Capillary Wave Theory Research Articles

Second inflection point of water surface tension in the deeply supercooled regime revealed by entropy anomaly and surface structure using molecular dynamics simulations.

The surface tension of supercooled water is of fundamental importance in physical chemistry and materials and atmospheric sciences. Controversy, however, exists over its temperature dependence in the supercooled regime, especially on the existence of the "second inflection point (SIP)". Here, we use molecular dynamics simulations of the SPC/E water model to study the surface tension of water (σw) as a function of temperature down to 198.15 K, and find a minimum point of surface excess entropy per unit area around ∼240-250 K. Additional simulations with the TIP4P/2005 water model also show consistent results. Hence, we predict an SIP of σw roughly in this region, at the boundary where the "no man's land" happens. The increase of surface entropy with decreasing temperature in the region below the inflection point is clearly an anomalous behavior, unknown for simple liquids. Furthermore, we find that σw has a near-linear correlation with the interfacial width, which can be well explained by the capillary wave theory. Deep in the supercooled regime, a compact water layer at the interface is detected in our simulations, which may be a key component that contributes to the deviation of surface tension from the International Association for the Properties of Water and Steam relationship. Our findings may advance the understanding of the origin of the anomalous properties of liquid water in the supercooled regime.

Understanding of interfacial tension and interface thickness of liquid/liquid interface at a finite concentration of alkyl phosphate by molecular dynamics simulation

The Mulliken charge embedded newly developed OPLS force field has been applied for computation of various structural and dynamical properties of water–dodecane biphasic system. The interface thickness has been investigated in the presence of finite concentration of third component, a lipophilic ligand, tri-isoamyl phosphate (TiAP) and acid employing molecular dynamics simulation. The physical properties at the interface like interface structure, interfacial tension, interface thickness have been studied for a wide range of mole fraction of TiAP and with various aqueous phase acidity. The interfacial tension is found to be decreased with increasing mole fraction of TiAP whereas increased with the acid concentration. The inverse relation between interface thickness and interfacial tension has been established. The surface tension computed from pressure tensor was found to be in excellent agreement with the experimental results, which is then used to determine the interface thickness employing capillary wave theory (CWT) using a simple scheme of finding the bulk correlation length by adopting conductor like screening model for real solvents. Furthermore, a simple equation has been obtained by fitting the MD results of total interface thickness for a wide range of composition of third component. The value of interface thickness calculated from the model equation was found to be in good agreement with the available experimental and MD results for a wide variety of oil-water biphasic systems. Additionally, the stability of the dimer of TiAP with different orientation was established by computing the dimerization energy using DFT which was also captured in the MD simulation. Furthermore, the present MD data shows that the water extraction is enhanced at higher mole fraction of TiAP because of wider interface thickness at higher composition of TiAP which induced the water transport to the organic phase. Again, the calculated values reveal that the water extractability is decreased with increasing aqueous phase acidity as the interface thickness is reduced at higher acidity. The present results might be useful in the frontier area of interfacial science and engineering as well as in partitioning of drug molecules at the biological interfaces.

Surface reconstruction amendment to the intrinsic sampling method.

The intrinsic sampling method (ISM) is a powerful tool that allows the exploration of interfacial properties from molecular simulations by fitting a function that represents the local boundary between two phases. However, owing to the non-physical nature of an "intrinsic" surface, there remains an ambiguity surrounding the comparison of theoretical properties with the physical world. It is therefore important that the ISM remains internally consistent when reproducing simulated properties which match experiments, such as the surface tension or interfacial density distribution. We show that the current ISM procedure causes an over-fitting of the surface to molecules in the interface region, leading to a biased distribution of curvature at these molecular coordinates. We assert that this biased distribution is a cause of the disparity between predicted interfacial densities upon convolution to a laboratory frame, an artefact which has been known to exist since the development of the ISM. We present an improvement to the fitting procedure of the ISM in an attempt to alleviate the ambiguity surrounding the true nature of an intrinsic surface. Our "surface reconstruction" method is able to amend the shape of the interface so as to reproduce the global curvature distribution at all sampled molecular coordinates. We present the effects that this method has on the ISM predicted structure of a simulated Lennard-Jones fluid air-liquid interface. Additionally, we report an unexpected relationship between surface thermodynamic predictions of our reconstructed ISM surfaces and those of extended capillary wave theory, which is of current interest.

Study on vibration of dragon wash basin and free surface waves inside

We conducted experimental and numerical studies on the vibrating modes of a dragon wash basin (DWB) and the free surface waves inside the DWB. Both the vibration of the DWB and the sound produced were studied carefully. It was found that the DWB can be excited at different intrinsic modes under different excitation, including striking and rubbing it fast/slowly. However, with gentle rubbing, the DWB will be excited mainly at the first vibrating mode. We showed that the concave side wall of a DWB decreases the intrinsic frequencies (compared with a straight side wall), and the ears of a DWB lead to breaking of the vibrating-axisymmetry and cause the separation of modes I/II and IV/V as well. A theoretical model, in which the water is assumed to be incompressible and inviscid, is applied to the first order vibration and predicts the relation of vibrating frequency versus water depth in the system. The measurement shows that both the radial and azimuthal waves are produced as DWB is working. The frequency of the first component of the surface wave is twice as large as the second one induced by non-linear effects. For both the radial and azimuthal waves, the dispersion relation is presented in the framework of capillary wave theory.

Effect of vibration frequency and displacement on melt expulsion characteristics and geometric parameters for ultrasonic vibration-assisted laser drilling of steel

Recently, the applications of ultrasonic vibration assistance to laser-based manufacturing processes are rapidly proliferating. Ultrasonic vibration-assisted laser drilling (UVLD) process involves simultaneous application of high frequency vertical vibrations to the workpiece while being irradiated with a continuous wave laser beam. In UVLD, the ultrasonic vibration assistance causes expulsion of droplets from the laser melted surface, resulting in the formation of deep holes. In this paper, systematic analysis of the effects of ultrasonic vibration frequency (20–40 kHz) and displacement (16–32 µm) on melt expulsion characteristics in early stages of drilling and geometric/quality features of the holes for UVLD of AISI 316 is presented. Based on the analysis of initiation of droplet ejection from the melt pool and particle size of the ejected droplets, mechanisms of droplet ejection based on capillary wave theory are proposed. It was observed that while increasing both ultrasonic vibration frequency and displacement resulted in reduction in droplet ejection initiation time and the formation of deeper holes for the given laser irradiation time (100 ms), the effect of vibration displacement was much more pronounced than the frequency on the variation.

On the Diffuse Structure of the Toluene–Water Interface

The electric density profile along the normal to the phase interface between aromatic hydrocarbon toluene and water has been studied by X-ray reflectometry using synchrotron radiation. According to the experimental data, the width of the interface under normal conditions is (5.7 +/- 0.2) Angstrom. This value is much larger than a theoretical value of (3.9 +/- 0.1) Angstrom predicted by the theory of capillary waves with an interphase tension of (36.0 +/- 0.1) mN/m. The observed broadening of the interface is attributed to its own diffuse near-surface structure with a width no less than 4 Angstroms, which is about the value previously discussed for high-molecular-weight n-alkane - water and 1,2-dichloroethane - water interfaces.

Model-Independent X-Ray Scattering Study of a Silica Sol Surface

The structure of the adsorbed layer of alkali ions on the surface of colloidal silica solutions with a particle size of ~27 nm has been studied by reflectometry and diffuse scattering of synchrotron radiation with a photon energy of about 71 keV. Electron density profiles in the direction perpendicular to the surface have been reconstructed from experimental data and spectra of the correlation function of heights in the surface plane have been obtained. The revealed deviation of the integral and frequency characteristics of the roughness spectra of the silica sol surface from predictions of the capillary-wave theory is of a fundamental character. This deviation is due to the contribution from roughnesses with low spatial frequencies and to the interference of diffuse scattering from different layer interfaces of the surface structure.

Capillary waves as eigenmodes of the density correlation at liquid surfaces

We analyze the density correlations in a liquid-vapor surface to establish a quantitative connection between the Density Functional (DF) formalism, Molecular Dynamic (MD) simulations, and the Capillary Wave (CW) theory. Instead of the integrated structure factor, we identify the CW fluctuations as eigenmodes of the correlation function. The square-gradient DF approximation appears as fully consistent with the use of the thermodynamic surface tension to describe the surface fluctuations for any wavevector because it misses the upper cutoff in the surface Hamiltonian from the merging of the CW mode with the non-CW band. This mesoscopic cutoff may be accurately predicted from the main peak in the structure factor of the bulk liquid. We explore the difference between the full density-density correlation mode and the bare CW that represents the correlation between the corrugation of the intrinsic surface and the density at the interfacial region. The non-local decay of the CW effects, predicted from DF analysis and observed in MD simulations with the intrinsic sampling method, is found to characterize the bare CW fluctuations, which also require a wavevector-dependent surface tension.

In-plane characterization of structural and thermodynamic properties for steps at faceted chemically heterogeneous solid/liquid interfaces

We present a methodology for studying steps at faceted chemically heterogeneous solid/liquid interfaces, based on equilibrium molecular-dynamics simulations. The methodology is applied to a faceted Al(111)/Pb(liquid) interface (750 K, ambient pressure), yielding a direct calculation of step free energy and extensive atomic-scale characterization for the interfacial layer containing the step. We demonstrate the power spectrum of the equilibrium step fluctuations obeys the capillary wave theory, and the calculated step free energy is consistent with experimental measurement [Acta Mater 2001; 49:4259]. The step fluctuations are identified to be governed by the attachment/detachment limited kinetics. Furthermore, we characterize the step by calculating the in-plane profiles of density, concentration, potential energy, pressure components and stresses. The fundamental properties of interface solid and interface liquid extracted from the in-plane profiles show orders of magnitudes difference in comparing with those predicted from the bulk Al-Pb alloy phase diagram. Several excess step properties are also determined along with defining a generalized Gibbs dividing surface.

Non-equilibrium surface tension of the vapour-liquid interface of active Lennard-Jones particles.

We study a three-dimensional system of self-propelled Brownian particles interacting via the Lennard-Jones potential. Using Brownian dynamics simulations in an elongated simulation box, we investigate the steady states of vapour-liquid phase coexistence of active Lennard-Jones particles with planar interfaces. We measure the normal and tangential components of the pressure tensor along the direction perpendicular to the interface and verify mechanical equilibrium of the two coexisting phases. In addition, we determine the non-equilibrium interfacial tension by integrating the difference of the normal and tangential components of the pressure tensor and show that the surface tension as a function of strength of particle attractions is well fitted by simple power laws. Finally, we measure the interfacial stiffness using capillary wave theory and the equipartition theorem and find a simple linear relation between surface tension and interfacial stiffness with a proportionality constant characterized by an effective temperature.

Capillary wave theory of adsorbed liquid films and the structure of the liquid-vapor interface.

In this paper we try to work out in detail the implications of a microscopic theory for capillary waves under the assumption that the density is given along lines normal to the interface. Within this approximation, which may be justified in terms of symmetry arguments, the Fisk-Widom scaling of the density profile holds for frozen realizations of the interface profile. Upon thermal averaging of capillary wave fluctuations, the resulting density profile yields results consistent with renormalization group calculations in the one-loop approximation. The thermal average over capillary waves may be expressed in terms of a modified convolution approximation where normals to the interface are Gaussian distributed. In the absence of an external field we show that the phenomenological density profile applied to the square-gradient free energy functional recovers the capillary wave Hamiltonian exactly. We extend the theory to the case of liquid films adsorbed on a substrate. For systems with short-range forces, we recover an effective interface Hamiltonian with a film height dependent surface tension that stems from the distortion of the liquid-vapor interface by the substrate, in agreement with the Fisher-Jin theory of short-range wetting. In the presence of long-range interactions, the surface tension picks up an explicit dependence on the external field and recovers the wave vector dependent logarithmic contribution observed by Napiorkowski and Dietrich. Using an error function for the intrinsic density profile, we obtain closed expressions for the surface tension and the interface width. We show the external field contribution to the surface tension may be given in terms of the film's disjoining pressure. From literature values of the Hamaker constant, it is found that the fluid-substrate forces may be able to double the surface tension for films in the nanometer range. The film height dependence of the surface tension described here is in full agreement with results of the capillary wave spectrum obtained recently in computer simulations, and the predicted translation mode of surface fluctuations reproduces to linear order in field strength an exact solution of the density correlation function for the Landau-Ginzburg-Wilson Hamiltonian in an external field.

Ultrasonic vibration-assisted laser atomization of stainless steel

In this paper, a novel ultrasonic vibration-assisted laser atomization process for producing fine metallic powder with average particle diameter of about 75–95μm is proposed. The process involves irradiation of a high power continuous wave laser on a consumable metallic substrate vibrating at an ultrasonic frequency. The laser irradiation on the vibrating substrate causes surface melting and expulsion of fine droplets. Preliminary results are presented for the atomization of AISI 316 stainless steel using CO2 laser power of 950W and vibration frequency of 20kHz. The average particle size and size distribution is not significantly influenced by vibration displacement consistent with capillary wave theory of atomization. The microstructure of the larger atomized particles showed fine dendritic structure at the surface and shrinkage porosity at the center of particles indicating multiple surface nucleation for solidification.

Ab initio study of intrinsic profiles of liquid metals and their reflectivity

The free surfaces of liquid metals are known to exhibit a stratified profile that, in favourable cases, shows up in experiments as a peak in the ratio between the reflectivity function and that of an ideal step-like profile. This peak is located at a wave-vector related to the distance between the layers of the profile. In fact the surface roughness produced by thermally induced capillary waves causes a depletion of the previous so called intrinsic reflectivity by a damping factor that may hinder the observation of the peak. The behaviour of the intrinsic reflectivity below the layering peak is however far from being universal, with systems as Ga or In where the reflectiviy falls uniformly towards the q → 0 value, others like Sn or Bi where a shoulder appears at intermediate wavevectors, and others like Hg which show a minimum. We have performed extensive ab initio simulations of the free liquid surfaces of Bi, Pb and Hg, that yield direct information on the structure of the profiles and found that the macroscopic capillary wave theory usually employed in order to remove the capillary wave components fails badly in some cases for the typical sample sizes affordable in ab initio simulations. However, a microscopic method for the determination of the intrinsic profile is shown to be succesful in obtaining meaningful intrinsic profiles and corresponding reflectivities which reproduce correctly the qualitative behaviour observed experimentally.

Capillary waves and the decay of density correlations at liquid surfaces.

Wertheim predicted strong density-density correlations at free liquid surfaces, produced by capillary wave fluctuations of the interface [M. S. Wertheim, J. Chem. Phys. 65, 2377 (1976)JCPSA60021-960610.1063/1.433352]. That prediction has been used to search for a link between capillary wave (CW) theory and density functional (DF) formalism for classical fluids. In particular, Parry etal. have recently analyzed the decaying tails of these CW effects moving away from the interface as a clue for the extended CW theory [A. O. Parry et al., J. Phys.: Condens. Matter 28, 244013 (2016)JCOMEL0953-898410.1088/0953-8984/28/24/244013], beyond the strict long-wavelength limit studied by Wertheim. Some apparently fundamental inconsistencies between the CW and the DF theoretical views of the fluid interfaces arose from the asymptotic analysis of the CW signal. In this paper we revisit the problem of the CW asymptotic decay with a separation of local non-CW surface correlation effects from those that are a truly nonlocal propagation of the CW fluctuations from the surface towards the liquid bulk.

Capillary wave Hamiltonian for the Landau–Ginzburg–Wilson density functional

We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau–Ginzburg–Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers.

Generalized model for laser-induced surface structure in metallic glass**Project supported by the National Natural Science Foundation of China (Grant Nos. 10572002, 10732010, and 11332002).

The details of the special three-dimensional micro-nano scale ripples with a period of hundreds of microns on the surfaces of a Zr-based and a La-based metallic glass irradiated separately by single laser pulse are investigated. We use the small-amplitude capillary wave theory to unveil the ripple formation mechanism through considering each of the molten metallic glasses as an incompressible viscous fluid. A generalized model is presented to describe the special morphology, which fits the experimental result well. It is also revealed that the viscosity brings about the biggest effect on the monotone decreasing nature of the amplitude and the wavelength of the surface ripples. The greater the viscosity is, the shorter the amplitude and the wavelength are.

Interfacial free energy of the NaCl crystal-melt interface from capillary wave fluctuations.

In this work we study, by means of molecular dynamics simulations, the solid-liquid interface of NaCl under coexistence conditions. By analysing capillary waves, we obtain the stiffness for different orientations of the solid and calculate the interfacial free energy by expanding the dependency of the interfacial free energy with the solid orientation in terms of cubic harmonics. We obtain an average value for the solid-fluid interfacial free energy of 89 ± 6 mN m(-1) that is consistent with previous results based on the measure of nucleation free energy barriers [Valeriani et al., J. Chem. Phys. 122, 194501 (2005)]. We analyse the influence of the simulation setup on interfacial properties and find that facets prepared as an elongated rectangular stripe give the same results as those prepared as squares for all cases but the 111 face. For some crystal orientations, we observe at small wave-vectors a behaviour not consistent with capillary wave theory and show that this behavior does not depend on the simulation setup.

Liquid-gas asymmetry and the wave-vector-dependent surface tension

Attempts to extend the capillary-wave theory of fluid interfacial fluctuations to microscopic wavelengths, by introducing an effective wave-vector (q)-dependent surface tension σeff(q), have encountered difficulties. There is no consensus as to even the shape of σeff(q). By analyzing a simple density functional model of the liquid-gas interface, we identify different schemes for separating microscopic observables into background and interfacial contributions. In order for the backgrounds of the density-density correlation function and local structure factor to have a consistent and physically meaningful interpretation in terms of weighted bulk gas and liquid contributions, the background of the total structure factor must be characterized by a microscopic q-dependent length ζ(q) not identified previously. The necessity of including the q dependence of ζ(q) is illustrated explicitly in our model and has wider implications; i.e., in typical experimental and simulation studies, an indeterminacy in ζ(q) will always be present, reminiscent of the cutoff used in capillary-wave theory. This leads inevitably to a large uncertainty in the q dependence of σeff(q).

Modeling of bubble coalescence in saline water in the presence of flotation frothers

This paper proposes a model based on the capillary wave theory of Valkovska, Danov and Ivanov to predict the lifetimes (τ) of small foam films confined between air bubbles in saline water containing flotation frothers such as sodium dodecyl sulfate (SDS), polypropylene glycol (PPG) with a molecular weight of 400, and methyl isobutyl carbinol (MIBC). The model considers the important issues of intersurface force, bubble size, surface tension, and film radius. The predicted τ values of these foam films were compared to the experimental ones. Under the assumption of tangentially immobile film surfaces, excellent agreement between model and experiment for τ was obtained for SDS and PPG, whereas τ was slightly under-predicted for MIBC. The model can be improved by adding an adjustable parameter that is related to the lateral diffusion constant and surface concentration of frother molecules at the air/water interface.

Crystal growth from a supersaturated melt: relaxation of the solid-liquid dynamic stiffness.

We discuss the growth process of a crystalline phase out of a metastable over-compressed liquid that is brought into contact with a crystalline substrate. The process is modeled by means of molecular dynamics. The particles interact via the Lennard-Jones potential and their motion is locally thermalized by Langevin dynamics. We characterize the relaxation process of the solid-liquid interface, showing that the growth speed is maximal for liquid densities above the solid coexistence density, and that the structural properties of the interface rapidly converge to equilibrium-like properties. In particular, we show that the off-equilibrium dynamic stiffness can be extracted using capillary wave theory arguments, even if the growth front moves fast compared to the typical diffusion time of the compressed liquid, and that the dynamic stiffness converges to the equilibrium stiffness in times much shorter than the diffusion time.