat the behavior of sliding drops at the nanoscale mirrors that seen in macroscopic experiments, that the local microscopic contact angle is velocity dependent in a way that is consistent with the molecular-kinetic theory (MKT), and that observations at this scale shed light on the pearling transition seen with larger drops. MethodsWe use large-scale molecular dynamics (MD) to model a nanodrop of liquid sliding across a solid surface under the influence of an external force. The simulations enable us to extract the shape of the drop, details of flow within the drop and the local dynamic contact angle at all points around its periphery. FindingsOur results confirm the macroscopic observation that the dynamic contact angle at all points around the drop is a function of the velocity of the contact line normal to itself, Ucmsinϕ, where Ucm is the velocity of the drop’s center of mass and ϕ is the slope of the contact line with respect to the direction of travel. Flow within the drop agrees with that observed on the surface of macroscopic drops. If slip between the first layer of liquid molecules and the solid surface is accounted for, the velocity-dependence of the dynamic contact angle is identical with that found previous MD simulations of spreading drops, and consistent with the MKT. If the external force is increased beyond a certain point, the drop elongates and a neck appears between the front and rear of the drop, which separate into two distinct zones. This appears to be the onset of the pearling transition at the tip of a macroscopic drop. The receding contact angle at the tip of the drop is far removed from its equilibrium value but non-zero and approaches a more-or-less constant critical value as the transition progresses.

Wetting failure condition on rough surfaces**Project supported by the National Natural Science Foundation of China (Grant Nos. 11472220 and 11872315).

Wetting states and processes attract plenty of interest of scientific and industrial societies. Air entrainment, i.e., wetting failure, on smooth plate in wetting process has been investigated carefully before. Liquid bath entries of “rough” silicon wafers are studied experimentally in the present work, and the air entrainment condition is analyzed specially with the lubrication theory. The roughness effects on the moving contact lines are therefore explored. The contact line pinning is found to be the main reason for the dynamically enhanced hydrophobicity of rough surface, which implies an effective microscopic contact angle of where θY is the Youngʼs contact angle of the material. Our results suggest that the solid surfaces can be considered as hydrophobic ones for a wide range of dynamic process, since they are normally rough. The work can also be considered as a starting point for investigating the high-speed advancing of moving contact line on rough surfaces.

Impact of Advanced Oxidation Products on Nanofiltration Efficiency

The aim of the work was to determine the influence of salicylic acid (SA) oxidation products on the effectiveness of their further removal in the membrane filtration process. Two commercial polyamide-based polymer membranes, HL (GE Osmonics) and TS80 (TriSepTM), were used and characterized by SEM microscopic analysis, contact angles, and free surface energy. The products of salicylic acid oxidation, 2,3- and 2,5-dihydroxybenzoic acid and catechol, were determined and their impact on the removal of unreacted salicylic acid in the nanofiltration process was investigated. It was also checked to what extent and why they were retained or not by the membranes. The results of the research have shown that the main product of salicylic acid oxidation, 2,3-dihydroxybenzoic acid, has a negative impact on the retention of salicylic acid in the nanofiltration stage, while the other product, catechol, improves SA retention. The determined values of contact angles correlate well with solubility (S) of the tested compounds, which increases in the following order SSA < S2,3-DHBA < SCAT, while the contact angle of the membrane decreases. Nevertheless, it has been shown that some oxidation products can penetrate the environment due to poorer membrane separation properties of these products.

Contact-line fluctuations and dynamic wetting

HypothesisThe thermal fluctuations of the three-phase contact line formed between a liquid and a solid at equilibrium can be used to determine key parameters that control dynamic wetting. MethodsWe use large-scale molecular dynamics simulations and Lennard-Jones potentials to model a liquid bridge between two molecularly smooth solid surfaces and study the positional fluctuations of the contact lines so formed as a function of the solid–liquid interaction. FindingsWe show that the fluctuations have a Gaussian distribution and may be modelled as an overdamped one-dimensional Langevin oscillator. Our analysis allows us to extract the coefficients of friction per unit length of the contact lines ζ, which arise from the collective interaction of the contact-line’s constituent liquid atoms with each other and the solid surface. We then compare these coefficients with those obtained by measuring the dynamic contact angle as a function of contact-line speed in independent simulations and applying the molecular-kinetic theory of dynamic wetting. We find excellent agreement between the two, with the same dependence on solid–liquid interaction and, therefore, the equilibrium contact angle θ0. As well as providing further evidence for the underlying validity of the molecular-kinetic model, our results suggest that it should be possible to predict the dynamics of wetting and, in particular, the velocity-dependence of the local, microscopic dynamic contact angle, by experimentally measuring the fluctuations of the contact line of a capillary system at equilibrium. This would circumvent the need to measure the microscopic dynamic contact angle directly.

Understanding the asymmetry between advancing and receding microscopic contact angles.

By means of molecular dynamics simulation, the advancing and receding microscopic contact angles were analyzed for a shear flow of two mono-atomic fluids confined between parallel non-polar solid walls. We defined the microscopic dynamic contact angle based on the coarse-grained microscopic density distribution of the fluids (the instantaneous interface method [Willard and Chandler, J. Phys. Chem. B, 2010, 114, 1954-1958]) near the moving contact line. We have found that the asymmetric change of fluid density near the wall with respect to the moving contact line results in a different dependence between the advancing and receding contact angles on the contact line velocity in a system where the two fluids across the interface have unequal wettability to the solid wall. This difference between the advancing and receding contact angles leads to different flow resistance caused by the advancing and receding contact lines, which should have impact on the industrial applications of the fine fluid transportation with contact lines.

Fluid Flow and Thin-Film Evolution near the Triple Line during Droplet Evaporation of Self-Rewetting Fluids.

The microscopic region near the triple line plays an important role in the heat and mass transfer of droplets, although the mechanisms of evaporation and internal flow remain unclear. This paper describes an experimental study of fluid flow and thin-film evolution near the triple line in sessile droplets of self-rewetting fluids, aqueous solutions of alcohols with the number of carbon atoms varying from 1 to 7, to analyze the influence of various factors on the mesoscale flows. The mechanism of internal flow for self-rewetting fluid droplets was different from that of conventional fluids, and hence, a novel expression of the in-plane average velocity was fitted for them. The temporal and spatial evolution of the thin-film thickness near the triple line during droplet evaporation was obtained by using a proposed subregion method, which was developed from an evanescent-wave-based multilayer nanoparticle image velocimetry technique. The self-rewetting fluids are conducive to increase the microscopic critical contact angle and the energy barrier of the contact line, which reduces the rate of thin-film thickness variation. The inhibited impact of self-rewetting fluids on evaporation increases gradually with an increasing number of carbon atoms.

Dipole model of vorticity at the moving contact line

In theoretical analyses of the moving contact line, an infinite force along the solid wall has been reported based off the non-integrable stress along a single interface. In this investigation we demonstrate that the stress singularity is integrable and results in a finite force at the moving contact line if the contact line is treated as a one-dimensional manifold and all three interfaces that make up the moving contact line are taken into consideration. This is due to the dipole nature of the vorticity and pressure distribution around the moving contact line. Mathematically, this finite force is determined by summing all the forces that act over an infinitesimally small cylindrical control volume that encloses the entire moving contact line. With this finite force, we propose a new dynamic Young’s equation for microscopic dynamic contact angle that is a function of known parameters only, specifically the interface velocity, surface tension, and fluid viscosity. We combine our model with Cox’s model for apparent dynamic contact angle and find good agreement with published dynamic contact angle measurements.

Surface roughness effects on contact line motion with small capillary number

In this work, we investigate how surface roughness influences contact line dynamics by simulating forced wetting in a capillary tube. The tube wall is decorated with microgrooves and is intrinsically hydrophilic. A phase-field method is used to capture the fluid interface and the moving contact line. According to the numerical results, a criterion is proposed to judge whether the grooves are entirely wetted or not at vanishing capillary numbers. When the contact line moves over a train of grooves, the apparent contact angle exhibits a periodic nature, no matter whether the Cassie-Baxter or the Wenzel state is achieved. The oscillation amplitude of apparent contact angle is analyzed and found to be inversely proportional to the interface area. The contact line motion can be characterized as stick-jump-slip in the Cassie-Baxter state and stick-slip in the Wenzel state. By comparing to the contact line dynamics on smooth surfaces, equivalent microscopic contact angles and slip lengths are obtained. The equivalent slip length in the Cassie-Baxter state agrees well with the theoretical model in the literature. The equivalent contact angles are, however, much greater than the predictions of the Cassie-Baxter model and the Wenzel model for equilibrium stable states. Our results reveal that the pinning of the contact line at surface defects effectively enhances the hydrophobicity of rough surfaces, even when the surface material is intrinsically hydrophilic and the flow is under the Wenzel state.

Temperature Dependence in Heterogeneous Nucleation with Application to the Direct Determination of Cluster Energy on Nearly Molecular Scale

A re-examination of measurements of heterogeneous nucleation of water vapor on silver nanoparticles is presented here using a model-free framework that derives the energy of critical cluster formation directly from measurements of nucleation probability. Temperature dependence is correlated with cluster stabilization by the nanoparticle seed and previously found cases of unusual increasing nucleation onset saturation ratio with increasing temperature are explained. A necessary condition for the unusual positive temperature dependence is identified, namely that the critical cluster be more stable, on a per molecule basis, than the bulk liquid to exhibit the effect. Temperature dependence is next examined in the classical Fletcher model, modified here to make the energy of cluster formation explicit in the model. The contact angle used in the Fletcher model is identified as the microscopic contact angle, which can be directly obtained from heterogeneous nucleation experimental data by a recently developed analysis method. Here an equivalent condition, increasing contact angle with temperature, is found necessary for occurrence of unusual temperature dependence. Our findings have immediate applications to atmospheric particle formation and nanoparticle detection in condensation particle counters (CPCs).

Temporal and spatial evolution of the thin film near triple line during droplet evaporation

The evaporation process of the thin film region near the triple line for a liquid suspended with nanoparticles involves important interfacial phenomena such as contact line movement, deposition, and evaporation. In this paper, droplets that are seeded with fluorescent nanoparticles of different diameters and of the same particle numbers were investigated for their evaporation rates, deposition patterns, and in-plane average velocities within the field-of-view. The results present different modes of deposition patterns for the fluorescent nanoparticles, and stronger evaporation can be obtained using nanoparticles of small diameter. The temporal and spatial evolution of velocities and thicknesses in the thin films near the triple lines during the droplet evaporation were obtained by using a proposed sub-region method, which is developed from an evanescent wave based nanoparticle image velocimetry technique. It shows that, depending on the nanoparticle size, the spatial variation of the local thin film thickness can be linear or nonlinear. The fluorescent nanoparticles can affect the evaporation modes, the internal flow, and the temporal and spatial evolution of the thin film during the droplet evaporation through the interaction between the particles and the interface near the contact line and their influence on the change of the microscopic contact angle during the pinning process of the contact line. This work can help capture insights on how nanosized particles affect the droplet evaporation near the triple line.

Apparent and microscopic dynamic contact angles in confined flows

An abundance of empirical correlations between a dynamic contact angle and a capillary number representing a translational velocity of a contact line have been provided for the last decades. The experimentally obtained dynamic contact angles are inevitably apparent contact angles but often undistinguished from microscopic contact angles formed right on the wall. As Bonn et al. [“Wetting and spreading,” Rev. Mod. Phys. 81, 739–805 (2009)] pointed out, however, most of the experimental studies simply report values of angles recorded at some length scale which is quantitatively unknown. It is therefore hard to evaluate or judge the physical validity and the generality of the empirical correlations. The present study is an attempt to clear this clutter regarding the dynamic contact angle by measuring both the apparent and the microscopic dynamic contact angles from the identical data sets in a well-controlled manner, by means of numerical simulation. The numerical method was constructed so that it reproduced the fine details of the flow with a moving contact line predicted by molecular dynamics simulations [T. Qian, X. Wang, and P. Sheng, “Molecular hydrodynamics of the moving contact line in two-phase immiscible flows,” Commun. Comput. Phys. 1, 1–52 (2006)]. We show that the microscopic contact angle as a function of the capillary number has the same form as Blake’s molecular-kinetic model [T. Blake and J. Haynes, “Kinetics of liquid/liquid displacement,” J. Colloid Interface Sci. 30, 421–423 (1969)], regardless of the way the flow is driven, the channel width, the mechanical properties of the receding fluid, and the value of the equilibrium contact angle under the conditions where the Reynolds and capillary numbers are small. We have also found that the apparent contact angle obtained by the arc-fitting of the interface behaves surprisingly universally as claimed in experimental studies in the literature [e.g., X. Li et al., “An experimental study on dynamic pore wettability,” Chem. Eng. Sci. 104, 988–997 (2013)], although the angle deviates significantly from the microscopic contact angle. It leads to a practically important point that it suffices to measure arc-fitted contact angles to make formulae to predict flow rates in capillary tubes.

Silver nanoparticles/graphene oxide decorated carbon fiber synergistic reinforcement in epoxy-based composites

A novel two-layer reinforced carbon fiber (CF), i.e., Ag nanoparticles (Ag NPs)/graphene oxide (GO) reinforced CF (named as CF/Ag/GO) was prepared by an electrochemical deposition and electrophoretic deposition (EPD) consequently. The modified fiber showed an increased interfacial shear strength (IFSS) and tensile strength. Transmission electron microscopy (TEM), scanning electron microscopy (SEM), Fourier transform infrared spectra (FTIR), X-ray photoelectron spectroscopy (XPS), Raman spectrometer, atomic force microscopic (AFM) and dynamic contact angle analysis (DCA) were carried out to investigate CF reinforced composites. And test results demonstrated that the presence of Ag NPs and GO sheets increased the surface roughness and surface energy of CFs significantly. IFSS of CF/epoxy and the tensile strength of CFs were increased by 86.1% and 36.8%, respectively. Ag NPs filled in the cracks in CF effectively to enhance the tensile strength, while GO sheets improved the wettability of resin on CFs and formed mechanical interlocking between CFs and epoxy resin. These Ag NPs and GO sheets worked together in a ferocious synergy on the interface of CF and epoxy to cause the enhanced mechanical properties.

Line tensions of galena (001) and sphalerite (110) surfaces: A molecular dynamics study

We used molecular dynamics (MD) simulation to determine the line tension of two sulfide mineral surfaces, namely galena (PbS)(001) and sphalerite (ZnS)(110) at 298K. Density functional theory (DFT) calculations were used to estimate the partial charges, and the force field parameters were derived based on the nature of the surfaces and the governing potential terms. The computed bulk structures, surface energies and water adsorption energies of the minerals using such partial charges and force field parameters agree well with experiment or DFT results. Contact angles of a series of nano-sized water clusters with different sizes were determined from the MD simulations. Line tensions and macroscopic contact angles of the two mineral surfaces were then determined using the modified Young's equation. The macroscopic contact angles (~84° and 40° for galena and sphalerite surfaces) agree well with the experimental data. The resultant line tensions are on the order of 10−11J/m for both surfaces but with different signs. Here, the line tension for PbS(001) with very low wettability is positive, and for the hydrophilic ZnS(110) surface is negative. Examination of the orientation of the water molecules on the two mineral surfaces showed that the tetrahedron structure present in bulk water (order parameter (q)=0.61) was significantly perturbed on the ZnS(110) surface (q=0.11) compared to the PbS(001) surface (q=0.47). In particular, the average angle between water dipole moment and the surface normal and the radial distribution functions of the water molecules show that the oxygen in water molecules tends to orient itself to the cationic sites (Zn atom) in the sphalerite surface, while such orientation to the Pb atom in the galena surface is minimal. The above results explain that the favorable interaction between water molecules and sphalerite causes the microscopic contact angles to be smaller than the macroscopic value, which in turn yields a negative line tension. On the contrary, stronger affinity of water molecules to the bulk region rather than to galena surface results in bigger microscopic contact angles compared to the macroscopic value and a positive line tension.

Smoothed particle hydrodynamics study of the roughness effect on contact angle and droplet flow.

We employ a pairwise force smoothed particle hydrodynamics (PF-SPH) model to simulate sessile and transient droplets on rough hydrophobic and hydrophilic surfaces. PF-SPH allows modeling of free-surface flows without discretizing the air phase, which is achieved by imposing the surface tension and dynamic contact angles with pairwise interaction forces. We use the PF-SPH model to study the effect of surface roughness and microscopic contact angle on the effective contact angle and droplet dynamics. In the first part of this work, we investigate static contact angles of sessile droplets on different types of rough surfaces. We find that the effective static contact angles of Cassie and Wenzel droplets on a rough surface are greater than the corresponding microscale static contact angles. As a result, microscale hydrophobic rough surfaces also show effective hydrophobic behavior. On the other hand, microscale hydrophilic surfaces may be macroscopically hydrophilic or hydrophobic, depending on the type of roughness. We study the dependence of the transition between Cassie and Wenzel states on roughness and droplet size, which can be linked to the critical pressure for the given fluid-substrate combination. We observe good agreement between simulations and theoretical predictions. Finally, we study the impact of the roughness orientation (i.e., an anisotropic roughness) and surface inclination on droplet flow velocities. Simulations show that droplet flow velocities are lower if the surface roughness is oriented perpendicular to the flow direction. If the predominant elements of surface roughness are in alignment with the flow direction, the flow velocities increase compared to smooth surfaces, which can be attributed to the decrease in fluid-solid contact area similar to the lotus effect. We demonstrate that classical linear scaling relationships between Bond and capillary numbers for droplet flow on flat surfaces also hold for flow on rough surfaces.

Direct numerical simulation of nucleate pool boiling at large microscopic contact angle and moderate Jakob number

In this paper, we present Direct Numerical Simulations of Nucleate Boiling on a single site in configurations involving both a large microscopic contact angle, a moderate Jakob number (less than 50) and a high density ratio between the two phases. A detailed study on the validation of the numerical simulations is presented. Several issues about the numerical modelling of the contact line are addressed in order to define a global strategy to perform accurate and predictive simulations. Benchmarks from pioneering studies (Son et al., 1999) have been reproduced with more recent numerical methods and thinner grids in order to define the most relevant strategy for successful simulations. In particular, the grid sensitivity of the solution is thoroughly investigated by performing simulations with four successive grids. The numerical results are compared favorably with experimental data, since the discrepancy between the numerical solutions and the experimental data is always less than 10% whether the departure diameter or the departure frequency are considered. The influence on the numerical solution of the thermal conduction in the solid heater is also assessed and we report that this parameter has no influence in the configurations of thick and highly conductive materials that have been considered in this study. We also present clarifications about the requirement of a specific modelling in the contact line region in order to account for a possible impact of the micro-region. Finally, based on the results of this analysis of our numerical simulations, we formulate the following unusual conclusion: the implementation of a micro-region model and an additional coupling between the overall solver and such a model is not required to perform well-resolved and accurate numerical simulations in the case of high density ratio, high microscopic contact angle (up to 30°) and moderate Jakob number. Next, we present some comparisons on the bubble shape evolution between the numerical simulations and a static force balance model, in order to investigate the mechanisms leading to the bubble detachment. Finally, we conclude this paper by presenting a parametric study, by varying the Jakob number, in order to propose a new correlation on the bubble detachment radius depending on the latter dimensionless number.

Wetting at the nanoscale: A molecular dynamics study.

A novel method to calculate the solid-liquid contact angle is introduced in this study. Using the 3D configuration of a liquid droplet on a solid surface, this method calculates the contact angle along the contact line and provides an angular distribution. Although this method uses the 3D configuration of liquid droplets, it does not require the calculation of the 3D density profile to identify the boundaries of the droplet. This decreases the computational cost of the contact angle calculation greatly. Moreover, no presumption about the shape of the liquid droplet is needed when using the method introduced in this study. Using this method, the relationship between the size and the contact angle of water nano-droplets on a graphite substrate was studied. It is shown that the contact angle generally decreases by increasing the size of the nano-droplet. The microscopic contact angle of 83.0° was obtained for water on graphite which is in a good agreement with previous experimental and numerical studies. Neglecting other nanoscale effects which may influence the contact angle, the line tension of SPC/E (extended simple point charge model) water was calculated to be 3.6×10-11 N, which is also in good agreement with the previously calculated values.

Modeling the Hydrophobicity of Nanoparticles and Their Interaction with Lipids and Proteins.

We present a method of modeling nanoparticle (NP) hydrophobicity using coarse-grained molecular dynamics (CG MD) simulations, and apply this to the interaction of lipids with nanoparticles. To model at a coarse-grained level the wettability or hydrophobicity of a given material, we choose the MARTINI coarse-grained force field, and determine through simulation the contact angles of MARTINI water droplets residing on flat regular surfaces composed of various MARTINI bead types (C1, C2, etc.). Each surface is composed of a single bead type in each of three crystallographic symmetries (FCC, BCC, and HCP). While this method lumps together several atoms (for example, one cerium and two oxygens of CeO2) into a single CG bead, we can still capture the overall hydrophobicity of the actual material by choosing the MARTINI bead type that gives the best fit of the contact angle to that of the actual material, as determined by either experimental or all-atom simulations. For different MARTINI bead types, the macroscopic contact angle is obtained by extrapolating the microscopic contact angles of droplets of eight different sizes (containing Nw = 3224-22978 water molecules) to infinite droplet size. For each droplet, the contact angle was computed from a best fit of a circular curve to the droplet interface extrapolated to the first layer of the surface. We then examine how small nanoparticles of differing wettability interact with MARTINI dipalmitoylphosphotidylcholine (DPPC) lipids and SP-C peptides (a component of lung surfactant). The DPPC shows a transition from tails coating the nanoparticle to a hemimicelle coating the water-wet NP, as the contact angle of a water droplet on the surface is lowered below ∼60°. The results are relevant to developing a taxonomy describing the potential nanotoxicity of nanoparticle interactions with components in the lung.

Evaporating thin film profile near the contact line of a partially wetting water droplet under environmental heating

To understand the thin film evaporation in a partial wetting system, water morphology near the receding contact line driven by evaporation has been investigated experimentally. A state-of-the-art tapping-mode atomic force microscopy (TM-AFM) was used to obtain the nanoscale film profile. The test section first reached equilibrium in an enclosed chamber. Then a small amount of heat was supplied to increase the gas temperature to achieve an environmental heating. The droplet was evaporating and the receding velocity of the contact line was below 20nm/s. The film profiles were found following the macroscopic profile, which was about linear, till about 2nm thickness from the contact line which was already the limitation of the measurement. The results indicate that the microscopic contact angle at nanoscale was approximately equal to the optically detected macroscopic contact angle under this weak environmental heating.