The aim of this work is to study the problem of the existence of a fundamental relation between the interfacial tension of a system of two partially miscible liquids and the surface tensions of the pure substances. It is shown that these properties cannot be correlated from the physical point of view. However, an accurate relation between them may be developed using a mathematical artifact. In the light of this work, the basis of the empirical formula of Girifalco and Good is examined. The weakness of this formula as well as the approximation leading to it are exposed and discussed and, a new equation connecting interfacial and surface tensions is proposed.
Hydrodynamic instabilities in miscible fluids are ubiquitous, from natural phenomena up to geological scales, to industrial and technological applications, where they represent the only way to control and promote mixing at low Reynolds numbers, well below the transition from laminar to turbulent flow. As for immiscible fluids, the onset of hydrodynamic instabilities in miscible fluids is directly related to the physics of their interfaces. The focus of this review is therefore on the general mechanisms driving the growth of disturbances at the boundary between miscible fluids, under a variety …
We exploit the deformation of drops spinning in a denser background fluid to investigate the effective interfacial tension (EIT) between miscible molecular fluids. We find that for sufficiently low interfacial tension, spinning drops develop dumbbell shapes, with two large heads connected by a thinner central body. We show that this shape depends not only on the density and viscosity contrast between the drop and background fluids, but also on the fluid molecular structure, and hence on the stresses developing at their interface due to different molecular interaction. We systematically investi…
We study the phase behavior and the interfacial tension of the screened Coulomb (Yukawa) restricted primitive model (YRPM) of oppositely charged hard spheres with diameter s using Monte Carlo simulations. We determine the gas-liquid and gas-solid phase transition using free energy calculations and grand-canonical Monte Carlo simulations for varying inverse Debye screening length k. We find that the gas-liquid phase separation is stable for k s <= 4, and that the critical temperature decreases upon increasing the screening of the interaction (decreasing the range of the interaction). In additio…
In passive fluid-fluid phase separation, a single interfacial tension sets both the capillary fluctuations of the interface and the rate of Ostwald ripening. We show that these phenomena are governed by two different tensions in active systems, and compute the capillary tension $σ_{cw}$ which sets the relaxation rate of interfacial fluctuations in accordance with capillary wave theory. We discover that strong enough activity can cause negative $σ_{cw}$. In this regime, depending on the global composition, the system self-organizes, either into a microphase-separated state in which coalescence …
We present a microscopic theory for the nonequilibrium interfacial tension $γ_{\rm gl}$ of the free interface between gas and liquid phases of active Brownian particles. The underlying square gradient treatment and the splitting of the force balance in flow and structural contributions is general and applies to inhomogeneous nonequilibrium steady states. We find $γ_{\rm gl}\geq 0$, which opposes claims by Bialké et al. [Phys. Rev. Lett. $\bf{115}$, 098301 (2015)] and delivers the theoretical justification for the widely observed interfacial stability in active Brownian dynamics many-body simul…
We study the fingering instability of the interface between two miscible fluids, a colloidal suspension and its own solvent. The temporal evolution of the interface in a Hele-Shaw cell is found to be governed by the competition between the non-linear viscosity of the suspension and an off-equilibrium, effective surface tension $Γ_e$. By studying suspensions in a wide range of volume fractions, $Φ_\mathrm{C}$, we show that $Γ_e \sim Φ_\mathrm{C}^2$, in agreement with Korteweg's theory for miscible fluids. The surface tension exhibits an anomalous increase with particle size, which we account fo…
A theory is presented to account for the increase in surface tension of water in the presence of electrolyte. Unlike the original ``grand-canonical'' calculation of Onsager and Samaras, which relied on the Gibbs adsorption isotherm and lead to a result which could only be expressed as an infinite series, our approach is ``canonical'' and produces an analytic formula for the excess surface tension. For small concentrations of electrolyte, our result reduces to the Onsager-Samaras limiting law.
The concept of a non-equilibrium interfacial tension, defined via the work required to deform the system such that the interfacial area is changed while the volume is conserved, is investigated theoretically in the context of the relaxation of an initial perturbation of a colloidal fluid towards the equilibrium state. The corresponding general formalism is derived for systems with planar symmetry and applied to fluid models of colloidal suspensions and polymer solutions. It is shown that the non-equilibrium interfacial tension is not necessarily positive, that negative non-equilibrium interfac…
We study the electrical double layer at the interface between a protein crystal and a salt solution or a dilute solution of protein, and estimate the double layer's contribution to the interfacial tension of this interface. This contribution is negative and decreases in magnitude with increasing salt concentration. We also consider briefly the interaction between a pair of protein surfaces.
We develop a methodology for the calculation of surface free energies based on the probability distribution of a wandering interface. Using a simple extension of the NpT sampling, we allow the interface area to randomly probe the available space and evaluate the surface free energy from histogram analysis and the corresponding average. The method is suitable for studying systems with either continuous or discontinuous potentials, as it does not require explicit evaluation of the virial. The proposed algorithm is compared with known results for the surface tension of Lennard--Jones and Square W…
We study numerically a model for active suspensions of self-propelled repulsive particles, for which a stable phase separation into a dilute and a dense phase is observed. We exploit that for non-square boxes a stable "slab" configuration is reached, in which interfaces align with the shorter box edge. Evaluating a recent proposal for an intensive active swimming pressure, we demonstrate that the excess stress within the interface separating both phases is negative. The occurrence of a negative tension together with stable phase separation is a genuine non-equilibrium effect that is rationaliz…
The interfacial tension of a liquid droplet surrounded by another liquid in the presence of microscopic ions is studied as a function of the droplet radius. An analytical expression for the interfacial tension is obtained within a linear Poisson-Boltzmann theory and compared with numerical results from non-linear Poisson-Boltzmann theory. The excess liquid-liquid interfacial tension with respect to the pure, salt-free liquid-liquid interfacial tension is found to decompose into a curvature-independent part due to short-ranged interfacial effects and a curvature-dependent electrostatic contribu…
Interfaces involving coexisting phases in condensed matter are essential in various examples of soft matter phenomena such as wetting, nucleation, morphology, phase separation kinetics, membranes, phase coexistence in nanomaterials, etc. Most analytical theories available use concepts derived from mean field theory which does not describe adequately these systems. Satisfactory numerical simulations for interfaces at atomistic to mesoscopic scales remains a challenge. In the present work, the interfacial tension between mixtures of organic solvents and water is obtained from mesoscopic computer…
We present a theory that is able to account quantitatively for the surface and interfacial tensions of different electrolyte solutions. It is found that near the interface, ions can be separated into two classes: the kosmotropes and the chaotropes. While the kosmotropes remain hydrated near the interface and are repelled from it, the chaotropes loose their hydration sheath and become adsorbed to the surface. The anionic adsorption is strongly correlated with the Jones-Dole viscosity B-coefficient. Both hydration and polarizability must be taken into account to obtain a quantitative agreement w…
We map molecular dynamics simulations of fluid-fluid interfaces onto mesoscale continuum theories for partially miscible fluids. Unlike most previous work, we examine not only the interface order parameter and density profiles, but also the stress. This allows a complete mapping from the length scales of molecular dynamics simulations onto a mesoscale model suitable for a lattice Boltzmann or other mesoscale simulation method. Typical assumptions of mesoscale models, such as incompressibility, are found to fail at the interface, and this has a significant impact on the surface tension. Spuriou…
One of the long standing challenges in molecular simulation is the description of interfaces. On the molecular length scale, finite size effects significantly influence the properties of the interface such as its interfacial tension, which can be reliably investigated by molecular dynamics simulation of planar vapor-liquid interfaces. For the Lennard-Jones fluid, finite size effects are examined here by varying the thickness of the liquid slab. It is found that the surface tension and density in the center of the liquid region decreases significantly for thin slabs. The influence of the slab t…
The critical behavior of a model colloid-polymer mixture, the so-called AO model, is studied using computer simulations and finite size scaling techniques. Investigated are the interfacial tension, the order parameter, the susceptibility and the coexistence diameter. Our results clearly show that the interfacial tension vanishes at the critical point with exponent 2ν~ 1.26. This is in good agreement with the 3D Ising exponent. Also calculated are critical amplitude ratios, which are shown to be compatible with the corresponding 3D Ising values. We additionally identify a number of subtleties t…
The isotropic to nematic transition in a system of soft spherocylinders is studied by means of grand canonical Monte Carlo simulations. The probability distribution of the particle density is used to determine the coexistence density of the isotropic and the nematic phases. The distributions are also used to compute the interfacial tension of the isotropic--nematic interface, including an analysis of finite size effects. Our results confirm that the Onsager limit is not recovered until for very large elongation, exceeding at least L/D=40, with L the spherocylinder length and D the diameter. Fo…
Mixtures of ideal polymers with hard spheres whose diameters are smaller than the radius of gyration of the polymer, exhibit extensive immiscibility. The interfacial tension between demixed phases of these mixtures is estimated, as is the barrier to nucleation. The barrier is found to scale linearly with the radius of the polymer, causing it to become large for large polymers. Thus for large polymers nucleation is suppressed and phase separation proceeds via spinodal decomposition, as it does in polymer blends.
Coexistence between the isotropic and the nematic phase in suspensions of rods is studied using grand canonical Monte Carlo simulations with a bias on the nematic order parameter. The biasing scheme makes it possible to estimate the interfacial tension gamma in systems of hard and soft rods. For hard rods with L/D=15, we obtain gamma ~ 1.4 kB T/L^2, with L the rod length, D the rod diameter, T the temperature, and kB the Boltzmann constant. This estimate is in good agreement with theoretical predictions, and the order of magnitude is consistent with experiments.
The interfacial tension between immiscible liquids is studied as a function of a model linear surfactant length and concentration using coarse grained, dissipative particle dynamics numerical simulations. The adsorption isotherms obtained from the simulations are found to be in agreement with Langmuir model. The reduction of the interfacial tension with increasing surfactant concentration is found to display some common characteristics for all the values of chain length modeled, with our predictions being in agreement with Szyszkowski equation. Lastly, the critical micelle concentration is pre…
In the presence of surfactants, the interfacial tension (IFT) of microscopic droplets differs significantly from IFT of macroscopic drops for the same surfactant solutions. As a result, IFT between two immiscible liquids can strongly depend on the experimental design. In the present work a simple theoretical description of two possible techniques for measurement of IFT at microdroplet surfaces is proposed: the spinning drop and the micropipette methods. We take into account that for microdroplets the IFT can be not the unique parameter determining the surface elastic energy. The previous inter…
Microgels are soft colloidal particles constituted by cross-linked polymer networks with a high potential for applications. In particular, after adsorption at a fluid interface, interfacial tension provides two-dimensional (2D) confinement for microgel monolayers and drives the reconfiguration of the particles, enabling their deployment in foam and emulsion stabilization and in surface patterning for lithography, sensing and optical materials. However, most studies focus on systems of fluids with a high interfacial tension, e.g. alkanes/ or air/water interfaces, which imparts similar propertie…
The self assembly of linear surfactants into reverse micelles (RMs) in nonpolar solvents and their efficiency in reducing the interfacial tension is studied using dissipative particle dynamics simulations. Given the importance of RMs as thickeners, among many other applications, their properties are studied here when formed in oil and in supercritical carbon dioxide (scCO2). Our simulations are found to be in agreement with experimental results of surfactant self assembly in scCO2 that found viscosity increments of up to 90 percent with 10 wt percent of surfactants. The role played by a small …
An extension of the Asakura-Oosawa-Vrij model of hard sphere colloids and non-adsorbing polymers, that takes polymer non-ideality into account through a repulsive stepfunction pair potential between polymers, is studied with grand canonical Monte Carlo simulations and density functional theory. Simulation results validate previous theoretical findings for the shift of the bulk fluid demixing binodal upon increasing strength of polymer-polymer repulsion, promoting the tendency to mix. For increasing strength of the polymer-polymer repulsion, simulation and theory consistently predict the interf…
It is theoretically shown that the excess liquid-liquid interfacial tension between two electrolyte solutions as a function of the ionic strength I behaves asymptotically as O(- I^0.5) for small I and as O(+- I) for large I. The former regime is dominated by the electrostatic potential due to an unequal partitioning of ions between the two liquids whereas the latter regime is related to a finite interfacial thickness. The crossover between the two asymptotic regimes depends sensitively on material parameters suggesting that, depending on the actual system under investigation, the experimentall…
Surface tension plays a ubiquitous role in phase transitions including condensation or evaporation of atmospheric liquid droplets. Especially, understanding of interfacial thermodynamics of the critical nucleus of 1 nm scale is important for molecular characterization of the activation energy barrier of nucleation. Here, we investigate surface tension of spherical nanodroplets with both molecular dynamics and density functional theory, and find that surface tension decreases appreciably below 1 nm radius, whose analytic expression is consistently derived from the classic Tolman's equation. In …
In the dilute limit Eshelby's inclusion theory captures the behavior of a wide range of systems and properties. However, because Eshelby's approach neglects interfacial stress, it breaks down in soft materials as the inclusion size approaches the elastocapillarity length $L$. Here, we use a three-phase generalized self-consistent method to calculate the elastic moduli of composites comprised of an isotropic, linear-elastic compliant solid hosting a spatially random monodisperse distribution of spherical liquid droplets. As opposed to similar approaches, we explicitly capture the liquid-solid i…
Dispersions of immiscible liquids, such as emulsions and polymer blends, are at the core of many industrial applications which makes the understanding of their properties (morphology, stability, etc.) of great interest. A wide range of these properties depend on interfacial phenomena, whose understanding is therefore of particular importance. The behaviour of interfacial tension in emulsions and polymer blends is well-understood -both theoretically and experimentally -in the case of non-reactive stabilization processes using pre-made surfactants. However, this description of the interfacial te…
We present a generalized theory for studying phase separation in blends of polymers containing dipoles on their backbone. The theory is used to construct co-existence curves and to study the effects of dipolar interactions on interfacial tension for a planar interface between the coexisting phases. We show that a mismatch in monomeric dipole moments, or equivalently a mismatch in the dielectric constant of the pure components, leads to destabilization of the homogeneous phase. Corrections to the Flory-Huggins phase diagram are predicted using the theory. Furthermore, we show that the interfaci…
By extending the theoretical framework derived in our previous study [Y. Imaizumi et al., J. Chem. Phys. 153, 034701 (2020)], we successfully calculated the solid-liquid (SL) and solid-vapor (SV) interfacial tensions of a simple Lennard-Jones fluid around solid cylinders with nanometer-scale diameters from single equilibrium molecular dynamics (MD) systems, in which a solid cylinder was vertically immersed into a liquid pool. The SL and SV interfacial tensions $γ_\mathrm{SL} - γ_\mathrm{S0}$ and $γ_\mathrm{SV} - γ_\mathrm{S0}$ relative to that for bare solid surface $γ_\mathrm{S0}$, respective…
We experimentally study the viscous fingering instability in a fluid-fluid phase separated colloid-polymer mixture by means of laser scanning confocal microscopy and microfluidics. We focus on three aspects of the instability. (i) The interface between the two demixed phases has an ultralow surface tension, such that we can address the role of thermal interface fluctuations. (ii) We image the interface in three dimensions allowing us to study the interplay between interface curvature and flow. (iii) The displacing fluid wets all walls completely, in contrast to traditional viscous fingering ex…
Molecular anatomy of the pressure anisotropy in the interface of one and two component fluids: local thermodynamic description of the interfacial tension
We present confocal microscopy studies of novel particle-stabilized emulsions. The novelty arises because the immiscible fluids have an accessible upper critical solution temperature. The emulsions have been created by beginning with particles dispersed in the single-fluid phase. On cooling, regions of the minority phase nucleate. While coarsening these nuclei become coated with particles due to the associated reduction in interfacial energy. The resulting emulsion is arrested, and the particle-coated interfaces have intriguing properties. Having made use of the binary-fluid phase diagram to c…
We study and predict the interfacial tension, solubility parameters and Flory-Huggins parameters of binary mixtures as functions of pressure and temperature, using multiscale numerical simulation. A mesoscopic approach is proposed for simulating the pressure dependence of the interfacial tension for binary mixtures, at different temperatures, using classical Dissipative Particle Dynamics (DPD). The thermodynamic properties of real systems are reproduced via the parametrization of the repulsive interaction parameters as functions of pressure and temperature via Molecular Dynamics simulations. U…
We have given theoretical expressions for the forces exerted on a quasi-2D flat and smooth solid plate immersed into a liquid pool of a simple liquid. All forces given by the theory, the local forces on the top, the contact line and the bottom of the plate as well as the total force, showed an excellent agreement with the MD simulation results. We also revealed that the local forces around the bottom and top of the solid plate can be related to the SL and SV interfacial tensions γ_{SL} and γ_{SV}, and this was verified through the comparison with the SL and SV works of adhesion obtained by the…
We propose a description for transient penetration simulations of miscible and immiscible fluid mixtures into anisotropic porous media, using the lattice Boltzmann (LB) method. Our model incorporates hydrodynamic flow, diffusion, surface tension, and the possibility for global and local viscosity variations to consider various types of hardening fluids. The miscible mixture consists of two fluids, one governed by the hydrodynamic equations and one by diffusion equations. We validate our model on standard problems like Poiseuille flow, the collision of a drop with an impermeable, hydrophobic in…
Spontaneous rotation of a droplet induced by the Marangoni flow is analyzed in a two-dimensional system. The droplet with the small particle which supplies a surfactant at the interface is considered. We calculated flow field around the droplet using Stokes equation and found that advective nonlinearity breaks symmetry for rotation. Theoretical calculation indicates that the droplet spontaneously rotates when the radius of the droplet is an appropriate size. The theoretical results were validated through comparison with the experiments.
In this contribution to the special issue of the Journal of Statistical Physics dedicated to Michael Fisher on his 70'th birthday, I shall review two thermodynamically distinct routes for obtaining the interfacial tension of liquid-vapor interfaces in mixtures. A specific application to the calculation of the excess surface tension of aqueous electrolyte solutions will be presented.
Ferrofluids are strongly magnetic fluids consisting of magnetic nanoparticles dispersed in a carrier fluid. Besides their technological applications, they have a tendency to form beautiful and intriguing patterns when subjected to external static and dynamic magnetic fields. Most of the patterns occur in systems consisting of two fluids: one ferrofluidic and one non-magnetic (oil, air, etc.), wherein the fluid-fluid interface deforms as a response to magnetic fields. Usually, the fluids are completely immiscible and so the interfacial energy in this systems is very large. Here we show that it …
In this paper we review simulation and experimental studies of thermal capillary wave fluctuations as an ideal means for probing the underlying disjoining pressure and surface tensions, and more generally, fine details of the Interfacial Hamiltonian Model. We discuss recent simulation results that reveal a film-height-dependent surface tension not accounted for in the classical Interfacial Hamiltonian Model. We show how this observation may be explained bottom-up from sound principles of statistical thermodynamics and discuss some of its implications.
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…
We have carried out extensive equilibrium molecular dynamics (MD) simulations to study the structure and the interfacial properties in the liquid-vapor (LV) phase coexistence of partially miscible binary Lennard-Jones (LJ) mixtures. By analyzing the structural properties as a function of the miscibility parameter, $ α$, we found that at relatively low temperatures the system separates forming a liquid A-liquid B interface in coexistence with the vapor phase. At higher temperatures and, $ 0<α\leq 0.5 $, we found a temperature range, $T^{*}_{w}(α) \leq T^{*} < T^{*}_{cons}(α)$, where the liquid …
We have analyzed the mechanical properties of surfactant loaded tensionless balanced liquid/liquid interfaces using self-consistent field theory implementing a coarse grained model. Such a tensionless state, as occurring in microemulsions, signals a first-order interfacial phase transition. Consequently, the interfacial area is set by the amount of surfactant in the system. Near the bulk critical point, such systems suffer an interfacial, so-called superflexibility (SF) critical point as soon as the tensionless state ceases to exist. This happens when the width of the L/L interface becomes com…
Several model fluids in contact with planar, spherical, and cylindrical walls are investigated for small number densities within density functional theory. The dependence of the solid-fluid interfacial tension on the curvature of spherical and cylindrical walls is examined and compared with the corresponding expression derived within the framework of morphometric thermodynamics. Particular attention is paid to the implications of the choice of the interface location, which underlies the definition of the interfacial tension. We find that morphometric thermodynamics is never exact for the consi…
The study of the modification of interfacial properties between an organic solvent and aqueous electrolyte solutions is presented by using electrostatic Dissipative Particle Dynamics (DPD) simulations. In this article the parametrization for the DPD repulsive parameters aij for the electrolyte components is calculated considering the dependence of the Flory-Huggins \c{hi} parameter on the concentration and the kind of electrolyte added, by means of the activity coefficients. In turn, experimental data was used to obtain the activity coefficients of the electrolytes as a function of their conce…
Using fluorescence microscopy we study the adsorption of single latex microparticles at a water/water interface between demixing aqueous solutions of polymers, generally known as a water-in-water emulsion. Similar microparticles at the interface between molecular liquids have exhibited an extremely slow relaxation preventing the observation of expected equilibrium states. This phenomenon has been attributed to "long-lived" metastable states caused by significant energy barriers $Δ{\cal F}\sim γA_d\gg k_B T$ induced by high interfacial tension ($γ\sim 10^{-2}$ N/m) and nanoscale surface defects…
A systematically designed study has been conducted to understand and clearly demarcate the degree of contribution by the constituting elements to the surface tension of nanocolloids. The effects of elements such as surfactants, particles and the combined effects of these on the interfacial tension of these complex fluids are studied employing pendant drop shape analysis method by fitting Young Laplace equation. Only particle has shown considerable increase in surface tension with particle concentration in a polar medium like DI water whereas only marginal effect particles on surface tension in…
Attempts to extend the capillary-wave theory of fluid interfacial fluctuations to microscopic wavelengths, by introducing an effective wave-vector ($q$) dependent surface tension $σ_\text{eff}(q)$, have encountered difficulties. There is no consensus as to even the shape of $σ_\text{eff}(q)$. By analysing 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 cons…
Eshelby's theory is the foundation of composite mechanics, allowing calculation of the effective elastic moduli of composites from a knowledge of their microstructure. However it ignores interfacial stress and only applies to very dilute composites -- i.e. where any inclusions are widely spaced apart. Here, within the framework of the Mori-Tanaka multiphase approximation scheme, we extend Eshelby's theory to treat a composite with interfacial stress in the non-dilute limit. In particular we calculate the elastic moduli of composites comprised of a compliant, elastic solid hosting a non-dilute …
