Showing papers on "Surface tension published in 2002"
TL;DR: In this article, a criterion based on contact line density is proposed for predicting the conditions that produce ultrahydrophobic surfaces, where, above a critical value, drops are suspended by asperities.
Abstract: Very rough surfaces can suspend small water drops, prevent wetting, and cause contact angles to approach 180°. A criterion based on contact line density is proposed for predicting the conditions that produce these ultrahydrophobic surfaces, where, above a critical value, drops are suspended by asperities. Critical values of the contact line density can be calculated from contact angles, asperity shape, and information about the contact liquid, such as density and surface tension. The criterion was found to correctly predict suspension for several model surfaces prepared by lithography techniques. Apparent contact angles from suspended and collapsed drops also were modeled by accounting for rough edges and employing a linear average of contact angle along the perimeter of the drop, rather than an area average of cosine. This linear model suggests that, for suspended drops, both advancing and receding angles should increase. Alternatively, for drops that have collapsed over surface asperities, advancing con...
568 citations
TL;DR: In this article, the authors developed an accurate representation of the body force due to surface tension, which effectively eliminates spurious currents, and called this algorithm PROST: parabolic reconstruction of surface tension.
544 citations
TL;DR: In this paper, an expression for the size-dependent melting for low-dimensional systems is derived on the basis of an analogy with the liquid-drop model and compared with other theoretical models as well as the available experimental data in the literature.
Abstract: Empirical relations are established between the cohesive energy, surface tension, and melting temperature of different bulk solids. An expression for the size-dependent melting for low-dimensional systems is derived on the basis of an analogy with the liquid-drop model and these empirical relations, and compared with other theoretical models as well as the available experimental data in the literature. The model is then extended to understand (i) the effect of substrate temperature on the size of the deposited cluster and (ii) the superheating of nanoparticles embedded in a matrix. It is argued that the exponential increase in particle size with the increase in deposition temperature can be understood by using the expression for the size-dependent melting of nanoparticles. Superheating is possible when nanoparticles with a lower surface energy are embedded in a matrix with a material of higher surface energy in which case the melting temperature depends on the amount of epitaxy between the nanoparticles and the embedding matrix. The predictions of the model show good agreement with the experimental results. A scaling for the size-dependent melting point suppression is also proposed.
543 citations
TL;DR: In this paper, the classical hybrid combustion theory is generalized to solid fuels that form a liquid layer on their burning surface, leading to substantial droplet entrainment into the gas stream.
Abstract: In this paper classical hybrid combustion theory is generalized to solid fuels that form a liquid layer on their burning surface. For several classes of liquefying fuels, the layer is hydrodynamically unstable in a gas e ow environment leading to substantial droplet entrainment into the gas stream. The susceptibility of a given fuel to this shear driven instability increases with decreasing viscosity and surface tension of the melt layer. The entrainment mass transfer, which acts in addition to the conventional gasie cation mechanism, is not affected by the blocking phenomenon induced by blowing from the surface. For practical oxidizer e ux levels encountered in hybrid rocket applications, droplet entrainment can dominate direct gasie cation. Such liquefying fuels can exhibit greatly increased surface regression rates compared to classical materials such as Hydroxyl Terminated Polybutadiene. One application of the theory is to solid cryogenic hybrids, which utilize frozen materials for the solid propellant. The theory successfully predicts why high regression rates are observed in tests of cryogenic solid pentane, solid methane, and solid oxygen. In addition, the theory explains the dependence of the burning rates of other tested cryogenic materials on the physical properties of the liquid layer. The theory also leads to the conclusion that certain noncryogenic materials such as parafe n and Polyethylene waxes will also exhibit high regression rates. This important result is cone rmed by lab scale tests performed at Stanford University on a high melting point parafe n wax.
367 citations
TL;DR: In this paper, surface tension measurements have long been used in the study of interaction between water soluble polymers and surfactants, and a brief discussion of the use of three of them, namely electron spin resonance, photon correlation spectroscopy, and atomic force microscopy, is given.
343 citations
TL;DR: In this paper, a three-dimensional model was developed to simulate the fluid dynamics, heat transfer and phase change that occur when a molten metal droplet falls onto a flat substrate.
328 citations
TL;DR: In this article, the effect of weak solute−solvent attractions on the solvation of nonpolar molecules in water at ambient conditions using an extension and improved parameterization of the theory of solvation due to Lum, Chandler, and Weeks was studied.
Abstract: We have studied the effect of weak solute−solvent attractions on the solvation of nonpolar molecules in water at ambient conditions using an extension and improved parameterization of the theory of solvation due to Lum, Chandler, and Weeks [J. Phys. Chem. B 1999, 103, 4570]. With a reasonable strength of alkane−water interactions, an accurate prediction of the alkane−water interfacial tension is obtained. As previously established for solutes with no attractive interactions with water, the free energy of solvation scales with volume for small solutes and with surface area for large solutes. The crossover to the latter regime occurs on a molecular length scale. It is associated with the formation of a liquid−vaporlike interface, a drying interface, between the large hydrophobic solute and liquid water. In the absence of attractions, this interface typically lies more than one solvent molecular diameter away from the hard sphere surface. With the addition of attractive interactions between water and the har...
327 citations
TL;DR: Among the four approaches, LW-AB was found to give the most consistent results and provides more detailed information about the microbial cell surface and the electron-donor parameter differentiates different type of cell surfaces.
303 citations
TL;DR: In this paper, a liquid drop (1−2 μL) is placed on a surface possessing a continuous gradient of wettability, it moves toward the more wettable part of the gradient with typical speeds of 1−2 mm/s.
Abstract: When a liquid drop (1−2 μL) is placed on a surface possessing a continuous gradient of wettability, it moves toward the more wettable part of the gradient with typical speeds of 1−2 mm/s. This low speed arises because the driving force due to surface tension is reduced by contact angle hysteresis. The hysteresis force acting on a drop on a gradient surface is, however, spatially asymmetricits magnitude against the gradient being larger than that along the gradient. If a periodic force is applied to a drop resting on such a gradient surface, the force against the gradient is rectified whereas it is enhanced along the gradient. This half-wave rectification of periodic force causes 1−2 μL size drops to move with enhanced speeds of 5−10 mm/s.
294 citations
TL;DR: The proposed modified Poisson-Boltzmann (MPB) theory accurately predicts newly measured disjoining pressures of thin-liquid foam films stabilized by polyethylene oxide n-alkyl ether surfactants and explains the fascinating existence of a surface tension minimum in dilute electrolyte solutions, known as the Jones-Ray effect.
261 citations
TL;DR: In this article, the pendant drop method was used for high-pressure measurement of the interfacial tension in a two-phase system of water and compressed carbon dioxide. But the experimental error of measurement is smaller than 2%.
Abstract: A novel apparatus, PeDro, for high-pressure measurement of the interfacial tension using the pendant drop method is presented. This apparatus was constructed for accurate measurements in the two-component system of water and compressed carbon dioxide. The main influences on accurate and reproducible results have been investigated, and the results have led to an optimized experimental setup and a quasi-static measuring method. PeDro was calibrated against well-established data for water + air. The experimental error of measurement is smaller than 2%. In this two-phase system measurements were conducted in the ranges (278 to 335) K and (0.1 to 20) MPa. The interfacial tension showed a pronounced dependence on pressure and temperature. A regression function has been found which describes the experimental data in the range investigated with high precision.
01 Jan 2002
TL;DR: A survey of the most common techniques used in interfacial tension measurements can be found in this paper, where Drelich et al. present a very brief overview of the methods used in inter-facial tension measurement.
Abstract: J. DrelichCh. FangC.L. WhiteMichigan Technological University, Houghton, MichiganINTRODUCTIONFor more than a century, a variety of techniques have beenused to measure interfacial tensions between immisci-ble fluid phases. A recent monograph by Rusanov andProkhorov (1) provides a broad review of the technicalliterature on the interfacial tension techniques with de-tailed discussion of the theoretical bases and instrumenta-tion. Additional valuable sources of information on the in-terfacial tension measurement methods include selectedchapters in Refs. 2–5. In this article, we present a verybrief overview of the most common techniques used ininterfacial tension measurements. The reader is encou-raged to explore Refs. 1–5 and references therein for fur-ther details.This article is organized as follows. ‘‘Classical Inter-facial Tension Measurement Methods’’ reviews the me-thods that are used in surface chemistry laboratories. Ashort comparison of these techniques is presented at theend of the section. This comparison has been prepared toguide a selection of the experimental method for mea-surements of interfacial tension in liquid-fluid systems,including systems with surfactants, viscous liquids, ormol-ten metals. Many of the industrial operations involve theliquid-fluid interfaces, for which the composition is cons-tantly refreshed and does not reach equilibrium. The im-portance of such dynamic interfacial tensions is increa-singly recognized to be essential to the understanding andcontrol of interfacial processes in multiphase, multicom-ponent systems. ‘‘Dynamic Interfacial Tension Measure-ments’’ discusses a freshly created interface. In ‘‘Measure-ment of Ultralow Interfacial Tension’’ an example of:when the value of interfacial tension is significantly lessthan 1 mN/m is discussed. Ultralow interfacial tensionsare common in the fluid systems of advanced tech-nologies of liquid-liquid emulsification processes wheneffective surfactant solutions are used. Finally, in ‘‘Mic-rotensiomery,’’ we discuss the methods of interfacialtension measurements that have been applied (or havepotential to be applied) to microinterfaces of microdrop-lets. Fundamental research on the interfacial properties ofnanomaterials (materials and particles with microstructur-al features on the micrometer or nanometer scale) anddroplets of micrometer-sized or nanometer-sized dimen-sion will be an important challenge in the rapidly deve-loping field of nanotechnology.CLASSICAL INTERFACIAL TENSIONMEASUREMENT METHODSFig. 1 shows a classification of common interfacial ten-sion measurement methods, both classical and modern.Group I represents examples of techniques commonlyused for direct measure of the interfacial tension with amicrobalance. The techniques in group II are those inwhich interfacial tension can be determined from directmeasurement of capillary pressure. Analysis of equilib-rium between capillary and gravity forces is employed inthe techniques of groups III and IV. Group III techniquesrely on the balance between surface tension forces and avariable volume of liquid, whereas Group IV techniquesfix the volume of a liquid drop and measure the distortionof that drop under the influence of gravity. Group V in-cludes techniques where the shapes of fluid drops are dis-torted by centrifugal forces and are used to measure ultra-low interfacial tensions.Group I: Direct MeasurementUsing a MicrobalanceInterfacial tension at fluid-fluid interfaces is a reflectionof the excess energy associated with unsaturated inter-molecular interactions at the interface. This excess energytends to drive interfaces to adopt geometries that mini-mize the interfacial area, and this tendency can be inter-preted as a physical force per unit length (i.e., a tension)
TL;DR: In this paper, the authors investigated the emulsification behavior at different flow velocities of the dispersed phase using MCs with different sizes and analogous shapes and found a critical flow velocity over which the character of flow changed drastically.
Abstract: Recently, we proposed a microchannel (MC) emulsification technique, which is a novel method for making a monodispersed emulsion from a microfabricated channel array. The droplet formation mechanism for MC emulsification is a unique one, in which the distorted dispersed phase is spontaneously transformed into spherical droplets by interfacial tension. The objective of this study was to characterize the flow in MC emulsification. We investigated the emulsification behavior at different flow velocities of the dispersed phase using MCs with different sizes and analogous shapes and found a critical flow velocity over which the character of flow changed drastically. The formed droplet diameters were almost constant below the critical velocity, and monodispersed emulsions were formed. The droplet diameters increased drastically above the critical velocity, and polydispersed emulsions were formed. The critical velocities were independent of MC size. Analysis using a dimensionless number revealed that the critical...
TL;DR: In this article, the second-gradient method is used to compute energy exchanges between surface and kinetic energies so that energy is strictly conserved, and the parasitic currents are reduced to round-off.
TL;DR: Protein-protein interactions were measured for ovalbumin and for lysozyme in aqueous salt solutions to correlated with a proposed potential of mean force equal to the free energy to desolvate the protein surface that is made inaccessible to the solvent due to the protein-protein interaction.
Abstract: Protein-protein interactions were measured for ovalbumin and for lysozyme in aqueous salt solutions. Protein-protein interactions are correlated with a proposed potential of mean force equal to the free energy to desolvate the protein surface that is made inaccessible to the solvent due to the protein-protein interaction. This energy is calculated from the surface free energy of the protein that is determined from protein-salt preferential-interaction parameter measurements. In classical salting-out behavior, the protein-salt preferential interaction is unfavorable. Because addition of salt raises the surface free energy of the protein according to the surface-tension increment of the salt, protein-protein attraction increases, leading to a reduction in solubility. When the surface chemistry of proteins is altered by binding of a specific ion, salting-in is observed when the interactions between (kosmotrope) ion-protein complexes are more repulsive than those between the uncomplexed proteins. However, salting-out is observed when interactions between (chaotrope) ion-protein complexes are more attractive than those of the uncomplexed proteins.
TL;DR: In this article, the Navier-Stokes equations with a free surface and surface tension are solved using a marker-chain approach using least-squares methods using a set of variables.
Abstract: We study numerically bubbles bursting at a free surface and the subsequent jet formation The Navier–Stokes equations with a free surface and surface tension are solved using a marker-chain approach Differentiation and boundary conditions near the free surface are satisfied using least-squares methods Initial conditions involve a bubble connected to the outside atmosphere by a preexisting opening in a thin liquid layer The evolution of the bubble is studied as a function of bubble radius A jet forms with or without the formation of a tiny air bubble at the base of the jet The radius of the droplet formed at the tip of the jet is found to be about one tenth of the initial bubble radius A series of critical radii exist, for which a transition from a dynamics with or without bubbles exist For some parameter values, the jet formation is close to a singular flow, with a conical cavity shape and a large curvature or cusp at the bottom This is compared to similar singularities investigated in other contexts such as Faraday waves
TL;DR: In this article, three phase H−LW−V equilibrium curves of pore hydrates were shifted to the higher pressure region depending on pore sizes when compared with those of bulk hyddrates, and the activities of water were expressed with a correction term to account for both capillary effect and activity decrease.
Abstract: Hydrate phase equilibria for the binary CH4 + water and CO2 + water mixtures in silica gel pores of nominal diameters 6.0, 15.0, and 30.0 nm were measured and compared with the calculated results based on van der Waals and Platteeuw model. At a specified temperature, three phase H−LW−V equilibrium curves of pore hydrates were shifted to the higher pressure region depending on pore sizes when compared with those of bulk hydrates. The activities of water in porous silica gels were expressed with a correction term to account for both capillary effect and activity decrease. By using the values of interfacial tension between hydrate and liquid water phases which were recently presented by Uchida et al.,5 the calculation values were in better agreement with the experimental ones. The structure and hydration number of CH4 hydrate in silica gel pores (6.0, 15.0, and 30.0 nm) were found to be identical with those of bulk CH4 hydrate through NMR spectroscopy.
TL;DR: In this paper, the dynamics of drop formation under gravity were investigated using a set of low-viscosity, ideal elastic fluids and an equivalent Newtonian glycerol-water solution.
Abstract: The dynamics of drop formation under gravity has been investigated as a function of elasticity using a set of low-viscosity, ideal elastic fluids and an equivalent Newtonian glycerol-water solution. All solutions had the same shear viscosity, equilibrium surface tension, and density, but differed greatly in elasticity. The minimum drop radius in the early stages of drop formation (necking) was found to scale as expected from potential flow theory, independent of the elasticity of the solutions. Thus, during this stage of drop formation when viscous force is still weak, the dynamics are controlled by a balance between inertial and capillary forces, and there is no contribution of elastic stresses of the polymer. However, upon formation of the pinch regions, there is a large variation in the drop development to break-off observed between the various solutions. The elastic solutions formed secondary fluid threads either side of a secondary drop from the necked region of fluid between the upper and lower pinches, which were sustained for increasing amounts of time. The break-off lengths and times increase with increasing elasticity of the solutions. Evolution of the filament, length is, however, identical in shape and form for all of the polymer solutions tested, regardless of differing elasticity. This de-coupling between filament growth rate and break-up time (or equivalently, final filament length at break-up) is rationalised. A modified force balance to that of Jones and Rees [48] is capable of correctly predicting the filament growth of these low-viscosity, elastic fluids in the absence of any elastic contributions due to polymer extension within the elongating filament. The elongation of the necked region of fluid (which becomes the filament) is dominated by the inertia of the drop, and is independent of the elasticity of the solution. However, elasticity does strongly influence the resistance of the pinch regions to break-off, with rapid necking resulting in extremely high rates of surface contraction on approach to the pinch point, initiating extension of the polymer chains within the pinch regions. This de-coupling phenomenon is peculiar to low-viscosity, elastic fluids as extension does not occur prior to the formation of the pinch points (i.e. just prior to break-up), as opposed to the high viscosity counterparts in which extension of polymers in solution may occur even during necking. Once steady-state extension of the polymers is achieved within the pinch at high extension rates, the thread undergoes elasto-capillary break-up as the capillarity again overcomes the viscoelastic forces. The final length at detachment and time-to-break-off (relative to the equivalent Newtonian fluid) is shown to be linearly proportional to the longest relaxation time of the fluid. (C) 2002 Elsevier Science B.V. All rights reserved.
TL;DR: Photolithography was used in combination with photocleavable self-assembled monolayers to pattern surface free energies inside microchannels enabling the control of the boundary between immiscible liquids.
Abstract: Photolithography was used in combination with photocleavable self-assembled monolayers to pattern surface free energies inside microchannels enabling the control of the boundary between immiscible liquids. While aqueous solutions are confined to the hydrophilic pathways by surface forces alone, organic liquids are confined to the hydrophobic region only if the aqueous liquid first occupies the hydrophilic region. In this way, stable liquid boundaries between immiscible liquids are possible as long as the pressures are maintained below critical values. The maximum pressures are determined by the interfacial tension of the aqueous solution and organic liquid, channel depth, and advancing contact angle (θa). Experimental results on maximum pressures are in good agreement with the analytical values. The ability to confine and position the boundary between immiscible liquids inside microchannels leads to a broad range of applications in microfluidic systems, which is exemplified by fabrication of a semipermeab...
TL;DR: In this paper, surface tension was used to investigate the composition and structure of the surfactant−polymer mixture of sodium dodecyl sulfate, SDS, and the cationic polymer poly(dimethyldially-lammonium chloride) at the air−water interface.
Abstract: Specular neutron reflection and surface tension have been used to investigate the composition and structure of the surfactant−polymer mixture of sodium dodecyl sulfate, SDS, and the cationic polymer poly(dimethyldiallylammonium chloride) at the air−water interface. The variation of surface tension with SDS concentration shows a complex behavior, with a marked increase between the concentrations normally associated with the critical aggregation concentration and the critical micellar concentration. The neutron reflectivity measurements show that this change in surface tension is associated with changes in the amount of SDS and polymer at the interface. The changes are attributed to the competition between the formation of surface and solution surfactant−polymer complexes.
TL;DR: In this article, extended x-ray absorption fine structure spectroscopy of liquid microjets has been employed to observe the intermolecular O-O distance undergo a 5.9% expansion at the liquid water interface, in contrast to liquid methanol for which there is a 4.6% surface contraction.
Abstract: X-ray absorption spectroscopy is a powerful probe of local electronic structure in disordered media. By employing extended x-ray absorption fine structure spectroscopy of liquid microjets, the intermolecular O–O distance has been observed to undergo a 5.9% expansion at the liquid water interface, in contrast to liquid methanol for which there is a 4.6% surface contraction. Despite the similar properties of liquid water and methanol (e.g., abnormal heats of vaporization, boiling points, dipole moments, etc.), this result implies dramatic differences in the surface hydrogen bond structure, which is evidenced by the difference in surface tension of these liquids. This result is consistent with surface vibrational spectroscopy, which indicates both stronger hydrogen bonding and polar ordering at the methanol surface as a consequence of “hydrophobic packing” of the methyl group.
TL;DR: In this article, the surface wettability and hydrophilicity of terminally grafted PVP and PVAc on smooth silicon wafers were investigated by advancing and receding contact angle measurements.
TL;DR: The physico-chemical aspects of the interaction between the membrane and mammalian cells in order to provide guidelines to the selection of cytocompatible membranes are investigated and it is observed that cell adhesion increased with increasing base parameter of membrane surface tension.
TL;DR: In this article, a theoretical model for ice growth due to droplets of supercooled fluid impacting on a subzero substrate is presented, which is valid for thin water layers and the Peclet number is small.
Abstract: A theoretical model for ice growth due to droplets of supercooled fluid impacting on a subzero substrate is presented. In cold conditions rime (dry) ice forms and the problem reduces to solving a simple mass balance. In milder conditions glaze (wet) ice forms. The problem is then governed by coupled mass and energy balances, which determine the ice height and water layer thickness. The model is valid for “thin” water layers, such that lubrication theory may be applied and the Peclet number is small; it is applicable to ice accretion on stationary and moving structures. A number of analytical solutions are presented. Two- and three-dimensional numerical schemes are also presented, to solve the water flow equation, these employ a flux-limiting scheme to accurately model the capillary ridge at the leading edge of the flow. The method is then extended to incorporate ice accretion. Numerical results are presented for ice growth and water flow driven by gravity, surface tension, and a constant air shear.
TL;DR: In this article, the influence of surface roughness on the thermodynamic interactions between carbon particles and polymer melts was investigated using low-molecular-weight analogues of polymers as probes.
Abstract: This work attempts to clarify the influence of surface roughness on the thermodynamic interactions between carbon particles and polymer melts. The surface energy of carbon black (CB) and short carbon fibers (VGCF) having different surface roughnesses was estimated by inverse gas chromatography (IGC) and highly sensitive isothermal calorimeter (HS−ITC) measurements using low-molecular-weight analogues of polymers as probes. We confirmed that the carbon surfaces possess energetic heterogeneity with the most active sites at the graphite crystalline edges, and the interactions in play are van der Waals in nature. Competitive adsorption of two chemically different polymers by incorporation of the carbon particles into the polymer blends was investigated based on SEM and TEM observations. We found that the selective location of CB in the polymer blends does not always depend on the surface tension of polymers but seems to be governed largely by the flexibility of the polymer chains. In VGCF-filled HDPE/PMMA com...
TL;DR: The surface tension and viscosity of liquid niobium, zirconium, and titanium have been determined by the oscillation drop technique using a vacuum electrostatic levitation furnace.
Abstract: The surface tension and viscosity of liquid niobium, zirconium, and titanium have been determined by the oscillation drop technique using a vacuum electrostatic levitation furnace. These properties are reported over wide temperature ranges, covering both superheated and undercooled liquid. For niobium, the surface tension can be expressed as σ(T)=1.937×103−0.199(T−T
m) (mN·m−1) with T
m=2742 K and the viscosity as η(T)=4.50−5.62×10−3(T−T
m) (mPa·s), over the 2320 to 2915 K temperature range. Similarly, over the 1800 to 2400 K temperature range, the surface tension of zirconium is represented as σ(T)=1.500×103−0.111(T−T
m) (mN·m−1) and the viscosity as η(T)=4.74−4.97 ×10−3(T−T
m) (mPa·s) where T
m=2128 K. For titanium (T
m=1943 K), these properties can be expressed, respectively, as σ(T)=1.557×103−0.156(T−T
m) (mN·m−1) and η(T)=4.42−6.67×10−3(T−T
m) (mPa·s) over the temperature range of 1750 to 2050 K.
TL;DR: In this article, an experimental flow visualization system was devised to facilitate observation of flow characteristics in filling into micro-channels, and a numerical analysis system was developed taking into account the surface tension effect with a contact angle concept.
Abstract: Understanding filling flow into micro-channels is important in designing micro-injection molding, micro-fluidic devices and an MIMIC (micromolding in capillaries) process. In this paper, we investigated, both experimentally and numerically, 'transient filling' flow into micro-channels, which differs from steady-state completely 'filled' flow in micro-channels. An experimental flow visualization system was devised to facilitate observation of flow characteristics in filling into micro-channels. Three sets of micro-channels of various widths of different thicknesses (20, 30, and 40 μm) were fabricated using SU-8 on the silicon substrate to find a geometric effect with regard to pressure gradient, viscous force and, in particular, surface tension. A numerical analysis system has also been developed taking into account the surface tension effect with a contact angle concept. Experimental observations indicate that surface tension significantly affects the filling flow to such an extent that even a flow blockage phenomenon was observed at channels of small width and thickness. A numerical analysis system also confirms that the flow blockage phenomenon could take place due to the flow hindrance effect of surface tension, which is consistent with experimental observation. For proper numerical simulations, two correction factors have also been proposed to correct the conventional hydraulic radius for the filling flow in rectangular cross-sectioned channels.
TL;DR: Neutral polymeric surfactants synthesized by covalent attachment of hydrophobic groups onto a polysaccharide backbone (dextran) behaved like classical associative polymers as demonstrated by viscometric measurements.
TL;DR: In this article, a numerical algorithm for the linear equation of state is developed for the volume-of-fluid interface-tracking code SURFER++, using the continuous surface stress formulation for the description of interfacial tension.
Abstract: A numerical algorithm for the linear equation of state is developed for the volume-of-fluid interface-tracking code SURFER++, using the continuous surface stress formulation for the description of interfacial tension. This is applied to deformation under simple shear for a liquid drop in a much more viscous matrix liquid. We choose a Reynolds number and capillary number at which the drop settles to an ellipsoidal steady state, when there is no surfactant. The viscosity ratio is selected in a range where experiments have shown tip streaming when surfactants are added. Our calculations show that surfactant is advected by the flow and moves to the tips of the drop. There is a threshhold surfactant level, above which the drop develops pointed tips, which are due to surfactant accumulating at the ends of the drop. Fragments emitted from these tips are on the scale of the mesh size, pointing to a shortcoming of the linear equation of state, namely that it does not provide a lower bound on interfacial tension. One outcome is the possibility of an unphysical negative surface tension on the emitted drops.