Hydrodynamics of nanoscopic capillary waves

Single Particle Dynamics at the Free Surface of Imidazolium-Based Ionic Liquids

In this work, we carry out a systematic computer simulation investigation of the single particle dynamics at the free surface of imidazolium-based room temperature ionic liquids by applying intrinsic surface analysis. Besides assessing the effect of the potential model and temperature, we focus in particular on the effect of changing the anion type, and, hence, their shape and size. Further, we also address the role of the length of the cation alkyl chains, known to protrude into the vapor phase, on the surface dynamics of the ions. We observe that the surface dynamics of ionic liquids, being dominated by strong electrostatic interactions, is about 2 orders of magnitude slower than that for common molecular liquids. Furthermore, the free energy driving force for exposing apolar chains to the vapor phase "pins" the cations at the surface layer for much longer than anions, allowing them to perform noticeable lateral diffusion at the liquid surface during their stay there. On the other hand, anions, accumulated in the second layer beneath the liquid surface, stay considerably longer here than in the surface layer. The ratio of the mean surface residence time of the cations and anions depends on the relative size of the two ions: larger size asymmetry typically corresponds to larger values of this ratio. We also find, in a clear contrast with the bulk liquid phase behavior, that anions typically diffuse faster at the liquid surface than cations. Finally, our results show that the surface dynamics of the ions is largely determined by the apolar layer of the cation alkyl chains at the liquid surface, as in the absence of such a layer, cations and anions are found to behave similarly with respect to their single particle dynamics.

Interfacial Thermal Fluctuations Stabilize Bulk Nanobubbles

Consensus on bulk nanobubble stability remains elusive, despite accepted indirect evidence for longevity. We develop a nanobubble evolution model by incorporating thermal capillary wave theory that reveals that dense nanobubbles generated by acoustic cavitation tend to shrink and intensify interfacial thermal fluctuations; this significantly reduces surface tension to neutralize enhanced Laplace pressure, and secures their stabilization at a finite size. A stability criterion emerges: thermal fluctuation intensity scales superlinearly with curvature: sqrt[⟨h^{2}⟩]∝(1/R)^{n}, n>1. The model prolongs the time frame for nanobubble contraction to 2 orders of magnitude beyond classical theory estimates, and captures the equilibrium radius (90-215 nm) within the experimental range.

Surface viscosity in simple liquids

The response of Newtonian liquids to small perturbations is usually considered to be fully described by homogeneous transport coefficients like shear and dilatational viscosity. However, the presence of strong density gradients at the liquid/vapor boundary of fluids hints at the possible existence of an inhomogeneous viscosity. Here, we show that a surface viscosity emerges from the collective dynamics of interfacial layers in molecular simulations of simple liquids. We estimate the surface viscosity to be 8-16 times smaller than that of the bulk fluid at the thermodynamic point considered. This result can have important implications for reactions at liquid surfaces in atmospheric chemistry and catalysis.

Thermal capillary waves on bounded nanoscale thin films

The effect of confining walls on the fluctuation of a nanoscale thin film's free surface is studied using stochastic thin-film equations (STFEs). Two canonical boundary conditions are employed to reveal the influence of the confinement: (1) an imposed contact angle and (2) a pinned contact line. A linear stability analysis provides the wave eigenmodes, after which thermal-capillary-wave theory predicts the wave fluctuation amplitudes. Molecular dynamics (MD) simulations are performed to test the predictions, and a Langevin diffusion model is proposed to capture oscillations of the contact lines observed in MD simulations. Good agreement between the theoretical predictions and the MD simulation results is recovered, and it is discovered that confinement can influence the entire film. Notably, a constraint on the length scale of wave modes is found to affect fluctuation amplitudes from our theoretical model, especially for 3D films. This opens up challenges and future lines of inquiry.

The Intrinsic Fragility of the Liquid-Vapor Interface: A Stress Network Perspective

The evolution of the liquid-vapor interface of a Lennard-Jones fluid is examined with molecular dynamics simulations using the intrinsic sampling method. Results suggest clear damping of the intrinsic profiles with increasing temperature. Investigating the surface stress distribution, we have identified a linear variation of the space-filling nature (fractal dimension) of the stress clusters at the intrinsic surface with increasing surface tension or, equivalently, with decreasing temperature. A percolation analysis of these stress networks indicates that the stress field is more disjointed at higher temperatures. This leads to more fragile (or poorly connected) interfaces which result in a reduction in surface tension.

Intrinsic structure perspective for MIPS interfaces in two-dimensional systems of active Brownian particles

Suspensions of active Brownian particles (ABPs) undergo motility-induced phase separation (MIPS) over a wide range of mean density and activity strength, which implies the spontaneous aggregation of particles due to the persistence of their direction of motion, even in the absence of an explicit attraction. Both similarities and qualitative differences have been obtained when the MIPS is analysed in the same terms as a liquid-gas phase coexistence in an equilibrium attractive system. Negative values of the mechanical surface tension have been reported, from the total forces across the interface, while stable fluctuations of the interfacial line could be interpreted as a positive capillary surface tension; in equilibrium liquid surfaces, these two magnitudes are equal. We present here the analysis of 2D-ABP interfaces in terms of the intrinsic density and force profiles, calculated with the particle distance to the instantaneous interfacial line. Our results provide new insight into the origin of MIPS from the local rectification of the random active force on the particles near the interface. As has been reported, this effect acts as an external potential that produces a pressure gradient across the interface, such that the mechanical surface tension of the MIPS cannot be described as that of equilibrium coexisting phases; however, our analysis shows that most of that effect comes from the tightly caged particles at the dense (inner) side of the MIPS interface, rather than from the free moving particles at the outer side that collide with the dense cluster. Moreover, a clear correlation appears between the decay of the hexatic order parameter at the dense slab and the end of the MIPS as the strength of the active force is lowered. We show that, using the strong active forces required for MIPS, the interfacial structure and properties are very similar for ABPs with purely repulsive interactions (the Weeks-Chandler-Andersen-Lennard-Jones (WCA-LJ) model truncated at its minimum) and when the interaction includes a range of the LJ attractive force.

Relaxation of Thermal Capillary Waves for Nanoscale Liquid Films on Anisotropic-Slip Substrates

The relaxation dynamics of thermal capillary waves for nanoscale liquid films on anisotropic-slip substrates are investigated using both molecular dynamics (MD) simulations and a Langevin model. The anisotropy of slip on substrates is achieved using a specific lattice plane of a face-centered cubic lattice. This surface's anisotropy breaks the simple scalar proportionality between slip velocity and wall shear stress and requires the introduction of a slip-coefficient tensor. The Langevin equation can describe both the growth of capillary wave spectra and the relaxation of capillary wave correlations, with the former providing a time scale for the surface to reach thermal equilibrium. Temporal correlations of interfacial Fourier modes, measured at thermal equilibrium in MD, demonstrate that (i) larger slip lengths lead to a faster decay in wave correlations and (ii) unlike isotropic-slip substrates, the time correlations of waves on anisotropic-slip substrates are wave-direction-dependent. These findings emerge naturally from the proposed Langevin equation, which becomes wave-direction-dependent, agrees well with MD results, and allows us to produce experimentally verifiable predictions.

Single-Particle Dynamics at the Intrinsic Surface of Aqueous Alkali Halide Solutions

The distribution of ions in the proximity of the liquid-vapor interface of their aqueous solution has been the subject of an intense debate during the last decade. The effects of ionic polarizability have been one of its salient aspects. Much less has been said about the corresponding dynamical properties, which are substantially unexplored. Here, we investigate the single-particle dynamics at the liquid-vapor interface of several alkali halide solutions, using molecular dynamics simulations with polarizable and nonpolarizable force fields and intrinsic surface analysis. We analyze the diffusion coefficient, residence time, and velocity autocorrelation function of water and ions and investigate how these properties depend on the molecular layer where they reside. While anions are found in the first molecular layer for relatively long times, cations are only making quick excursions into it, thanks to thermal fluctuations. The in-layer residence time of ions and their molar fraction in the layer turned out to be linearly dependent on each other. We interpret this unexpected result using a simple two-state model. In addition, we found that, unlike water and other neat molecular liquids that show a different diffusion mechanism at the surface than in the bulk of their liquid phase, ions do not enjoy enhanced mobility in the surface layer of their aqueous solution. This result indicates that ions in the surface layer are shielded by their nearest water neighbors from being exposed to the vapor phase as much as possible. Such positions are available for the ions at the negatively curved troughs of the molecularly rugged liquid surface.

Hydrodynamics across a fluctuating interface

Understanding what happens inside the rippling and dancing surface of a liquid remains one of the great challenges of fluid dynamics. Using molecular dynamics, we can pick apart the interface structure and understand surface tension. In this work, we derive an exact mechanical formulation of hydrodynamics for a liquid-vapor interface using a control volume, which moves with the surface. This mathematical framework provides the local definition of hydrodynamic fluxes at any point on the surface. These are represented not only by the flux of molecules and intermolecular interactions acting across the surface but also as a result of the instantaneous local curvature and movement of the surface itself. By explicitly including the surface dynamics in the equations of motion, we demonstrate an exact balance between kinetic and configurational pressure normal to the surface. The hydrodynamic analysis makes no assumptions regarding the probability distribution function, so it is valid for any system arbitrarily far from thermodynamic equilibrium. The presented equations provide a theoretical basis for the study of time-evolving interface phenomena, such as bubble nucleation, droplet dynamics, and liquid-vapor instabilities.

Curvature corrections to the nonlocal interfacial model for short-ranged forces

In this paper we revisit the derivation of a nonlocal interfacial Hamiltonian model for systems with short-ranged intermolecular forces. Starting from a microscopic Landau-Ginzburg-Wilson Hamiltonian with a double-parabola potential, we reformulate the derivation of the interfacial model using a rigorous boundary integral approach. This is done for three scenarios: a single fluid phase in contact with a nonplanar substrate (i.e., wall); a free interface separating coexisting fluid phases (say, liquid and gas); and finally a liquid-gas interface in contact with a nonplanar confining wall, as is applicable to wetting phenomena. For the first two cases our approaches identifies the correct form of the curvature corrections to the free energy and, for the case of a free interface, it allows us to recast these as an interfacial self-interaction as conjectured previously in the literature. When the interface is in contact with a substrate our approach similarly identifies curvature corrections to the nonlocal binding potential, describing the interaction of the interface and wall, for which we propose a generalized and improved diagrammatic formulation.

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.

Marangoni effect on small-amplitude capillary waves in viscous fluids

We derive a general integro-differential equation for the transient behavior of small-amplitude capillary waves on the planar surface of a viscous fluid in the presence of the Marangoni effect. The equation is solved for an insoluble surfactant solution in concentration below the critical micelle concentration undergoing convective-diffusive surface transport. The special case of a diffusion-driven surfactant is considered near the the critical damping wavelength. The Marangoni effect is shown to contribute to the overall damping mechanism, and a first-order term correction to the critical wavelength with respect to the surfactant concentration difference and the Schmidt number is proposed.

Capillary fluctuations of surface steps: An atomistic simulation study for the model Cu(111) system

Molecular dynamics (MD) simulations are employed to investigate the capillary fluctuations of steps on the surface of a model metal system. The fluctuation spectrum, characterized by the wave number (k) dependence of the mean squared capillary-wave amplitudes and associated relaxation times, is calculated for 〈110〉 and 〈112〉 steps on the {111} surface of elemental copper near the melting temperature of the classical potential model considered. Step stiffnesses are derived from the MD results, yielding values from the largest system sizes of (37±1)meV/A[over ˚] for the different line orientations, implying that the stiffness is isotropic within the statistical precision of the calculations. The fluctuation lifetimes are found to vary by approximately four orders of magnitude over the range of wave numbers investigated, displaying a k dependence consistent with kinetics governed by step-edge mediated diffusion. The values for step stiffness derived from these simulations are compared to step free energies for the same system and temperature obtained in a recent MD-based thermodynamic-integration (TI) study [Freitas, Frolov, and Asta, Phys. Rev. B 95, 155444 (2017)2469-995010.1103/PhysRevB.95.155444]. Results from the capillary-fluctuation analysis and TI calculations yield statistically significant differences that are discussed within the framework of statistical-mechanical theories for configurational contributions to step free energies.

Surface hydrodynamics of viscoelastic fluids and soft solids: Surfing bulk rheology on capillary and Rayleigh waves

From the recent advent of the new soft-micro technologies, the hydrodynamic theory of surface modes propagating on viscoelastic bodies has reinvigorated this field of technology with interesting predictions and new possible applications, so recovering its scientific interest very limited at birth to the academic scope. Today, a myriad of soft small objects, deformable meso- and micro-structures, and macroscopically viscoelastic bodies fabricated from colloids and polymers are already available in the materials catalogue. Thus, one can envisage a constellation of new soft objects fabricated by-design with a functional dynamics based on the mechanical interplay of the viscoelastic material with the medium through their interfaces. In this review, we recapitulate the field from its birth and theoretical foundation in the latest 1980s up today, through its flourishing in the 90s from the prediction of extraordinary Rayleigh modes in coexistence with ordinary capillary waves on the surface of viscoelastic fluids, a fact first confirmed in experiments by Dominique Langevin and me with soft gels [Monroy and Langevin, Phys. Rev. Lett. 81, 3167 (1998)]. With this observational discovery at sight, we not only settled the theory previously formulated a few years before, but mainly opened a new field of applications with soft materials where the mechanical interplay between surface and bulk motions matters. Also, new unpublished results from surface wave experiments performed with soft colloids are reported in this contribution, in which the analytic methods of wave surfing synthetized together with the concept of coexisting capillary-shear modes are claimed as an integrated tool to insightfully scrutinize the bulk rheology of soft solids and viscoelastic fluids. This dedicatory to the figure of Dominique Langevin includes an appraisal of the relevant theoretical aspects of the surface hydrodynamics of viscoelastic fluids, and the coverage of the most important experimental results obtained during the three decades of research on this field.

Towards the Irving-Kirkwood limit of the mechanical stress tensor

The probability density functions (PDFs) of the local measure of pressure as a function of the sampling volume are computed for a model Lennard-Jones (LJ) fluid using the Method of Planes (MOP) and Volume Averaging (VA) techniques. This builds on the study of Heyes, Dini, and Smith [J. Chem. Phys. 145, 104504 (2016)] which only considered the VA method for larger subvolumes. The focus here is typically on much smaller subvolumes than considered previously, which tend to the Irving-Kirkwood limit where the pressure tensor is defined at a point. The PDFs from the MOP and VA routes are compared for cubic subvolumes, V=ℓ3. Using very high grid-resolution and box-counting analysis, we also show that any measurement of pressure in a molecular system will fail to exactly capture the molecular configuration. This suggests that it is impossible to obtain the pressure in the Irving-Kirkwood limit using the commonly employed grid based averaging techniques. More importantly, below ℓ≈3 in LJ reduced units, the PDFs depart from Gaussian statistics, and for ℓ=1.0, a double peaked PDF is observed in the MOP but not VA pressure distributions. This departure from a Gaussian shape means that the average pressure is not the most representative or common value to arise. In addition to contributing to our understanding of local pressure formulas, this work shows a clear lower limit on the validity of simply taking the average value when coarse graining pressure from molecular (and colloidal) systems.

Single Particle Dynamics at the Intrinsic Surface of Various Apolar, Aprotic Dipolar, and Hydrogen Bonding Liquids As Seen from Computer Simulations

We investigate the single molecule dynamics at the intrinsic liquid/vapor interface of five different molecular liquids (carbon tetrachloride, acetone, acetonitrile, methanol, and water). After assessing that the characteristic residence times in the surface layer are long enough for a meaningful definition of several transport properties within the layer itself, we characterize the dynamics of the individual molecules at the liquid surface by analyzing their normal and lateral mean-square displacements and lateral velocity autocorrelation functions and, in the case of the hydrogen bonding liquids (i.e., water and methanol), also the properties of the hydrogen bonds. Further, dynamical properties as well as the clustering of the molecules residing unusually long in the surface layer are also investigated. The global picture emerging from this analysis is that of a noticeably enhanced dynamics of the molecules at the liquid surface, with diffusion coefficients up to 4 times larger than in the bulk, and the disappearance of the caging effect at the surface of all liquids but water. The dynamics of water is dominated by the strong hydrogen bonding structure also at the liquid surface.

Modeling multiphase flow using fluctuating hydrodynamics

Fluctuating hydrodynamics provides a model for fluids at mesoscopic scales where thermal fluctuations can have a significant impact on the behavior of the system. Here we investigate a model for fluctuating hydrodynamics of a single-component, multiphase flow in the neighborhood of the critical point. The system is modeled using a compressible flow formulation with a van der Waals equation of state, incorporating a Korteweg stress term to treat interfacial tension. We present a numerical algorithm for modeling this system based on an extension of algorithms developed for fluctuating hydrodynamics for ideal fluids. The scheme is validated by comparison of measured structure factors and capillary wave spectra with equilibrium theory. We also present several nonequilibrium examples to illustrate the capability of the algorithm to model multiphase fluid phenomena in a neighborhood of the critical point. These examples include a study of the impact of fluctuations on the spinodal decomposition following a rapid quench, as well as the piston effect in a cavity with supercooled walls. The conclusion in both cases is that thermal fluctuations affect the size and growth of the domains in off-critical quenches.

Effect of dispersion forces on the capillary-wave fluctuations of liquid surfaces

We present molecular dynamics evidence for the nonanalytic effects of the long-range dispersion forces on the capillary waves fluctuations of a Lennard-Jones liquid surface. The results of the intrinsic sampling method, for the analysis of the instantaneous interfacial shape, are obtained in large systems for several cut-off distances of the potential tail, and they show good agreement with the theoretical prediction by Napiórkowski and Dietrich, based on a density functional analysis. The enhancement of the capillary waves is quantified to be within 1% for a simple liquid near its triple point.

Intrinsic profiles and the structure of liquid surfaces

We present a brief review of the advances made in the characterization of liquid surfaces over the last decade. We focus particularly on the links between the capillary wave theory, the density functional formalism and the direct evaluation of the intrinsic density profiles from computer simulations. A new perspective of the liquid surfaces is appearing, with a sharper view of their molecular structure, which opens new challenges for theoretical and experimental studies. Novel results on the intrinsic interfacial structure of molten salt liquid-vapor interfaces are presented.

Thermal fluctuations of clusters with the long-range interaction

Analysis of surface fluctuation spectra is performed for a large cluster of particles interacting via a sum of the short-range Lennard-Jones potential and long-range ±1/r potential, where the positive sign corresponds to the gravity, and negative corresponds to the electrostatic interaction. The spectral amplitudes of thermally driven capillary modes in a self-consistent field induced by cluster particles including the modes with no axial symmetry are derived in the approximation of small amplitudes. It is demonstrated that within used approximation, the surface tension is independent of the field strength. The low wave vector amplitudes are damped by attracting field that compresses the cluster and magnified by repulsing field leading to cluster fission. The fission threshold is found to be different from that found by Bohr and Wheeler and Frenkel due to the replacement of the ordinary surface tension by the bare one. Molecular dynamics study of a cluster with the long-range interaction in the vapor environment is performed using a novel integrator for a multiscale system. Simulation scheme implies rotation of the long-range components of forces acting on cluster particles thus vanishing an artificial torque. Simulation results justify theoretical conclusion of modes damping and independence of the surface tension of the field strength. Fission threshold evaluated from simulation data is in a good agreement with theory.

Capillary waves of compressible fluids

The interplay of thermal noise and molecular forces is responsible for surprising features of liquids on sub-micrometer lengths-in particular at interfaces. Not only does the surface tension depend on the size of an applied distortion and nanoscopic thin liquid films dewet faster than would be expected from hydrodynamics, but also the dispersion relation of capillary waves differ at the nanoscale from the familiar macroscopic behavior. Starting with the stochastic Navier-Stokes equation we study the coupling of capillary waves to acoustic surface waves which is possible in compressible fluids. We find propagating 'acoustic-capillary waves' at nanometer wavelengths where in incompressible fluids capillary waves are overdamped.

The intrinsic interfacial structure of ionic surfactant monolayers at water–oil and water–vapour interfaces

Using computer simulations, we investigate the interfacial structure of sodium dodecyl sulphate (SDS) monolayers adsorbed at the water surface and water–oil interfaces. Using an algorithm that removes the averaging effect of the capillary waves, we obtain a detailed view of the solvation structure of water around the monolayer. We investigate surface concentrations between 45 and 33 Å 2 per surfactant, which are near experimental conditions corresponding to the critical micellar concentration and the formation of Newton black films. The surfactants induce a layering structure in water, which disappears at approximately 1 nm from the monolayer plane. The water molecules exhibit a preferred orientation with the dipoles pointing towards the monolayer. The orientational order decays slowly, but it does not influence the hydrogen bond structure of water, which is significantly disrupted in the interfacial region only. These structural changes are qualitatively the same in SDS–water and oil–SDS–water interfaces. In the latter case, we find a small degree of penetration of oil in the monolayer (between 0.2 and 0.25 molecules per SDS). This small penetration has a measurable effect on the monolayer, which increases its thickness by approximately 10 per cent. The bending modulus of the SDS monolayers is of the order of the thermal energy, k B T .

Laterally driven interfaces in the three-dimensional Ising lattice gas

We study the steady state of a phase-separated driven Ising lattice gas in three dimensions using computer simulations with Kawasaki dynamics. An external force field F(z) acts in the x direction parallel to the interface, creating a lateral order parameter current j^{x}(z) which varies with distance z from the interface. Above the roughening temperature, our data for "shearlike" linear variation of F(z) are in agreement with the picture wherein shear acts as effective confinement in this system, thus suppressing the interfacial capillary-wave fluctuations. We find sharper magnetization profiles and reduced interfacial width as compared to equilibrium. Pair correlations are more suppressed in the vorticity direction y than in the driving direction; the opposite holds for the structure factor. Lateral transport of capillary waves occurs for those forms of F(z) for which the current j^{x}(z) is an odd function of z , for example the shearlike drive, and a "steplike" driving field. For a V-shaped driving force no such motion occurs, but capillary waves are suppressed more strongly than for the shearlike drive. These findings are in agreement with our previous simulation studies in two dimensions. Near and below the (equilibrium) roughening temperature the effective-confinement picture ceases to work, but the lateral motion of the interface persists.

Nonequilibrium fluctuations of an interface under shear

The steady-state properties of an interface in a stationary Couette flow are addressed within the framework of fluctuating hydrodynamics. Our study reveals that thermal fluctuations are driven out of equilibrium by an effective shear rate that differs from the applied one. In agreement with experiments, we find that the mean-square displacement of the interface is reduced by the flow. We also show that nonequilibrium fluctuations present a certain degree of universality in the sense that all features of the fluids can be factorized into a single control parameter. Finally, the results are discussed in the light of recent experimental and numerical studies.

Kinetic theory of correlated fluids: from dynamic density functional to Lattice Boltzmann methods

Using methods of kinetic theory and liquid state theory we propose a description of the nonequilibrium behavior of molecular fluids, which takes into account their microscopic structure and thermodynamic properties. The present work represents an alternative to the recent dynamic density functional theory, which can only deal with colloidal fluids and is not apt to describe the hydrodynamic behavior of a molecular fluid. The method is based on a suitable modification of the Boltzmann transport equation for the phase space distribution and provides a detailed description of the local structure of the fluid and its transport coefficients. Finally, we propose a practical scheme to solve numerically and efficiently the resulting kinetic equation by employing a discretization procedure analogous to the one used in the Lattice Boltzmann method.

Solvent-mediated interactions between nanoparticles at fluid interfaces

We investigate the solvent-mediated interactions between nanoparticles adsorbed at a liquid-vapor interface in comparison to the solvent-mediated interactions in the bulk liquid and vapor phases of a Lennard-Jones solvent. Molecular dynamics simulation data for the latter are in good agreement with results from integral equations in the reference functional approximation and a simple geometric approximation. Simulation results for the solvent-mediated interactions at the interface differ markedly from the interactions of the particles in the corresponding bulk phases. We find that at short interparticle distances, the interactions are considerably more repulsive than those in either bulk phase. At long interparticle distances we find evidence for a long-ranged attraction. We discuss these observations in terms of interfacial interactions, namely, the three-phase line tension that would operate at short distances and capillary wave interactions for longer interparticle distances.