On the shape and size of liquid droplets on flat solid surfaces

Although Young's equation, γS=γSL+γL cos θC, is one of the oldest and most-used equations of classical physics and chemistry, it is in a rather delicate position scientifically, in that it is virtually impossible to prove experimentally. This is due, of course, to the uncertainties in the measurement of γS and γSL, the solid–air and solid–liquid surface tensions. Recently the validity of Young's equation has been questioned as the result of a theoretical analysis of the three-phase contact region where the liquid–air surface tension, γL, may be modified by interaction with the nearby substrate.The present paper argues that Young's equation is a "macroscopic" equation which does not concern itself with the microscopic shape of the liquid surface in the vicinity of the three-phase contact region. The concept of a microscopic contact angle θP is introduced. θP is the angle that the free liquid surface makes with the substrate when the liquid thickness is ≪∼ 10 Å, i.e., microscopically near the three-phase contact line. The contact angle θC given by Young's equation is shown to be the angle that the liquid surface makes with the substrate at microscopically large distances from the contact line where the modification of surface tensions by interaction is negligible (> 10 Å). The connection between θP and θC is established by making only very general statements about the nature of this interaction and does not impose the unphysical restrictions on the profile shape in the neighbourhood of the three-phase contact line which lead to the conclusions of Jameson and del Cerro.

The two-century old Young's equation has been widely used in petroleum engineering to depict wettability through contact angles and surface free energies. In order to address it's inadequacies, including the unaccounted vertical component of liquid-vapor interfacial tension and to accommodate the imbalance of intermolecular forces experienced by the three-phase confluence zone, the Young's equation has been modified in the recent literature to include a line tension term in case of solid-liquid-vapor (S-L-V) systems. In this paper, we would like to report on the results of our attempts to experimentally investigate the applicability of the line tension-based modification of the Young's equation to solid-liquid-liquid (rock-oil-brine) systems of interest to the petroleum industry. Both the ambient and reservoir condition optical cells have been used, with stock tank oil and live oil respectively, to determine the drop size dependency of dynamic contact angle subtended by the oil-brine interface against the rock surface. The experimental data have been correlated with the modified Young's equation to determine the magnitude of line tension in rock-oil-brine systems. To the best of our knowledge, this is the first attempt to apply the modified Young's equation to rock-oil-brine systems and to measure line tension for a rock-live crude oil-brine system at reservoir conditions of pressure and temperature. The measured line tension for solid-liquid-liquid (S-L-L) systems, while being positive and of the same order of magnitude as in solid-liquid-vapor (S-L-V) systems, correlates well with the water-advancing contact angle and the adhesion number, a ratio of adhesion force to capillary force. This experimental study indicates that the extent of deviation from the Young's equation exhibited by rock-oil-brine systems may be directly related to the adhesion phenomenon. This study reinforces the need to include the rock-oil adhesion forces in our consideration of rock-fluid interactions, wettability and their impact on improved oil recovery processes.

By extending the theoretical framework derived in our previous study [Imaizumi et al., J. Chem. Phys. 153, 034701 (2020)], we successfully calculated the solid-liquid (SL) and solid-vapor (SV) interfacial tensions of a simple Lennard-Jones fluid around solid cylinders with nanometer-scale diameters from single equilibrium molecular dynamics systems in which a solid cylinder was vertically immersed into a liquid pool. The SL and SV interfacial tensions γSL - γS0 and γSV - γS0 relative to that for bare solid surface γS0, respectively, were obtained by simple force balance relations on fluid-containing control volumes set around the bottom and top ends of the solid cylinder, which are subject to the fluid stress and the force from the solid. The theoretical contact angle calculated by Young's equation using these interfacial tensions agreed well with the apparent contact angle estimated by the analytical solution to fit the meniscus shape, showing that Young's equation holds even for the menisci around solids with nanoscale curvature. We have also found that the curvature effect on the contact angle was surprisingly small while it was indeed large on the local forces exerted on the solid cylinder near the contact line. In addition, the present results showed that the curvature dependence of the SL and SV interfacial free energies, which are the interfacial tensions, is different from that of the corresponding interfacial potential energies.

The equilibrium shape of a small liquid drop on a smooth rigid surface is governed by the minimization of energy with respect to the change in configuration, represented by the well-known Young's equation. In contrast, the equilibrium shape near the line separating three immiscible fluid phases is determined by force balance, represented by Neumann's Triangle. These two are limiting cases of the more general situation of a drop on a deformable, elastic substrate. Specifically, we have analyzed planar equilibrium shapes of a liquid drop on a deformable membrane. We show that to determine its equilibrium shape one must simultaneously satisfy configurational energy and mechanical force balance along with a constraint on the liquid volume. The first condition generalizes Young's equation to include changes in stored elastic energy upon changing the configuration. The second condition generalizes the force balance conditions by relating tensions to membrane stretches via their constitutive elastic behavior. The transition from Young's equation to Neumann's triangle is governed by the value of the elasto-capillary number, β = TRo/μh, where TRo is twice the surface tension of the solid-vapor interface, μ is the shear modulus of the membrane, and h is its thickness.

ABSTRACTThe shape of a liquid drop on a flat solid surface is examined by using the minimization of free energy. This free energy consists of the contributions from the gravitational potential energy of the drop mass and the energy of the interfacial surfaces. The minimization of free energy is solved by the Lagrange multipliers method keeping the drop volume constant. The generic differential equation for the shape of the drop and a relation among the contact angles (Young equation) are determined as a result of the minimization via the variation of a functional and by imposing the condition for equilibrium of the drop. The differential equation is solved analytically around the origin of the selected coordinate axis and for two special cases. For the general solution, the differential equation is solved numerically to obtain the general shape of the sessile drop. Furthermore, a new Axisymmetric Drop Shape Analysis method is proposed for non–wetting sessile drop.

Axisymmetric drop shape analysis by profile (ADSA-P) is a technique developed in colloid and surface science to simultaneously determine the contact angle and liquid surface tension from the profile of a droplet resting on a solid surface. In this paper is described how ADSA-P can be employed to assess bacterial biosurfactant production. Nine Streptococcus mitis strains, two of which are known to produce biosurfactants, and two S. salivarius strains, which do not produce biosurfactants, were suspended at two concentrations in a 10-mm potassium phosphate buffer, pH 7.0. Subsequently, a 100-μl droplet of each suspension was put on a fluoroethylenepropylene surface and the profile of the droplet determined with a contour monitor as a function of time up to 2 h. The surface tension of these suspensions was then calculated from the droplet profiles with ADSA-P. The surface tension of suspensions of the two non-producing strains remained stable within 4 mJ·m−2, whereas the surface tension of suspensions of five out of the nine S. mitis strains employed, including those of the known producer strains, decreased significantly (up to 26 mJ·m−2). This decrease was, in addition, concentration dependent. From these observations, we decided that all strains for which these concentration-dependent decreases were observed, could be regarded as biosurfactant producers. In order to rule out the possibility that the surface tension decreases observed were due to the collection of cells at the suspension-air interface, we investigated whether there was a relationship between surface tension decrease and hydrophobicity of the cells, as assessed by contact angle measurements and bacterial adhesion to hydrocarbons. Since no such a relationship was found, it can be concluded that ADSA-P is an excellent technique, based on using small amounts of cells to rapidly determine whether or not a bacterial strain produces biosurfactants.

One of the most important advantages of twin-fluid atomizers over other atomizers is the opportunity of atomizing liquids in a wide range of liquid properties efficiently. Thus, the fundamentals of spray dynamics, such as spray pattern, liquid breakup length, and spatial droplet size evolution using different liquid properties need to be investigated in some detail. The purpose of this study is therefore to examine and describe the influence of the liquid viscosity and surface tension on the spray performance of prefilming air-blast atomizers. A high-speed background shadowgraphy technique associated with particle tracking and Phase Doppler Anemometry (PDA) as a non-intrusive high-resolution local measurement technique were utilized to study the atomization process regarding the influence of the liquid properties on the spray quality. Generally, the break up mechanism is considerably influenced by the liquid viscosity. The breakup length ( ) is dependent on liquid viscosity with for Pa = 0.25 and 0.6 bar air pressure, respectively. Droplet size distribution profiles of different liquids in axial and radial directions are studied. No significant influences of the surface tension and viscosity were observed on the mean droplet velocity downstream of the spray. A minor increase of the droplet mean diameter was observed with liquid viscosity variations from 22 to 111 mPas, however, the liquid surface tension was verified to play an important role in the atomization process at prefilming airblast atomizers as well. According to the available experimental data, it has subsequently been possible to develop an original and descriptive model based on a dimensional approach at different air pressure ranges.

An experimental study on the behavior of droplets impinging on a solid flat surface was earned out in the present study. Breakup of a liquid droplet impinging on a solid surface has been investigated experimentally for various liquids With different properties The liquid droplet temperature and incident angle were chosen as major parameters Liquid droplet temperature and incident angle vaned in the range from -20℃ to 30℃ and from 30˚ to 60˚, respectively. it was found that the variation of droplet temperature influences upon the mean diameter and uniformity of droplets which were bounced out from the solid surface With increase of incident angle the dispersion mass fraction increases, causing the decrease of liquid film flow rate As the liquid temperature increases, dispersion mass fraction increases since the surface tension decreases.

Electric contribution to the surface tension of a dielectric liquid containing ions

This study reveals the microscopic mechanical balance at the three-phase contact line (TPCL) of an interfacial nanobubble on a substrate with a wettability pattern using molecular dynamics simulations. The apparent contact angle was compared to that evaluated using Young's equation, in which the interfacial tensions were computed using a mechanical route. The comparison was conducted by changing the wettability of the substrate from hydrophilic to neutral while maintaining a hydrophobic region in the center of the substrate. When the wettability pattern pins the TPCL at the wettability boundary, the contact angle computed by Young's equation is larger than the apparent contact angle because a pinning force exists in the inward direction of the nanobubble. Conversely, on the surfaces where the wettability pattern does not pin the TPCL, the contact angle computed by Young's equation agrees with the apparent contact angle because the pinning force disappears. The distribution of principal stresses around the TPCL, which was visualized for the first time in this study, indicates that large compressive principal stresses exist between the liquid phase and the solid substrate interface, which pin the TPCL at the surface wettability boundary, and that the maximum principal stress occurs in the inward direction of the nanobubbles at the TPCL. The normalized pinning force estimated from the maximum principal stress is equivalent to that measured experimentally.

Information on surface tension is necessary for modeling boiling processes in nanofluids. It was shown that the problem of predicting the surface tension of complex thermodynamic systems, such as nanofluids, remains outstanding. It should be noted that the surface tension of liquids and the saturated vapor pressure are due to a specific intermolecular interaction in the region of spatial heterogeneity of the substance (surface layer). Moreover, the compositions of the surface layer of nanofluid and its liquid phase are not equal. The presence of nanoparticles in the base fluid affects the composition of the surface layer of liquids. However, there are no methods for determining the composition of the surface layer of nanofluids and this fact complicates establishing the dependence of the surface tension on the state parameters of nanofluids. It should be mentioned that the number of possible methodological errors in measurements of the saturated vapor pressure of nanofluids is significantly lower than for the surface tension measurements. Therefore, in the development of models for predicting the surface tension, scientific and practical interest has establishing the relationship between the surface tension and the saturated vapor pressure of nanofluids. In the presented work, we consider the nanofluids of isopropanol/Al2O3 nanoparticles and o-xylene/fullerenes C60. Saturated vapor pressure and surface tension of nanofluids of isopropanol/Al2O3 nanoparticles have been studied in the temperature range 293 – 363 K and concentrations of Al2O3 nanoparticles 0-8.71 g/kg. Measurement of saturated vapor pressure and surface tension of nanofluids of o-xylene/fullerenes C60 have been performed in the temperature range 283 – 348 K and the concentration of C60 0-7.5 g/kg. It is shown that additives of Al2O3 nanoparticles and fullerenes C60 lead to a decrease in the surface tension and increase in the saturated vapor pressure. It is shown that there is a universal dependence between the reduced surface tension and saturated vapor pressure for the researched nanofluids.

Surface tension is a crucial property of liquids that depends on the liquid's composition. This study aims to compare the surface tension of water, chloroform, and acetone using the capillary rise method. It involves using a capillary tube with a known radius, dipping it vertically into a liquid, and measuring the height to which the liquid rises in the tube. The surface tension of the liquid can then be measured experimentally. This relates to height of the liquid in the tube, the radius of the tube, and the surface tension of the liquid. The height of the liquid in the tube is dependent on the radius of the tube, with a smaller radius resulting in a greater height. The surface tension of the liquid is inversely related to the radius of the capillary tube.

In this situation, the influence of surface tension of liquid on the bubble’s acoustic scattering is studied when the surface tension of liquid is equivalent to the static pressure of liquid. The continuity equation of velocity and pressure in the bubble’s surface is established, and the bubble’s surface tension of liquid is introduced into the continuity equation. We got the scattering coefficient and the scattering sound power of a single bubble in a symmetric vibration mode, and further deduced the equivalent incident sound field in the case of multi-bubble conditions. Numerical analysis shows that spherical bubble radius is about 10-6m when the surface tension equivalent to the liquid static pressure, in this case, the influence of bubble’s surface tension of liquid on the scattering coefficient and the scattering sound power of the single bubble can be shown when the angular frequency of the driving acoustic pressure is less than 105 rad/s. In the case of multiple bubbles, it will have a greater impact on the sound pressure amplitude of the equivalent incident sound field. While the influence will not appear clearly if the angular frequency of the driving acoustic pressure is bigger than 105 rad/s. For the acoustic scattering problem of bubbles, it bases on the specific issue to choose whether the surface tension of liquid should be taken into consideration.

Experimental measurements on liquid distribution in a trickle‐bed reactor are presented, as well as the effect of liquid and gas flow on radial liquid distribution. The influence of liquid density and surface tension was also investigated. The model for liquid distribution proposed by Herskowitz and Smith in 1978 was modified to incorporate the effect of particle orientation. Model parameters are correlated with liquid and gas flow rates, as well as liquid surface tension.

Interfacial Free Energies in Protein Solution Droplets on FEP-Teflon by Axisymmetric Drop Shape Analysis by Profile—IgG versus BSA