We report on the size dependence of the surface tension of a free surface of an isotropic fluid. The size dependence of the surface tension is evaluated based on the Gibbs-Tolman-Koenig-Buff equation for positive and negative values of curvatures and the Tolman lengths. For all combinations of positive and negative signs of curvature and the Tolman length, we succeed to have a continuous function, avoiding the existing discontinuity at zero curvature (flat interfaces). As an example, a water droplet in the thermodynamical equilibrium with the vapor is analyzed in detail. The size dependence of the surface tension and the Tolman length are evaluated with the use of experimental data of the International Association for the Properties of Water and Steam. The evaluated Tolman length of our approach is in good agreement with molecular dynamics and experimental data
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…
We study the breakup of a liquid thread inside another liquid at different surface tensions. In general, the pinch-off of a liquid thread is governed by the dynamics of fluid flow. However, when the interfacial tension is ultralow (2 to 3 orders lower than normal liquids), we find that the pinch-off dynamics can be governed by bulk diffusion. By studying the velocity and the profile of the pinch-off, we explain why the diffusion-dominated pinch-off takes over the conventional breakup at ultralow surface tensions.
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…
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.
A fluid constituted of hard spherocylinders is studied using a density functional theory for non-spherical hard particles, which can be written as a function of weighted densities. This is based on an extended deconvolution of the Mayer $f$-function for arbitrarily shaped convex hard bodies in tensorial weight functions, which depend each only on the shape and orientation of a single particle. In the course of an examination of the isotropic- nematic interface at coexistence the functional is applied to anisotropic and inhomogeneous problems for the first time. We find good qualitative agreeme…
In this paper we propose an analytic expression for surface tension of organic compounds. This new expression, originally derived from the statistical-mechanics is shown to represent the experimental surface tension data of 94 different organic compounds within 1.05 AAD%. We also propose another simpler expression. When this generalized expression is used surface tensions for all the 94 compounds can be predicted within 2.57 AAD% for all temperatures investigated.
Solid sheets and fluid membranes exhibit buckling under lateral compression. Here, it is revealed that fluid membranes have anisotropic buckling surface tension contrary to solid sheets. Surprisingly, the surface tension perpendicular to the buckling direction shows stronger dependence than that parallel to it. Our theoretical predictions are supported by numerical simulations of a meshless membrane model. This anisotropic tension can be used to measure the membrane bending rigidity. It is also found phase synchronization occurs between multilayered buckled membranes.
Breaking spatial symmetry is an essential requirement for phoretic active particles to swim at low Reynolds number. This fundamental prerequisite for swimming at the micro-scale is fulfilled either by chemical patterning of the surface of active particles or alternatively by exploiting geometrical asymmetries to induce chemical gradients and achieve self-propulsion. In the present manuscript, a far-field analytical model is employed to quantify the leading-order contribution to the induced phoretic velocity of a chemically homogeneous isotropic active colloid near a finite-sized disk of circul…
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 discuss the fluctuation-induced force, a finite-temperature analog of the Casimir force, between two inclusions embedded in a fluid membrane under tension. We suggest a method to calculate this Casimir interaction in the most general case, where membrane fluctuations are governed by the combined action of surface tension, bending modulus, and the Gaussian rigidity. We find that the surface tension strongly modifies the power law in the separation dependence of the Casimir interaction. This results in a strong suppression of the Casimir force at separations beyond a characteristic length, wh…
We study the dependence of the surface tension of a fluid interface on the density profile of a third suspended phase. By means of an approximated model for the binary mixture and of a perturbative approach we derive close formulas for the free energy of the system and for the surface tension of the interface. Our results show a remarkable non-monotonous dependence of the surface tension on the peak of the density of the suspended phase. Our results also predict the local value of the surface tension in the case in which the density of the suspended phase is not homogeneous along the interface…
A combination of fundamental measure density functional theory and Monte Carlo computer simulation is used to determine the orientation-resolved interfacial tension and stiffness for the equilibrium hard-sphere crystal-fluid interface. Microscopic density functional theory is in quantitative agreement with simulations and predicts a tension of 0.66 kT/σ^2 with a small anisotropy of about 0.025 kT and stiffnesses with e.g. 0.53 kT/σ^2 for the (001) orientation and 1.03 kT/σ^2 for the (111) orientation. Here kT is denoting the thermal energy and σthe hard sphere diameter. We compare our results …
We formulate a straightforward scheme of statistical mechanics for inhomogeneous systems that includes the virial series in powers of the activity for the grand free energy and density distributions. There, cluster integrals formulated for inhomogeneous systems play a main role. We center on second order terms that were analyzed in the case of hard-wall confinement, focusing in planar, spherical and cylindrical walls. Further analysis was devoted to the Lennard-Jones system and its generalization the 2k-k potential. For this interaction potentials the second cluster integral was evaluated anal…
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…
Molecular anatomy of the pressure anisotropy in the interface of one and two component fluids: local thermodynamic description of the interfacial tension
We analyze the effective potential for nanoparticles trapped at a fluid interface within a simple model which incorporates surface and line tensions as well as a thermal average over interface fluctuations (capillary waves). For a single colloid, a reduced steepness of the potential well hindering movements out of the interface plane compared to rigid interface models is observed, and an instability of the capillary wave partition sum in case of negative line tensions is pointed out. For two colloids, averaging over the capillary waves leads to an effective Casimir--type interaction which is l…
We identify a class of composite membranes: fluid bilayers coupled to an elastic meshwork, that are such that the meshwork's energy is a function $F_\mathrm{el}[A_ξ]$ \textit{not} of the real microscopic membrane area $A$, but of a \textit{smoothed} membrane's area $A_ξ$, which corresponds to the area of the membrane coarse-grained at the mesh size $ξ$. We show that the meshwork modifies the membrane tension $σ$ both below and above the scale $ξ$, inducing a tension-jump $Δσ=dF_\mathrm{el}/dA_ξ$. The predictions of our model account for the fluctuation spectrum of red blood cells membranes cou…
Within the Onsager theory we study free planar isotropic-nematic interfaces in binary mixtures of hard rods. For sufficiently different particle shapes the bulk phase diagrams of these mixtures exhibit a triple point, where an isotropic (I) phase coexists with two nematic phases ($N_1$ and $N_2$) of different composition. For all explored mixtures we find that upon approach of the triple point the $IN_2$ interface shows complete wetting by an intervening $N_1$ film. We compute the surface tensions of isotropic-nematic interfaces, and find a remarkable increase with fractionation, similar to th…
Molecular modelling and simulation of the surface tension of fluids with force fields is discussed. 29 real fluids are studied, including nitrogen, oxygen, carbon dioxide, carbon monoxide, fluorine, chlorine, bromine, iodine, ethane, ethylene, acetylene, propyne, propylene, propadiene, carbon disulfide, sulfur hexafluoride, and many refrigerants. The fluids are represented by two-centre Lennard-Jones plus point quadrupole models from the literature. These models were adjusted only to experimental data of the vapour pressure and saturated liquid density so that the results for the surface tensi…
Using density functionals from fundamental measure theory, phase diagrams and crystal-fluid surface tensions in additive and nonadditive (Asakura-Oosawa model) two-dimensional hard disk mixtures are determined for the whole range of size ratios $q$ between disks, assuming random disorder in the crystal phase. The fluid-crystal transitions are first-order due to the assumption of a periodic unit cell in the density functional calculations. Qualitatively, the shape of the phase diagrams is similar to the case of three-dimensional hard sphere mixtures. For the nonadditive case, a broadening of th…
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…
The thermodynamic properties of strong short-range attractive Yukawa fluids, k=10, 9, 8, and 7, are determined by combining the slab technique with the standard and the replica exchange Monte Carlo (REMC) methods. A good agreement was found among the coexistence curves of these systems calculated by REMC and those previously reported in the literature. However, REMC allows exploring the coexistence at lower temperatures, where dynamics turns glassy. To obtain the surface tension we employed, for both methods, a procedure that yields the pressure tensor components for discontinuous potentials. …
We present a new ternary free energy lattice Boltzmann model. The distinguishing feature of our model is that we are able to analytically derive and independently vary all fluid-fluid surface tensions and the solid surface contact angles. We carry out a number of benchmark tests: (i) double emulsions and liquid lenses to validate the surface tensions, (ii) ternary fluids in contact with a square well to compare the contact angles against analytical predictions, and (iii) ternary phase separation to verify that the multicomponent fluid dynamics is accurately captured. Additionally we also descr…
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…
We study the linear stability of an isotropic active fluid in three different geometries: a film of active fluid on a rigid substrate, a cylindrical thread of fluid, and a spherical fluid droplet. The active fluid is modeled by the hydrodynamic theory of an active nematic liquid crystal in the isotropic phase. In each geometry, we calculate the growth rate of sinusoidal modes of deformation of the interface. There are two distinct branches of growth rates; at long wavelength, one corresponds to the deformation of the interface, and one corresponds to the evolution of the liquid crystalline deg…
We have performed surface tension measurements on carbopol gels of different concentrations and yield stresses. Our setup, based on the force exerted by a capillary bridge on two parallel plates, allows to measure an effective surface tension of the complex fluid and to investigate the influence of flow history. More precisely the effective surface tension measured after stretching the bridge is always higher than after compressing it. The difference between the two values is due to the existence of a yield stress in the fluid. The experimental observations are successfully reproduced with a s…
The approach of global isomorphism between the fluid and the Ising model is applied to obtain an expression for the surface tension of the Lennard-Jones fluid on the basis of the information about the Ising model. This is done in a broad interval of temperatures along the phase coexistence, and is valid both in 2D and 3D. The relation between the critical amplitudes of the surface tension of the fluid and the Ising model is derived in the vicinity of the critical point. The obtained theoretical estimates agree well with the literature results for the surface tension. The methodology is demonst…
We analyze the surface tension exerted at the interface between an active fluid and a solid boundary in terms of tangential forces. Focusing on active systems known to possess an equation of state for the pressure, we show that interfacial forces are of a more complex nature. Using a number of macroscopic setups, we show that the surface tension is a combination of an equation-of-state abiding part and of setup-dependent contributions. The latter arise from generic setup-dependent steady currents which "dress" the measurement of the "bare" surface tension. The former shares interesting propert…
We consider a system of spherical colloidal particles with a size polydispersity and use a simple van der Waals description in order to study the combined effect of both the polydispersity and the spatial non-uniformity induced by a planar interface between a low-density fluid phase (enriched in small particles) and a high-density fluid phase (enriched in large particles). We find a strong adsorption of small particles at the interface, the latter being broadened with respect to the monodisperse case. We also find that the surface tension of the polydisperse system results from a competition b…
For isotropic fluids, classical nucleation theory predicts the nucleation rate, barrier height and critical droplet size by accounting for the competition between bulk energy and interfacial tension. The nucleation process in liquid crystals is less understood. We numerically investigate nucleation in monolayered nematogenic films using a mesoscopic framework, in particular, we study the mor- phology and kinetic pathway in spontaneous formation and growth of droplets of the stable phase in the metastable background. The parameter $κ$ that quantifies the anisotropic elastic energy plays a centr…
Comparing isotropic solids and fluids at either imposed volume or pressure we investigate various correlations of the instantaneous pressure and its ideal and excess contributions. Focusing on the compression modulus K it is emphasized that the stress fluctuation representation of the elastic moduli may be obtained directly (without a microscopic displacement field) by comparing the stress fluctuations in conjugated ensembles. This is made manifest by computing the Rowlinson stress fluctuation expression K_row of the compression modulus for NPT-ensembles. It is shown theoretically and numerica…
Two different tensions can be defined for a fluid membrane: the internal tension, $γ$, conjugated to the real membrane area in the Hamiltonian, and the frame tension, $τ$, conjugated to the projected (or frame) area. According to the standard statistical description of a membrane, the fluctuation spectrum is governed by $γ$. However, using rotational invariance arguments, several studies argued that fluctuation spectrum must be governed by the frame tension $τ$ instead. These studies disagree on the origin of the result obtained with the standard description yet: either a miscounting of config…
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 models of real fluids are validated by comparing the vapor-liquid surface tension from molecular dynamics (MD) simulation to correlations of experimental data. The considered molecular models consist of up to 28 interaction sites, including Lennard-Jones sites, point charges, dipoles and quadrupoles. They represent 38 real fluids, such as ethylene oxide, sulfur dioxide, phosgene, benzene, ammonia, formaldehyde, methanol and water, and were adjusted to reproduce the saturated liquid density, vapor pressure and enthalpy of vaporization. The models were not adjusted to interfacial prope…
Presenting simple coarse-grained models of isotropic solids and fluids in $d=1$, $2$ and $3$ dimensions we investigate the correlations of the instantaneous pressure and its ideal and excess contributions at either imposed pressure (NPT-ensemble, $λ=0$) or volume (NVT-ensemble, $λ=1$) and for more general values of the dimensionless parameter $λ$ characterizing the constant-volume constraint.
Using a geometry-based fundamental measure density functional theory, we calculate bulk fluid phase diagrams of colloidal mixtures of vanishingly thin hard circular platelets and hard spheres. We find isotropic-nematic phase separation with strong broadening of the biphasic region upon increasing the pressure. In mixtures with large size ratio of platelet and sphere diameter, there is also demixing between two nematic phases with differing platelet concentrations. We formulate a fundamental-measure density functional for mixtures of colloidal platelets and freely overlapping spheres, which rep…
We explore models of hard-rod fluids with a finite number of allowed orientations, and construct their bulk phase diagrams within Onsager's second virial theory. For a one-component fluid, we show that the discretization of the orientations leads to the existence of an artificial (almost) perfectly aligned nematic phase, which coexists with the (physical) nematic phase if the number of orientations is sufficiently large, or with the isotropic phase if the number of orientations is small. Its appearance correlates with the accuracy of sampling the nematic orientation distribution within its typ…
The mean field approximation is formulated within the framework of the density field theory to study the properties of a Maier-Saupe nematogenic fluid near a hard wall. The density and the order parameter profiles are obtained using the analytical expressions derived in the linearized mean field approximation. The temperature dependencies of the contact values of the density and order parameter profiles are analyzed in detail. To estimate a validity of the applied approximations, the obtained theoretical results are compared with the original computer simulation data.
Colloidal systems are often modelled as fluids of hard particles (possibly with an additional soft attraction, e.g. caused by polymers also contained in the suspension). in simulations of such systems, the virial theorem cannot be straightforwardly applied to obtain the components of the pressure tensor. In systems confined by walls, it is hence also not straightforward to extract the excess energy due to the wall (the "wall tension") from the pressure tensor anisotropy. A comparative evaluation of several methods to circumvent this problem is presented, using as examples fluids of hard sphere…
Although shear-induced isotropic-to-lamellar transitions in ternary systems of oil, water and surfactant have been observed experimentally and predicted theoretically by simple models for some time now, their numerical simulation has not been achieved so far. In this work we demonstrate that a recently introduced hydrodynamic lattice-gas model of amphiphilic fluids is well suited for this purpose: the two-dimensional version of this model does indeed exhibit a shear-induced isotropic-to-lamellar phase transition.
Motivated by a long-standing debate concerning the nature and interrelations of surface-tension variables in fluid membranes, we reformulate the thermodynamics of a membrane vesicle as a generic two-dimensional finite system enclosing a three-dimensional volume. The formulation is shown to require two tension variables, conjugate to the intensive constraints of area per molecule and volume-to-area ratio. We obtain the relation between these two variables in various scenarios, as well as their correspondence to other definitions of tension variables for membranes. Several controversies related …
It is shown that the interface model introduced in Phys. Rev. Lett. 86, 2369 (2001) violates fundamental symmetry requirements for vanishing gravitational acceleration $g$, so that its results cannot be applied to critical properties of interfaces for $g\to 0$.
Using computer simulations we show that lipid membranes can mediate linear aggregation of spherical nanoparticles binding to it for a wide range of biologically relevant bending rigidities. This result is in net contrast with the isotropic aggregation of nanoparticles on fluid interfaces or the expected clustering of isotropic insertions in biological membranes. We present a phase diagram indicating where linear aggregation is expected, and compute explicitly the free energy barriers associated with linear and isotropic aggregation. Finally, we provide simple scaling arguments to explain this …
We study fluctuation-induced interaction in confined fluids above the isotropic-lamellar transition. At an ideal continuous transition, the disjoining pressure has the asymptotic form $Π(d\to\infty)\approx -C k_BT q_0^2/d$, where $d$ is the interwall distance, $q_0$ is the wavenumber of the scattering peak, and $C= 1/(4π)$ in the strong anchoring limit. The long-rangedness is enhanced due to continuous distribution of soft modes in the ${\bf q}$-space. An unconventionally strong Casimir force with a range of several lamella thicknesses is realistic above the transition. We also find an oscilla…
Multi-particle collision dynamics is an appealing numerical technique aiming at simulating fluids at the mesoscopic scale. It considers molecular details in a coarse-grained fashion and reproduces hydrodynamic phenomena. Here, the implementation of multi-particle collision dynamics for isotropic fluids is analysed under the so-called Andersen-thermostatted scheme, a particular algorithm for systems in the canonical ensemble. This method gives rise to hydrodynamic fluctuations that spontaneously relax towards equilibrium. This relaxation process can be described by a linearized theory and used …
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 …
We apply a modified mean-field density functional theory to determine the phase behavior of binary mixtures of Stockmayer fluids whose spherical constituents interact according to Lennard-Jones (LJ) pair potentials with embedded pointlike dipole moments. On the basis of systematic numerical calculations we construct the global phase diagrams of these systems in the three-dimensional thermodynamic space of temperature, pressure, and chemical potential difference of the two components. The vapor-liquid, isotropic liquid - isotropic liquid, isotropic liquid - ferromagnetic liquid, and ferromagnet…
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…
A simple analytical microscopic expression for the surface tension of liquids $γ$ is obtained which is in a good agreement with available data of numerical experiments. We apply the integral transformation that maps the fluid Hamiltonian onto the field-theoretical Hamiltonian and show that the order parameter of the effective Hamiltonian corresponds to the one-body potential in the fluid. Revealing the physical meaning of the order parameter allows calculation of $γ$.
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…
The finger-like branching pattern that occurs when a less viscous fluid displaces a more viscous one confined between two parallel plates has been widely studied as a classical example of a mathematically-tractable hydrodynamic instability since the time of Saffman and Taylor. Fingering in such Hele-Shaw geometries have been generated not only with Newtonian fluids but also with various non-Newtonian fluids including fine granular material displaced by gas, liquid, or large grains. Here we study a granular Hele-Shaw system to explore whether the absence of cohesive forces in dry granular mater…
A generalized Van der Waals approach is developed for anisotropic fluids in disordered porous media. As the reference system a hard spherocylinder fluid in a disordered porous medium is considered and described in the framework of the scaled particle theory with the Carnahan-Starling and Parsons-Lee corrections. The attractive part of interaction is treated in the framework of the mean field approximation in which due to orientational dependence of the excluded volume of two spherocylinders, a coupling between attractive and repulsive contributions is found. We focus on spherocylinder fluids w…
