Line tension of a two dimensional gas-liquid interface

In two dimensional (2D) gas-liquid systems, the reported simulation values of line tension are known to disagree with the existing theoretical estimates. We find that while the simulation erred in truncating the range of the interaction potential, and as a result grossly underestimated the actual value, the earlier theoretical calculation was also limited by several approximations. When both the simulation and the theory are improved, we find that the estimate of line tension is in better agreement with each other. The small value of surface tension suggests increased influence of noncircular clusters in 2D gas-liquid nucleation, as indeed observed in a recent simulation.

The Determination of the Surface Tensions of Nickel Sulfur Alloys using the Electromagnetic Oscillating Droplet Technique

An oscillating droplet method combined with electromagnetic levitation technique has been applied to determine the surface tensions of liquid nickel sulphur alloys as a function of the temperature and composition. The natural frequency of the oscillating droplet is evaluated using a Fourier analyser, and the influence of magnetic field strength on the surface tension was considered. Furthermore, the applicability of Butler's equation and subregular solution model for the surface was shown to predict the surface tension of the systems containing the surface active elements.

Surface chemical characterisation of Paenibacillus polymyxa before and after adaptation to sulfide minerals

A heterotroph Paenibacillus polymyxa bacteria is adapted to pyrite, chalcopyrite, galena and sphalerite minerals by repeated subculturing the bacteria in the presence of the mineral until their growth characteristics became similar to the growth in the absence of mineral. The unadapted and adapted bacterial surface have been chemically characterised by zeta-potential, contact angle, adherence to hydrocarbons and FT-IR spectroscopic studies. The surface free energies of bacteria have been calculated by following the equation of state and surface tension component approaches. The aim of the present paper is to understand the changes in surface chemical properties of bacteria during adaptation to sulfide minerals and the projected consequences in bioflotation and bioflocculation processes. The mineral-adapted cells became more hydrophilic as compared to unadapted cells. There are no significant changes in the surface charge of bacteria before and after adaptation, and all the bacteria exhibit an iso-electric point below pH 2.5. The contact angles are observed to be more reliable for hydrophobicity assessment than the adherence to hydrocarbons. The Lifschitz–van der Waals/acid–base approach to calculate surface free energy is found to be relevant for mineral–bacteria interactions. The diffuse reflectance FT-IR absorbance bands for all the bacteria are the same illustrating similar surface chemical composition. However, the intensity of the bands for unadapted and adapted cells is significantly varied and this is due to different amounts of bacterial secretions underlying different growth conditions.

An improved free surface modeling for incompressible SPH

In Incompressible Smooth Particle Hydrodynamics (ISPH), a pressure Poisson equation (PPE) is solved to obtain a divergence free velocity field. When free surfaces are simulated using this method a Dirichlet boundary condition for pressure at the free surface has to be applied. In existing ISPH methods this is achieved by identifying free surface particles using heuristically chosen threshold of a parameter such as kernel sum, density or divergence of the position, and explicitly setting their pressure values. This often leads to clumping of particles near the free surface and spraying off of surface particles during splashes. Moreover, surface pressure gradients in flows where surface tension is important are not captured well using this approach. We propose a more accurate semi-analytical approach to impose Dirichlet boundary conditions on the free surface. We show the efficacy of the proposed algorithm by using test cases of elongation of a droplet and dam break. We perform two dimensional simulations of water entry and validate the proposed algorithm with experimental results. Further, a three dimensional simulation of droplet splash is shown to compare well with the Volume-of-Fluid simulations. (C) 2014 Elsevier Ltd. All rights reserved.

Capillary Effect on Vertically Excited Surface Wave in Circular Cylindrical Vessel

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions was developed in inviscid fluids to investigate the motion of single free surface standing wave including the effect of surface tension.

Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

Characters of Surface Deformation and Surface Wave in Thermal Capillary Convection

In the field of fluid mechanics, free surface phenomena is one of the most important physical processes. In the present research work, the surface deformation and surface wave caused by temperature difference of sidewalls in a rectangular cavity have been investigated. The horizontal cross-section of the container is 52 mmx42 mm, and there is a silicon oil layer of height 3.5 mm in the experimental cavity. Temperature difference between the two side walls of the cavity is increased gradually, and the flow on the liquid layer will develop from stable convection to un-stable convection. An optical diagnostic system consisting of a modified Michelson interferometer and image processor has been developed for study of the surface deformation and surface wave of thermal capillary convection. The Fourier transformation method is used to interferometer fringe analysis. The quantitative results of surface deformation and surface wave have been calculated from a serial of the interference fringe patterns.The characters of surface deformation and surface wave have been obtained. They are related with temperature gradient and surface tension. Surface deformation is fluctuant with time, which shows the character of surface wave. The cycle period of the wave is 4.8 s, and the amplitudes are from 0 to 0.55 mu m. The phase of the wave near the cool side of the cavity is opposite and correlative to that near the hot side. The present experiment proves that the surface wave of thermal capillary convection exists on liquid free surface, and it is wrapped in surface deformation.

Damping of Vertically Excited Surface Wave in Weakly Viscous Fluid

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.

Experimental Investigation Of Influence Of Interfacial Tension On Convection Of Two-Layer Immiscible Liquid

Benard-Marangoni convections of two-layer fluids heated from the bottom are investigated experimentally with a particle imagine velocimetry. The flows are visualized from the side, and various velocity fields near the onset of convection, such as three-layer vortex convective patterns, are observed when the depth ratio varies in a wide range. A new classification of the convective patterns is proposed with more detail than in previous studies. The analysis of the results indicates that the interface tension greatly influences the motion intensities of the bottom and top layers. The dimensionless wave number increases with the Bond number when the motion in the top layer is not more intense than that in the bottom layer, which agrees with the theoretical prediction.

Vertically forced surface wave in weakly viscous fluids bounded in a circular cylindrical vessel

Two-time scale perturbation expansions were developed in weakly viscous fluids to investigate surface wave motions by linearizing the Navier-Stokes equation in a circular cylindrical vessel which is subject to a vertical oscillation. The fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates a damping term and external excitation, was derived for the weakly viscid fluids. The condition for the appearance of stable surface waves was obtained and the critical curve was determined. In addition, an analytical expression for the damping coefficient was determined and the relationship between damping and other related parameters (such as viscosity, forced amplitude, forced frequency and the depth of fluid, etc.) was presented. Finally, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent.

The size-dependent bending elastic properties of nanobeams with surface effects

A theoretical model is presented to investigate the size-dependent bending elastic properties of a nanobeam with the influence of the surface relaxation and the surface tension taken into consideration. The surface layer and its thickness of a nanostructure are defined unambiguously. A three-dimensional (3D) crystal model for a nanofilm with n layers of relaxed atoms is investigated. The four nonzero elastic constants of the nanofilm are derived, and then the Young's modulus for simple tension is obtained. Using the relation of energy equilibrium, the size-dependent effective elastic modulus and effective flexural rigidity of a nanobeam with two kinds of cross sections are derived, and their dependence on the surface relaxation and the surface tension is analysed.

Surface effects in simple molecular systems

This thesis examines two problems concerned with surface effects in simple molecular systems. The first is the problem associated with the interaction of a fluid with a solid boundary, and the second originates from the interaction of a liquid with its own vapor.

For a fluid in contact with a solid wall, two sets of integro-differential equations, involving the molecular distribution functions of the system, are derived. One of these is a particular form of the well-known Bogolyubov-Born-Green-Kirkwood-Yvon equations. For the second set, the derivation, in contrast with the formulation of the B.B.G.K.Y. hierarchy, is independent of the pair-potential assumption. The density of the fluid, expressed as a power series in the uniform fluid density, is obtained by solving these equations under the requirement that the wall be ideal.

The liquid-vapor interface is analyzed with the aid of equations that describe the density and pair-correlation function. These equations are simplified and then solved by employing the superposition and the low vapor density approximations. The solutions are substituted into formulas for the surface energy and surface tension, and numerical results are obtained for selected systems. Finally, the liquid-vapor system near the critical point is examined by means of the lowest order B.B.G.K.Y. equation.

Effect of channel surface wettability and temperature gradients on the boiling flow pattern in a single microchannel

The objective of this paper is to investigate the effects of channel surface wettability and temperature gradients on the boiling flow pattern in a single microchannel. The test section consists of a bottom silicon substrate bonded with a top glass cover. Three consecutive parts of an inlet fluid plenum, a central microchannel and an outlet fluid plenum were etched in the silicon substrate. The central microchannel had a width of 800 mu m and a depth of 30 mu m. Acetone liquid was used as the working fluid. High outlet vapor qualities were dealt with here. The flow pattern consists of a fluid triangle (shrinkage of the liquid films) and a connected long liquid rivulet, which is generated in the central microchannel in the timescale of milliseconds. The peculiar flow pattern is formed due to the following reasons: (1) the liquid rivulet tends to have a large contact area with the top hydrophilic channel surface of the glass cover, but a smaller contact area with the bottom silicon hydrophobic surface. (2) The temperature gradient in the chip width direction at the top channel surface of the glass cover not only causes the shrinkage of the liquid films in the central microchannel upstream, but also attracts the liquid rivulet populated near the microchannel centerline. (3) The zigzag pattern is formed due to the competition between the evaporation momentum forces at the vapor-liquid interfaces and the force due to the Marangoni effect. The former causes the rivulet to deviate from the channel centerline and the latter draws the rivulet toward the channel centerline. (4) The temperature gradient along the flow direction in the central microchannel downstream causes the breakup of the rivulet to form isolated droplets there. (5) Liquid stripes inside the upstream fluid triangle were caused by the small capillary number of the liquid film, at which the large surface tension force relative to the viscous force tends to populate the liquid film locally on the top glass cover surface.

Numerical simulation of free surface behaviour of a molten liquid metal droplet with and without electromagnetic induction

Electromagnetic levitation of electrically conductive droplets by alternating magnetic fields is a technique used to measure the physical properties of liquid metallic alloys such as surface tension or viscosity. Experiments can be conducted under terrestrial conditions or in microgravity, to reduce electromagnetic stirring and shaping of the droplet. Under such conditions, the time-dependent behaviour of a point of the free surface is recorded. Then the signal is analysed considering the droplet as a harmonic damped oscillator. We use a spectral code, for fluid flow and free surface descriptions, to check the validity of this assumption for two cases. First when the motion inside the droplet is generated by its initial distortion only and second, when the droplet is located in a uniform magnetic field originating far from the droplet. It is found that some deviations exist which can lead to an overestimate of the value of viscosity.

Applying a QSPR correlation to the prediction of surface tensions of ionic liquids

Ionic liquids (ILs) have attracted large amount of interest due to their unique properties. Although large effort has been focused on the investigation of their potential application, characterization of ILs properties and structure–property relationships of ILs are poorly understood. Computer aided molecular design (CAMD) of ionic liquids (ILs) can only be carried if predictive computational methods for the ILs properties are available. The limited availability of experimental data and their quality have been preventing the development of such tools. Based on experimental surface tension data collected from the literature and measured at our laboratory, it is here shown how a quantitative structure–property relationship (QSPR) correlation for parachors can be used along with an estimation method for the densities to predict the surface tensions of ILs. It is shown that a good agreement with literature data is obtained. For circa 40 ionic liquids studied a mean percent deviation (MPD) of 5.75% with a maximum deviation inferior to 16% was observed. A correlation of the surface tensions with the molecular volumes of the ILs was developed for estimation of the surface tensions at room temperature. It is shown that it can describe the experimental data available within a 4.5% deviation. The correlations here developed can thus be used to evaluate the surface tension of ILs for use in process design or in the CAMD of new ionic liquids.