The role of surface tension in elastic wave scattering in an inhomogeneous poroelastic medium

It is well known that many porous media such as rocks have heterogeneities at nearly all scales. We applied Biot's poroelastic theory to study the propagation of elastic waves in isotropic porous matrix with spherical inclusions. It is assumed that the heterogeneity dimension exceeds significantly the pore size. Modified boundary conditions on poroelastic interface are used to take into account the surface tension effects. The effective wavenumber is calculated using the Waterman and Truell multiple scattering theory, which relates the effective wave number to the amplitude of the wave field scattered by a single inclusion. The calculations were performed for a medium containing fluid-filled cavities or porous inclusions contrasting in saturating fluid elastic properties. The results obtained show that when we consider elastic wave propagation in poroelastic medium containing soft inclusions, it is necessary to take into account the capillary pressure. The influence of the surface tension depends on the diffraction parameter and it is a maximum in the low frequency range.     

The role of surface tension in elastic wave scattering in an inhomogeneous poroelastic medium

It is well known that many porous media such as rocks have heterogeneities at nearly all scales. We applied Biot's poroelastic theory to study the propagation of elastic waves in isotropic porous matrix with spherical inclusions. It is assumed that the heterogeneity dimension exceeds significantly the pore size. Modified boundary conditions on poroelastic interface are used to take into account the surface tension effects. The effective wavenumber is calculated using the Waterman and Truell multiple scattering theory, which relates the effective wave number to the amplitude of the wave field scattered by a single inclusion. The calculations were performed for a medium containing fluid-filled cavities or porous inclusions contrasting in saturating fluid elastic properties. The results obtained show that when we consider elastic wave propagation in poroelastic medium containing soft inclusions, it is necessary to take into account the capillary pressure. The influence of the surface tension depends on the diffraction parameter and it is a maximum in the low frequency range.     

Electrostatic origin of the Frank elastic energy and anisotropic line tension of the domains in monolayers at the air-water interface

The free energy of condensed phase domains in monolayers at the air-water interface has been analyzed by taking into account the surface pressure, line tension, and electrostatic energy due to the normal and in-plane spontaneous polarization. We found that this free energy was reduced to the sum of the Frank elastic energy and anisotropic line tension, which were used to reproduce the shapes of domains in fatty acid monolayers, in the limit of small orientational deformation. Domains in monolayers are interesting systems as a meeting point between the physics of liquid crystals and electrostatics.     

Capillary analogue of the “dead water” effect in a stratified liquid with a charged interface

In terms of a linear mathematical model of a capillary-gravitational flow in a two-layer liquid with a finite-thickness upper layer, it is shown analytically that an analogue of the dead water phenomenon exists in the domain of capillary waves, which was previously observed only in gravitational waves. This phenomenon shows up as an exponential increase in the capillary wave amplitude at the interface with the surface tension coefficient at the interface tending to zero. It is found that an external electric field displaces this phenomenon toward the range of finite surface tension coefficients.     

Capillarity driven instability of a soft solid

We report the observation of a Plateau instability in a thin filament of solid gel with a very small elastic modulus. A longitudinal undulation of the surface of the cylinder reduces its area thereby triggering capillary instability, but is counterbalanced by elastic forces following the deformation. This competition leads to a nontrivial instability threshold for a solid cylinder. The ratio of surface tension to elastic modulus defines a characteristic length scale. The onset of linear instability is when the radius of the cylinder is one-sixth of this length scale, in agreement with theory presented here.     

Nematic liquid crystals at rough and fluctuating interfaces

Nematic liquid crystals at rough and fluctuating interfaces are analyzed within the Frank elastic theory and the Landau–de Gennes theory. We study specifically interfaces that locally favor planar anchoring. In the first part we reconsider the phenomenon of Berreman anchoring on fixed rough surfaces, and derive new simple expressions for the corresponding azimuthal anchoring energy. Surprisingly, we find that for strongly aligning surfaces, it depends only on the geometrical surface anisotropy and the bulk elastic constants, and not on the precise values of the chemical surface parameters. In the second part, we calculate the capillary waves at nematic-isotropic interfaces. If one neglects elastic interactions, the capillary wave spectrum is characterized by an anisotropic interfacial tension. With elastic interactions, the interfacial tension, i.e., the coefficient of the leading q² term of the capillary wave spectrum, becomes isotropic. However, the elastic interactions introduce a strongly anisotropic cubic q³ term. The amplitudes of capillary waves are largest in the direction perpendicular to the director. These results are in agreement with previous molecular dynamics simulations.     

Nanopore wall effect on surface tension of methane

Local pressure is known to be anisotropic across the interfaces separating fluids in equilibrium. Tangential pressure profiles show characteristic negative peaks as a result of surface tension forces parallel to the interface. Nearby attractive forces parallel to the interface are larger than the repulsive forces and, hence, constitute the surface tension. In this work, using molecular dynamics simulations of methane inside nano-scale pores, we show this surface tension behaviour could be significantly influenced by confinement effects. The layering structure, characterised by damped oscillations in local liquid density and tangential pressures, extends deep into the pore and can be a few nanometers thick. The surface tension is measured numerically using local pressures across the interface. Results show that the tension is smaller under confinement and becomes a variable in small pores, mainly controlled by the thickness of the liquid density layering (or liquid saturation) and the pore width. If the liquid saturation inside the pore is high enough, the vapour–liquid interface is not interfered by the pore wall and the surface tension remains the same as the bulk values. The results are important for understanding phase change and multi-phase transport phenomena in nanoporous materials.     

Experimental study of surface tension of ethane-methane solution in temperature range 213–283 K

The differential variation of the method of capillary rise was used to measure the capillary constant and to determine the surface tension of ethane-methane solution at “high” temperatures. Measurements were performed on the isotherms in the range of temperatures 213.15 ÷ 283.15 K at pressures up to 4 MPa. Decrease of ethane surface tension with the increase of pressure and concentration of methane in the solution is shown. The experimental data are compared with the results of surface tension calculation according to Rowlinson theory. Methane adsorption in the interface layer of solution is calculated.     

Spinodal dewetting of thin liquid films at soft interfaces

We study theoretically the behavior of nanoscopic liquid films L (thickness e) intercalated between a solid S and a rubber R (elastic modulus μ). Thickness modulations involve a healing length , which results from a competition between elastic and disjoining pressure. With van der Waals interactions, , where a is a molecular size and h₀ the rubber capillary length ( , interfacial tension). If the Hamaker constant of the intercalated liquid is negative, the film dewets by amplification of peristaltic fluctuations (“spinodal dewetting”). The typical size of the contacts is predicted to scale like for films of thicknesses . The rise time of the fastest mode, predicted to scale like , should be very sensitive to the film thickness. Received 11 February 2000 and Received in final form 22 May 2000     

A molecular dynamics study of effective parameters on nano-droplet surface tension

The main purpose of this paper is to numerically study the effect of droplet radius, temperature, and surface wettability on droplet surface tension. Moreover, the validity of Young-Laplace equation (Y-L) for nano-droplet is examined. Simulations of droplet surrounded by its vapor and droplet on solid surface are carried out and the results are compared to each other in order to comprehend the role of surface wettability on droplet surface tension. The pair potential for the liquid-liquid and liquid-solid interaction is considered using Lennard-Jones model. Different numbers of atoms and surface wettabilities are employed to generate droplet of different radiuses. In addition, contact angle of droplet on solid surface is computed. Pressure tensor and density profile is locally calculated. Furthermore, liquid pressure is evaluated far from the interface using the virial theorem and gas pressure is obtained using an equation of state. In order to calculate the surface tension, two different approaches are employed; Young-Laplace equation and direct molecular dynamics (MD) simulation. The surface tension increases with increase in droplet radius and it is seen that the surface wettability does not directly influence the surface tension.     

An auger investigation of oxygen-enhanced tin segregation on a liquid Pb−Sn alloy

Summary Auger measurements of the surface composition have been performed on solid and molten Pb-5at%Sn alloys. They confirm the theoretical predictions that, in the absence of oxygen, liquid or solid alloys exhibit no significant surface segregation. On the contrary, surface composition measurements and simultaneous surface tension measurements clearly show that oxygen adsorption strongly affects the segregation of tin at the liquid-vapour interface. This surface enrichment is driven by the contribution of the reaction free energy and of the products surface tension.     

汽液界面热毛细波的分子动力学模拟

用分子动力学模拟方法研究汽液界面性质,在NVT系综中,以氩原子为对象,对长方形模拟盒中汽液平衡系统进行不同温度下的模拟计算。计算结果表明,汽液界面存在热毛细波。界面上的热涨落将使界面变宽,它不仅与界面张力有关,还与温度、界面的横截面积有关。可以把汽液界面上热毛细波的均分根涨落值,作为汽液界面的宽度和粗糙度的指标。     

Numerical simulations of gas-liquid two-phase flows in a micro porous structure

The lattice Boltzmann method for two-phase fluid flows is applied to the simulations of gas-liquid two-phase flows in a micro porous structure for various capillary numbers at low Reynolds numbers. The behaviors of the gas-liquid interface and the velocities of the two-phase fluid in the structure are simulated, and the permeability of gas and liquid through the structure are estimated from the calculated results. By changing the void fraction, the contact angle of the interface on walls, and the surface tension, the effect of these properties on the behaviors and the permeability of the two-phase flows in the micro porous structure is investigated. It is found that the permeability of liquid flows depends on the contact angle and it increases for hydrophobic walls. It is also seen that liquid flows are choked in pores for large void fractions and low capillary numbers.     

Hydrocarbons imbibition for geometrical characterization of porous media through the effective radius approach

Surface energetic characterization of porous solids usually requires the determination of the contact angle. This quantity is deduced by imbibition experiments carried out in such media with high surface tension liquids. Now then, this methodology needs the geometrical characterization of the porous medium by means of the deduction of its effective radius. Normally, this is made by imbibition experiments with n-alkanes, liquids whose surface tension is low enough as to suppose their contact angles with the solid surface are null. However, this last procedure is not free from some criticisms. Among them, the possible influence of the imbibition velocity on the contact angle, the effect of the precursor liquid film ahead the advancing liquid front on the driving force that gives rise to the movement, or the dependence of the effective radius on the length of the hydrocarbon chain of the n-alkanes. In an attempt of going deeply in these questions, imbibition experiments with n-alkanes have been carried out in porous columns of powdered calcium fluoride. These experiments have consisted of the measurement of the increase in the weight of the columns caused by the migration of the liquids through their interstices. The analysis of their results has been carried out by means of a new procedure based on the study of the velocity profile associated to the weight increase. This analysis has permitted us to conclude that, at least in the calcium fluoride columns, the contact angle of the n-alkane is not influenced by the capillary rise velocity, it taking in fact a null value during the process. On the other hand, it has been also proved that the driving force of the movement is caused by the replacement of the solid-vapour interface by the solid-liquid interface that happens during the imbibition, which means that only the Laplace's pressure, and not the precursor liquid film, contributes to the development of the phenomenon. Finally, it has been compared the values of the effective radius associated to each n-alkane, similar values being found independently from the particular liquid employed in the experiments, fact that indicates that the porous solid can be considered as a bunch of cylindrical and parallel capillaries of the same radius.     

Shearing or compressing a soft glass in 2D: time-concentration superposition

We report surface shear rheological measurements on dense insoluble monolayers of micron sized colloidal spheres at the oil/water interface and of the protein beta-lactoglobulin at the air/water surface. As expected, the elastic modulus shows a changing character in the response, from a viscous liquid towards an elastic solid as the concentration is increased, and a change from elastic to viscous as the shear frequency is increased. Surprisingly, above a critical packing fraction, the complex elastic modulus curves measured at different concentrations can be superposed to form a master curve. This provides a powerful tool for the extrapolation of the material response function outside the experimentally accessible frequency range. The results are discussed in relation to recent experiments on bulk systems, and indicate that these two-dimensional monolayers should be regarded as being close to a soft glass state.     

Deformation of an elastic substrate by a three-phase contact line

Young's classic analysis of the equilibrium of a three-phase contact line ignores the out-of-plane component of the liquid-vapor surface tension. While it is expected that this unresolved force is balanced by the elastic response of the solid, a definitive analysis has remained elusive because of an apparent divergence of stress at the contact line. While a number of theories have been presented to cut off the divergence, none of them have provided reasonable agreement with experimental data. We measure surface and bulk deformation of a thin elastic film near a three-phase contact line using fluorescence confocal microscopy. The out-of-plane deformation is well fit by a linear elastic theory incorporating an out-of-plane restoring force due to the surface tension of the solid substrate. This theory predicts that the deformation profile near the contact line is scale-free and independent of the substrate elastic modulus.     

The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform,classical fluids

Recent theoretical work on the microscopic structure and surface tension of the liquid-vapour interface of simple (argon-like) fluids is critically reviewed. In particular, the form of pairwise intermolecular correlations in the liquid surface and the capillary wave treatment of the interface are examined in some detail. It is argued that conventional capillary wave theory, which leads to divergences in the width of the density profile, is unsatisfactory for describing all the equilibrium aspects of the interface. The density functional formalism which has been developed to study the liquid-vapour interface can also be profitably applied to other problems in the statistical mechanics of non-uniform fluids; here a new generalization of the ‘linear’ theory of spinodal decomposition is formulated and by considering a ‘nearly uniform’ fluid, some useful results for the long-wavelength behaviour of the liquid structure factor of various monatomic liquids are obtained. Some other topics of current interest in this area are briefly discussed.     

Effect of contact line curvature on solid-fluid surface tensions without line tension

For sessile droplets partially wetting a solid surface, it has been observed experimentally that the value of the contact angle depends on the contact line curvature and this dependence has been attributed to tension in the contact line. But previous analyses of these observations have neglected adsorption at the solid-liquid interface and its effect on the surface tension of this interface. We show that if this adsorption is taken into account the relation between the contact angle and contact line curvature is completely accounted for without introducing line tension. Further, from the observed relation between the contact angle and contact line curvature, the adsorption at the solid-liquid interface can be determined, as can the surface tensions of the solid-liquid and solid-vapor interfaces.     

Phase transition detection by surface photo charge effect in liquid crystals

The surface photo charge effect (SPCE) was applied for the first time at structure and phase transitions study of hydrogen bonded in dimer liquid crystals (HBDLCs). Due to the high sensitivity of this method, besides first-order phase transitions, characteristic for the p,n-octyloxibenzoic acids (8OBA), an order transition was definitely detected within the nematic range. We state that the SPCE, arising at the solid–HBDLCs interface due to the double electrical layer, is invariably concomitant with solid surface–liquid interfaces, and indicates that the changes of the characteristics of this layer, under incident optical irradiation, induce surface charge rearrangement and alternating potential difference. A mechanism of induction of the SPCE at the interface of solid surface–anisotropic liquids is proposed. We also indicate that this mechanism can be adapted for solid surface–isotropic liquid interface, including colloids (milk) and fog (aerosols)–condensed medium.     

Surface tension measurement of liquid metal with inelastic light-scattering spectroscopy of a thermally excited capillary wave

Thermally excited capillary waves propagate everywhere on a liquid surface. The relationship between the frequency and wavelength of the capillary wave reflects the surface tension of the liquid, and the lifetime of the capillary wave reflects the shear viscosity of the liquid. By observing a capillary wave with inelastic light-scattering spectroscopy, we can obtain the surface tension and the viscosity from the frequency modulation of the light and the spectral width of the scattered light. In this study, we observed capillary waves on liquid metal using high-resolution spectroscopy, and successfully measured their properties in a non-contact manner. In the experiment, values were obtained at a frequency of about 20 kHz. The values were equivalent to those at 0 Hz, since the properties of liquid metals are constant at least in the frequency region from 0 to several tens of kilohertz.