Liquid-vapor Surface Tension Research Articles

A generalized Young’s equation to bridge a gap between the experimentally measured and the theoretically calculated line tensions

A generalized Young’s equation, which takes into account two corrections to the line tension by the curvature dependence of the liquid–vapor surface tension and by the contact angle dependence of the intrinsic line tension, is derived from the thermodynamic free-energy minimization. The correction from the curvature dependence can be qualitatively estimated using Tolman’s formula. The correction from the contact angle dependence can be estimated for nanometer-scale droplets for which the analytical formula for the intrinsic line tension determined from the van der Waals interaction is available. The two corrections to the apparent line tension of this van der Waals nano-droplets are as small as nN, and lead to either a positive or a negative apparent line tension. The gravitational line tension for millimeter-scale droplets by the gravitational acceleration is also considered. The gravitational line tension is of the order of N so that the correction from the curvature dependence can be neglected. Yet, the contact angle dependence is so large that the apparent line tension becomes always negative though the intrinsic line tension without the correction is always positive. These two examples demonstrate clear distinction between the theoretically calculated intrinsic line tension and the experimentally determined apparent line tension which includes these two corrections. Naive comparison of the experimentally determined and the theoretically calculated line tension is not always possible.

Durable, scalable, and tunable omniphobicity on stainless steel mesh for separation of low surface tension liquid mixtures

Surface repellency to high and low surface tension (LST) liquids has a wide range of commercial applications such as non-fouling, self-cleaning and separation of liquids. However, little research has been achieved to control surface repellency to LST liquids due to difficulty of developing re-entrant surface curvatures. Here, we report an effective method to control surface repellency of stainless steel meshes for liquids that have LST. We used electrochemical etching followed by hydrophobic coating where adjusting the voltage and duration of electrochemical etching controllably cover the mesh surfaces with nanoscale re-entrant structures. Variation in re-entrant surface curvatures determines the mesh's sensitivity to liquid-vapor surface tension, and changed the apparent contact angles and sliding angles for LST liquids. The difference in sensitivity of surface tension of mesh was exploited to rapidly separate liquids in binary mixtures of general solvents. The meshes achieve fast separation, and can be reused. This method to provide omniphobicity is compatible with large-scale production.

How nanobubbles lose stability: Effects of surfactants

In contrast to stability theories of nanobubbles, the molecular mechanism of how nanobubbles lose stability is far from being understood. In this work, we try to interpret recent experimental observations that the addition of surfactants destabilizes nanobubbles with an unclear mechanism. Using molecular dynamics simulations, we identify two surfactant-induced molecular mechanisms for nanobubbles losing stability, either through depinning of a contact line or reducing vapor-liquid surface tension. One corresponds to the case with significant adsorption of surfactants on the substrates, which causes depinning of the nanobubble contact line and thus leads to nanobubble instability. The other stresses surfactant adsorption on the vapor-liquid interface of nanobubbles, especially for insoluble surfactants, which reduces the surface tension of the interface and leads to an irreversible liquid-to-vapor phase transition. Our finding can help improve our understanding in nanobubble stability, and the insight presented here has implications for surface nanobubbles involving with other amphiphilic molecules, such as proteins and contaminations.

Octagonal Wetting Interface Evolution of Evaporating Saline Droplets on a Micropyramid Patterned Surface.

Textured surfaces have been extensively employed to investigate the dynamics, wetting phenomena, and shape of liquid droplets. Droplet shape can be controlled via the manipulation of topographic or chemical heterogeneity of a solid surface by anchoring the three-phase line at specific sites. In this study, we demonstrate that droplet shape on a topographically patterned surface can be modified by varying the concentration of salt potassium chloride (KCl) in the droplet solution. It is found that at the beginning of evaporation the octagonal shape of the solid-liquid interface is changed to a rectangle with corners cut upon increasing the salt concentration. Such a variation in the solid-liquid interface versus the salt concentration is explained by the analysis of free energy difference. It indicates that the increases in solid-liquid and liquid-vapor surface tensions by raising the salt concentration result in a favored extension of the three-phase line intersecting the micropyramid bottom sides than the counterpart intersecting the micropyramid diagonal edges. The saline droplets experience a pinning stage at first and a depinning one afterward. The onset of depinning is delayed, and at which the instantaneous contact angle is larger upon raising the salt concentration. The three-phase line which intersects the micropyramid diagonal edges recedes ahead of the one along the micropyramid bottom sides, making the octagonal wetting interface evolve toward a circle. A close view at the droplet edge indicates that the three-phase line repeats "slow slip-rapid slip" across row by row of micropyramids during the depinning stage.

Structural and dynamic properties of liquid tin from a new modified embedded-atom method force field

A new modified embedded-atom method (MEAM) force field is developed for liquid tin. Starting from the Ravelo and Baskes force field [Phys. Rev. Lett. 79, 2482 (1997)], the parameters are adjusted using a simulated annealing optimization procedure in order to obtain better agreement with liquid-phase data. The predictive capabilities of the new model and the Ravelo and Baskes force field are evaluated using molecular dynamics by comparing to a wide range of first-principles and experimental data. The quantities studied include crystal properties (cohesive energy, bulk modulus, equilibrium density, and lattice constant of various crystal structures), melting temperature, liquid structure, liquid density, self-diffusivity, viscosity, and vapor-liquid surface tension. It is shown that although the Ravelo and Baskes force field generally gives better agreement with the properties related to the solid phases of tin, the new MEAM force field gives better agreement with liquid tin properties.

Vapour-liquid interfacial properties of square-well chains from density functional theory and Monte Carlo simulation.

The statistical associating fluid theory for attractive potentials of variable range (SAFT-VR) density functional theory (DFT) developed by [Gloor et al., J. Chem. Phys., 2004, 121, 12740-12759] is used to predict the interfacial behaviour of molecules modelled as fully-flexible square-well chains formed from tangentially-bonded monomers of diameter σ and potential range λ = 1.5σ. Four different model systems, comprising 4, 8, 12, and 16 monomers per molecule, are considered. In addition to that, we also compute a number of interfacial properties of molecular chains from direct simulation of the vapour-liquid interface. The simulations are performed in the canonical ensemble, and the vapour-liquid interfacial tension is evaluated using the wandering interface (WIM) method, a technique based on the thermodynamic definition of surface tension. Apart from surface tension, we also obtain density profiles, coexistence densities, vapour pressures, and critical temperature and density, paying particular attention to the effect of the chain length on these properties. According to our results, the main effect of increasing the chain length (at fixed temperature) is to sharpen the vapour-liquid interface and to increase the width of the biphasic coexistence region. As a result, the interfacial thickness decreases and the surface tension increases as the molecular chains get longer. The interfacial thickness and surface tension appear to exhibit an asymptotic limiting behaviour for long chains. A similar behaviour is also observed for the coexistence densities and critical properties. Agreement between theory and simulation results indicates that SAFT-VR DFT is only able to predict qualitatively the interfacial properties of the model. Our results are also compared with simulation data taken from the literature, including the vapour-liquid coexistence densities, vapour pressures, and surface tension.

Wetting of a partially immersed compliant rod

The force on a solid rod partially immersed in a liquid is commonly used to determine the liquid-vapor surface tension by equating the measured force required to remove the rod from the liquid to the vertical component of the liquid-vapor surface tension. Here, we study how this process is affected when the rod is compliant. For equilibrium, we enforce force and configurational energy balance, including contributions from elastic energy. We show that, in general, the contact angle does not equal that given by Young's equation. If surface stresses are tensile, the strain in the immersed part of the rod is found to be compressive and to depend only on the solid-liquid surface stress. The strain in the dry part of the rod can be either tensile or compressive, depending on a combination of parameters that we identify. We also provide results for compliant plates partially immersed in a liquid under plane strain and plane stress. Our results can be used to extract solid surface stresses from such experiments.

Temperature and pressure dependence of the interfacial free energy against a hard surface in contact with water and decane.

Theoretical descriptions of molecular-scale solvation frequently invoke contributions proportional to the solvent exposed area, under the tacit expectation that those contributions are tied to a surface tension for macroscopic surfaces. Here we examine the application of revised scaled-particle theory (RSPT) to extrapolate molecular simulation results for the wetting of molecular-to-meso-scale repulsive solutes in liquid water and decane to determine the interfacial free energies of hard, flat surfaces. We show that the RSPT yields interfacial free energies at ambient pressures that are consistently greater than that obtained from the liquid-vapor surface tensions of water and decane by ∼4%. Nevertheless, the hard surface and liquid-vapor interfacial free energies are parallel over a broad temperature range at 1 bar indicating similar entropic contributions. With increasing pressure, the hard, flat interfacial free energies exhibit a maximum in the vicinity of ∼1000 bars. This non-monotonic behavior in both water and decane reflects solvent dewetting at low pressures, followed by wetting at higher pressures as the solvents are pushed onto the solute. By comparing the results of RSPT against classic scaled-particle theory (CSPT), we show that CSPT systematically predicts greater entropic penalties for interface formation and makes inconsistent predictions between the pressure dependence of the interfacial free energy and solvent contact density with the solute surface.

Improved grand canonical sampling of vapour-liquid transitions

Simulation within the grand canonical ensemble is the method of choice for accurate studies of first order vapour-liquid phase transitions in model fluids. Such simulations typically employ sampling that is biased with respect to the overall number density in order to overcome the free energy barrier associated with mixed phase states. However, at low temperature and for large system size, this approach suffers a drastic slowing down in sampling efficiency. The culprits are geometrically induced transitions (stemming from the periodic boundary conditions) which involve changes in droplet shape from sphere to cylinder and cylinder to slab. Since the overall number density does not discriminate sufficiently between these shapes, it fails as an order parameter for biasing through the transitions. Here we report two approaches to ameliorating these difficulties. The first introduces a droplet shape based order parameter that generates a transition path from vapour to slab states for which spherical and cylindrical droplets are suppressed. The second simply biases with respect to the number density in a tetragonal subvolume of the system. Compared to the standard approach, both methods offer improved sampling, allowing estimates of coexistence parameters and vapor-liquid surface tension for larger system sizes and lower temperatures.

Origin of Surface-Driven Passive Liquid Flows.

Passive liquid flow occurs in nature in the transport of water up tall trees and is desired for high-heat flux removal in thermal management devices. Typically, liquid-vapor surface tension is used to generate passive flows (e.g., capillary and Marangoni flows). In this work, we perform a fundamental molecular study on passive liquid flow driven by the solid-liquid surface tension force. Such surface tension values are first estimated by placing a liquid film over the surface and simulating various surface temperatures, followed by which simulations are performed by differential heating of the liquid film over the surface. Very strong passive liquid flows are obtained that lead to steady-state, continuous, and high-heat flux removal close to the maximum theoretical limit, as predicted by the kinetic theory of evaporation. Nondimensional empirical relations are developed for surface tension gradient, flow velocity, and evaporation rate.

Vortex formation in coalescence of droplets with a reservoir using molecular dynamics simulations

The flow patterns generated by the coalescence of aqueous ethanol droplets with a water reservoir are investigated using molecular dynamics simulations. The influence of surface tension gradient, which leads to the spreading of the droplet along the liquid-vapor interface of the reservoir, is studied by changing the ethanol concentration of the droplet. The internal circulation (vortex strength) of the droplet and the reservoir are analyzed separately. Simulation results reveal the formation of swirling flows within the droplet at early times when the radius of the coalescence neck due to the capillary forces increases rapidly with time. The vortex strength is found to be higher at lower concentrations of ethanol (higher liquid-vapor surface tension of the droplet), where the driving force for the contact line movement (capillary force) is stronger. The circulation diminishes by moving the center of mass of the droplet toward the reservoir. The lower surface tension of the droplet compared to the reservoir leads to surface tension gradient driven flow, which transports the droplet molecules along the liquid-vapor interface of the reservoir. Such a flow motion results in the generation of convective flows in the underlying water, which forms swirling flows within the reservoir. Therefore, the vortex strength of the reservoir is higher at higher ethanol concentrations of the droplet. The reservoir circulation decays to zero as soon as the ethanol concentration becomes homogeneous along the interface of the pool. The time evolution of circulation within the droplet and the reservoir are correlated with the center of mass motion of the droplet toward the surface, the time variation of the precursor film radius and the dynamic surface tension of the reservoir.

Wetting behavior of patterned micro-pillar array predicted by an equivalent surface tension model

Micro-pillar array is widely applied to manipulate the wettability of surfaces. Cases where liquid has infiltrated such pillar arrays completely are drawing increased attention in miniaturized systems. An equivalent surface tension model is proposed to characterize the driving force of liquid evolution in patterned micro-pillar arrays after the Young-Laplace equation and surface energy analysis are applied on both the pillar unit and bulk liquid levels. The effects of local menisci induced from the wetting of pillars are bounded and treated as “equivalent liquid-vapor surface tension”, through which the bulk liquid profile is then obtained based on the principle of minimal surface energy. The model is found to be computationally efficient and can be easily obtained through numerical methods. A typical sample case is presented to demonstrate its advantages and simplicity. The bulk profile that considers the effects of pillar array is compared with the result without pillars. The influencing effects, including apparent tilt angle, pillar spacing, and pillar shape, are addressed.

On interfacial properties of tetrahydrofuran: Atomistic and coarse-grained models from molecular dynamics simulation.

We have determined the interfacial properties of tetrahydrofuran (THF) from direct simulation of the vapor-liquid interface. The molecules are modeled using six different molecular models, three of them based on the united-atom approach and the other three based on a coarse-grained (CG) approach. In the first case, THF is modeled using the transferable parameters potential functions approach proposed by Chandrasekhar and Jorgensen [J. Chem. Phys. 77, 5073 (1982)] and a new parametrization of the TraPPE force fields for cyclic alkanes and ethers [S. J. Keasler et al., J. Phys. Chem. B 115, 11234 (2012)]. In both cases, dispersive and coulombic intermolecular interactions are explicitly taken into account. In the second case, THF is modeled as a single sphere, a diatomic molecule, and a ring formed from three Mie monomers according to the SAFT-γ Mie top-down approach [V. Papaioannou et al., J. Chem. Phys. 140, 054107 (2014)]. Simulations were performed in the molecular dynamics canonical ensemble and the vapor-liquid surface tension is evaluated from the normal and tangential components of the pressure tensor along the simulation box. In addition to the surface tension, we have also obtained density profiles, coexistence densities, critical temperature, density, and pressure, and interfacial thickness as functions of temperature, paying special attention to the comparison between the estimations obtained from different models and literature experimental data. The simulation results obtained from the three CG models as described by the SAFT-γ Mie approach are able to predict accurately the vapor-liquid phase envelope of THF, in excellent agreement with estimations obtained from TraPPE model and experimental data in the whole range of coexistence. However, Chandrasekhar and Jorgensen model presents significant deviations from experimental results. We also compare the predictions for surface tension as obtained from simulation results for all the models with experimental data. The three CG models predict reasonably well (but only qualitatively) the surface tension of THF, as a function of temperature, from the triple point to the critical temperature. On the other hand, only the TraPPE united-atoms models are able to predict accurately the experimental surface tension of the system in the whole temperature range.

Stress and surface tension analyses of water on graphene-coated copper surfaces

Graphene-coated materials have recently emerged as promising materials for green renewable energy applications due to the benefits of combining graphene and metals. For these types of composites, the effect of graphene coating on the wettability of metal substrates has attracted much attention from researchers. In this paper, a series of molecular dynamics simulations, in which water droplets are deposited on bare Cu (111) and graphene-coated Cu (111), were conducted to investigate the influences of graphene coating on the wettability of copper. We found that water contact angles gradually increased and converged to the value measured on pure graphite surfaces as the number of graphene layers deposited on the Cu (111) surface increased. The “wetting transparency of graphene was proven to break down as demonstrated by the fact that the water contact angle of mono-layer graphene-coated copper was found to significantly increase as compared to that of bare copper. Density and stress profiles of water droplets were examined to confirm the effect of the number of graphene layers on copper-water interactions. We also examined the surface tensions of water droplets on graphene-coated copper substrates. We found that the liquid-vapor and solid-vapor surface tensions are constant while the solidliquid tension varies with the graphene coating; this leads to the variation in the water droplet contact angles

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

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

Surface tension of liquid mercury: a comparison of density-dependent and density-independent force fields

Motivated by growing interest in interfacial properties of liquid mercury we investigate by atomistic Molecular Dynamics simulation the ability of density-independent, empiric density-dependent, and recently proposed embedded-atom force fields to predict the surface tension and coexistence density of liquid mercury at room temperature, 293 K. The effect of the density dependence of the studied models on the liquid-vapor coexistence and surface tension is discussed in detail and our results are corroborated by Monte Carlo simulations and semi-analytic liquid-state theory. The latter approach is particularly useful to identify and rationalize artifacts that arise from an ad-hoc generalization of density-independent potentials by introducing density-dependent coefficients. In view of computational efficiency and thermodynamic robustness of density-independent model we optimize its functional form to obtain higher surface tension values in order to improve agreement with experiment.

Wetting and evaporation of salt-water nanodroplets: A molecular dynamics investigation.

We employ molecular dynamics simulations to study the wetting and evaporation of salt-water nanodroplets on platinum surfaces. Our results show that the contact angle of the droplets increases with the salt concentration. To verify this, a second simulation system of a thin salt-water film on a platinum surface is used to calculate the various surface tensions. We find that both the solid-liquid and liquid-vapor surface tensions increase with salt concentration and as a result these cause an increase in the contact angle. However, the evaporation rate of salt-water droplets decreases as the salt concentration increases, due to the hydration of salt ions. When the water molecules have all evaporated from the droplet, two forms of salt crystals are deposited, clump and ringlike, depending on the solid-liquid interaction strength and the evaporation rate. To form salt crystals in a ring, it is crucial that there is a pinned stage in the evaporation process, during which salt ions can move from the center to the rim of the droplets. With a stronger solid-liquid interaction strength, a slower evaporation rate, and a higher salt concentration, a complete salt crystal ring can be deposited on the surface.

Corresponding states law for a generalized Lennard-Jones potential.

It was recently shown that vapor-liquid coexistence densities derived from Mie and Yukawa models collapse to define a single master curve when represented against the difference between the reduced second virial coefficient at the corresponding temperature and that at the critical point. In this work, we further test this proposal for another generalization of the Lennard-Jones pair potential. This is carried out for vapor-liquid coexistence densities, surface tension, and vapor pressure, along a temperature window set below the critical point. For this purpose, we perform molecular dynamics simulations by varying the potential softness parameter to produce from very short to intermediate attractive ranges. We observed all properties to collapse and yield master curves. Moreover, the vapor-liquid curve is found to share the exact shape of the Mie and attractive Yukawa. Furthermore, the surface tension and the logarithm of the vapor pressure are linear functions of this difference of reduced second virial coefficients.

Effects of Free Surface Evaporation on Water Nanodroplet Wetting Kinetics: A Molecular Dynamics Study

The wetting kinetics of a water nanodroplet undergoing evaporation on a heated gold substrate were examined using molecular dynamics (MD) simulations. Various substrate and initial droplet temperatures were used to obtain different evaporation rates. The water molecule absorption–desorption behavior was analyzed in the vicinity of the contact line region to show the microscopic details of the spreading–evaporating droplet. Increasing substrate temperatures greatly affected the dynamic wetting process, while the initial water droplet temperature had very little effect. The effects of droplet size and substrate wettability on the droplet spreading–evaporating process were also examined. The radius versus time curves agree well with molecular kinetics theory (MKT) for spreading without evaporation but differ from MKT when the spreading induced evaporation. The enhancement of the wetting kinetics by the evaporation can be attributed to the reduction of the liquid–vapor surface tension and the increased water molecule motion in the contact line region and in the bulk droplet.

Coexistence and interfacial properties of a triangle-well mimicking the Lennard-Jones fluid and a comparison with noble gases.

Coexistence and interfacial properties of a triangle-well (TW) fluid are obtained with the aim of mimicking the Lennard-Jones (LJ) potential and approach the properties of noble gases. For this purpose, the scope of the TW is varied to match vapor-liquid densities and surface tension. Surface tension and coexistence curves of TW systems with different ranges were calculated with replica exchange Monte Carlo and compared to those data previously reported in the literature for truncated and shifted (STS), truncated (ST), and full Lennard-Jones (full-LJ) potentials. We observed that the scope of the TW potential must be increased to approach the STS, ST, and full-LJ properties. In spite of the simplicity of TW expression, a remarkable agreement is found. Furthermore, the variable scope of the TW allows for a good match of the experimental data of argon and xenon.