Young-Laplace Research Articles

Use of a Geometric Parameter for Characterizing Rigid Films at Oil-Water Interfaces.

Interfacial tension and dilatational rheology are often used to characterize the mechanical response of a liquid interface using axisymmetric drop shape analysis (ADSA). It is important to note that for systems dominated by adsorption/desorption of surfactants, the contributions of extra mechanical stresses are negligible; thus, the Young-Laplace equation remains valid. However, for interfaces dominated by extra stresses, as in the case of particle monolayers or asphaltenes that clearly exhibit a skin (a rigid film), the nature of the elastic response is fundamentally different and the validity of the equation is questionable. Calculation of the interfacial tension and dilatational elasticity using drop shape analysis depends critically on the drop shape following the Young-Laplace equation. If the interface becomes more like a solid, the drop shape will deviate from being purely Laplacian. Indeed, the drop will exhibit a wrinkled surface as collapse continues. The geometric parameter RV/A, defined as the ratio (dV/V)/(dA/A) with V is the volume of the drop and A is the area of the interface), allows one to measure the deviation of the drop shape from purely Laplacian. For a simple interface (pure liquids or surfactant solutions), RV/A is quite close to the theoretical value of 1.5 of a perfect sphere. Nevertheless, if the molecules adsorbed at the interface begin to interact strongly, the ratio can vary. In the limit of long-time-scale experiments, RV/A of some drops approaches 2. We studied the evolution of the parameter RV/A for different systems, from simple to complex, as a function of oscillation frequencies and amplitudes of drop volume. The results obtained were compared to the values of the interfacial moduli and drop shape behavior to better characterize the regime change.

Impact of Particle Sedimentation in Pendant Drop Tensiometry.

Understanding the interface-stabilizing properties of surface-active components is key in designing stable macroscopic multiphase systems, such as emulsions and foams. When poorly soluble materials are used as an interface stabilizer, the insoluble material may sediment and interfere with the analysis of interfacial properties in pendant (or hanging) drop tensiometry. Here, the impact of sedimentation of particles on the interfacial properties determined by pendant drop tensiometry was evaluated using a model system of whey protein isolate and (non surface-active) glass beads (2.2–34.7 μm). Although the glass beads did not adsorb to the air–water interface, a 1% (w/w) glass bead solution appeared to decrease the surface tension by nearly 12 mN/m after 3 h. A similar effect was shown for a mixture of whey proteins and glass beads: the addition of 1% (w/w) of glass beads led to an apparent surface tension decrease of 31 mN/m rather than the 20 mN/m observed for pure whey proteins. These effects are attributed to the sedimentation of particles near the apex of the droplet, leading to droplet shape changes, which are interpreted as a decrease in surface tension using tensiometer software. The droplet density at the apex increases due to sedimentation, and this density increase is not accounted for when fitting the droplet shape with the Young–Laplace equation. The result is the observed apparent decrease in surface tension. In contrast to the significant impact of sedimenting material on the surface tension measurements, the impact on the results of oscillatory deformations was limited. These findings show that the impact of sedimentation should be considered when studying the interface-stabilizing properties of materials with reduced solubility, such as certain plant protein extracts. The presence of such particles should be carefully considered when conducting pendant drop tensiometry.

The "Balloon-Like" Sign: Differential Diagnosis between Postoperative Air Leak and Residual Pleural Space: Radiological Findings and Clinical Implications of the Young-Laplace Equation.

Simple SummaryPostoperative residual pleural space and postoperative air leaks after lung resection are two different clinical entities requiring completely different approaches. Residual postoperative pleural space is a part of the pleural cavity that is not fully reoccupied by the remaining lung after pulmonary resection. No treatment is needed in the asymptomatic residual pleural space without any persistent air leak, and chest drain removal can be safely planned. On the contrary, an active and prolonged air leak after lung resection is an absolute contraindication to chest drain removal that may culminate in hypertensive pneumothorax, subcutaneous emphysema, and severe respiratory symptoms. In order to further contribute to an appropriate differential diagnosis between these two settings, we propose a radiological sign that is observed only in the case of residual plural space. In this case, in fact, the lung takes the form of a round balloon due to the hyperinflation condition, which is governed by the Young–Laplace equation describing the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of wall tension.In this paper, we propose a radiological sign for an appropriate differential diagnosis between postoperative pleural space and active air leak after lung resection. In the case of residual pleural space without any active air leak, the lung takes the form of a round balloon due to the hyperinflation condition, which is governed by the Young–Laplace equation describing the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of wall tension. The two principal mechanisms by which a lung forms a spherical image are shear-controlled detachment induced by shear stress on the membrane surface, and spontaneous detachment induced by a gradient in Young–Laplace pressure. On the contrary, the lung maintains its tapered shape in the case of an active air leak because the continuous air refill does not allow a complete parenchyma re-expansion.

Modeling and observation of fine gas compression in a confined narrow tube by electrowetting-on-dielectric

Capillarity describes liquid flowing against gravity in an open narrow tube with certain wettability and is well described by the Young–Laplace equation. However, the modeling of the gas compression in a confined narrow tube due to capillary action with variable wettability is yet to be established. Thus, this study observes and models the relation between the gas pressure increment in a confined narrow tube and water contact angle (CA) variation induced by electrowetting-on-dielectric (EWOD). An increment of 1.64 Pa/°CA was obtained for a confined tube with a 3 mm diameter, which well matched the measured result (1.48 Pa/°CA). Fine gas compression can be achieved by varying the voltage input. The gas compression process was determined to be an adiabatic process with a ∼10% conversion efficiency (CA varying from 110° to 65°). The concept and modeling of this EWOD-based gas compression process will pave the way for fine gas compressors in microfluidic applications.

Design optimization of gap distance for the capillary limitation of a heat pipe with annular-type wick structure

In this study, an experimental investigation was conducted on the rising height and contact angle of fluid in an annular wick-type heat pipe. The annular wick-type heat pipe was characterized by a small gap between the wick structure and tube wall, which compensated for the pressure drop along the porous media and created additional capillary force. To describe and model the advantage of this gap, the rising of a wetting liquid in the gap between a vertical solid plate and a mesh (with a small angle between them) was experimentally measured and analyzed. An additional experiment was performed to investigate the effect of curvature on the capillary rise using tubes and meshes of varying radii. Resultantly, we confirmed that the linear combination of the contact angles of the solid plate and mesh could be applied to calculate the rising height from the Laplace–Young equation. Furthermore, the effect of curvature on the rising height of the liquid was negligible. These results were extended to the investigation of finding the optimal gap distance for the annular wick-type heat pipe by referring to previous studies. We observed that a gap distance of 1.27 mm provided the largest permeability (K) over the effective pore radius (reff) value for a heat pipe with ethanol, which in turn resulted in the highest capillary limitation. For a sodium heat pipe, a gap distance of 0.84 mm resulted in the highest capillary limitation.

Control of the shape of bubble growth on underwater substrates with different sizes of superhydrophobic circles

Inspired by the everyday experience of changing the shape of a blown-up balloon by imposing a constraint, a method to control the shape of underwater bubbles is proposed by tangential constraint forces generated by the wettability difference (WD), and two bubble growth modes are distinguished based on the tangential constraint force strength and the minimum apparent contact angle (CA) of the bubble after the WD constraint. First, the critical growth shape of the bubble with a combined shape of a vertical cylinder and hemispherical top is identified, and its corresponding critical contact radius RCritical = 2.7 mm is solved by the Young–Laplace equation. Then, the effects of the radii of the superhydrophobic circle (SBC) on the bubble growth shapes are studied experimentally. The result shows that as the SBC radius decreases, the minimum apparent CA of the bubble decreases, and the minimum tangential constraint forces increase. Therefore, the bubble growth mode changes from the bell mode (with a minimum apparent CA greater than 90°) with a weaker constraint to the Ω mode (with a minimum apparent CA less than 90°) with a stronger constraint, and the bubble growth shape tends toward spherical from a flattened sphere. The maximum bubble trapping rate, Laplace pressure difference at the apex and bottom of the bubble, the aspect ratio, and the bubble filling ratio also increase as the SBC radius deceases. Furthermore, our results suggest that the proper WD-patterned arrays on underwater substrates can enhance their application efficiency, and the size of SBCS # R4 is probably the best choice in all cases.

Instabilities of thermocapillary flows in large Prandtl number liquid bridges between two coaxial disks with different radii

We explore the geometric effects on the thermocapillary flow instabilities in large Prandtl number (Pr = 1.4) liquid bridges between two coaxial disks with different radii under microgravity, focusing on the impacts of radius ratio Γr and aspect ratio Γ. The static deformation of the free surface is concerned by the solution of the Young–Laplace equation, and the linear stability analysis based on spectral element method is conducted for accurate identification of the instability characteristic. We observe that the flow stability is generally improved with the decrease in radius ratio Γr or aspect ratio Γ, especially for the liquid bridge heated from the upper disk. The critical oscillation frequency experiences an abrupt drop around Γr = 0.56 as Γr decreases for the liquid bridge with the bottom disk heated. Moreover, three transitions between two-dimensional axisymmetric steady flow and three-dimensional oscillatory flow are observed within the interval 0.87 < Γ ≤ 0.91 at Γr = 0.50 when the liquid bridge is heated from the upper disk. The energy analysis indicates that the instabilities for all cases are predominantly caused by the hydrothermal wave instability and the phenomenon of three transitions results from the variation of thermal energy transfer efficiency with the growth of the Marangoni number.

Numerical Analysis of the Deformation of Aqueous Drop Under Uniform Electric Field

This article presents a numerical analysis of the deformation of an aqueous drop in an oil phase under electric field. The configuration of analysis is a sessile aqueous drop located on an electrode. We use the charge simulation method (CSM) to calculate the electric field in the configuration. The drop profile is determined by solving the augmented Young–Laplace equation. The solution is obtained by iteratively adjusting the drop contour and the fictitious charge for the CSM. Experiments were carried out to observe the behavior of an aqueous sessile drop in a parallel electrode system. The comparison between the experimental and numerical results shows a good agreement of the drop profiles for a wide range of the applied electric field. The calculated critical electric field of drop instability is lower than the value from the experiments by 4%. We employ the numerical analysis to clarify the effects of drop size, interfacial tension coefficient, and mass density of the oil phase on the deformation and the critical electric field of the aqueous drop.

Fluid–structure interactions of energy-harvesting membrane hydrofoils

We study the kinematics, dynamics and flow fields generated by an oscillating, compliant membrane hydrofoil extracting energy from a uniform water stream at a chord-based Reynolds number $Re \approx 3 \times 10^4$ . Hydrodynamic forces during the foil's motion cause the membrane to dynamically morph its shape, effectively increasing the camber during the oscillation cycle. The membrane's deflection is modelled using the Young–Laplace equation, with pressure term approximated from thin-airfoil theory. Simultaneous tracking of the membrane deformation and the surrounding flow field using laser profiling and particle image velocimetry, respectively, reveals the role of dynamic cambering in stabilizing the leading-edge vortices on the membrane. In this regime of operation, we obtain up to 160 % higher power extraction when compared to a rigid, symmetric hydrofoil. The present work provides a demonstration of how passive compliance of soft materials interacting with fluids may be exploited in tidal and fluvial energy extraction.

A Fresh Look at the Young-Laplace Equation and Its Many Applications in Hydrostatics

The Young-Laplace (Y-L) equation relates the pressure difference across the interface of two fluids (such as air and water) to the curvature of the interface. The pressure rises on crossing a convex interface such as a rain drop and falls on crossing a concave interface such as the meniscus of water in a glass capillary. The relation between surface geometry and pressure difference across the interface provides the key concept in understanding a large collection of phenomena in hydrostatics. Of the many phenomena in hydrostatics that can be explained readily by the application of the Y-L equation, we consider the ones that are of particular interest in the introductory physics courses. These include the differential pressure within soap bubbles and liquid droplets, the rise and fall of liquids in capillaries, and the depth of liquid spills.

Clay-hydrogen and clay-cushion gas interfacial tensions: Implications for hydrogen storage

Rock/fluid interfacial tension (γrock−fluid) govern the fluid flow dynamics, the injection/withdrawal rates, the gas storage capacity, and containment integrity during gas (H2, CO2, N2) geo-storage. Clay-gas interfacial tension (γclay−gas) data, especially for the clay-H2(γclay−H2), the clay-N2(γclay−N2) and the clay-CO2(γclay−CO2) systems, have rarely been reported in the literature due to the challenging nature of these measurements in the laboratory. In this study, Neumann's equation of state and Young-Laplace equation was combined to compute clay-gas and clay-brine interfacial tensions (IFT) parameters at realistic geo-storage temperature (333 K) and pressure (5–20 MPa). Our results show that at similar thermodynamic conditions: γclay−H2>γclay−N2>γclay−CO2. Our calculations also showed that: γkaolinite−N2>γillite−N2>γmontmorillonite−N2, and γkaolinite−CO2>γillite−CO2>γmontmorillonite−CO2. In contrast, for hydrogen a negligible difference in γclay−H2 was obtained for the three clay types, although, the IFT between clay minerals and brine in presence of hydrogen is different for these three clay types. Overall, computed γclay−H2 values were higher than γclay−N2 and γclay−CO2 values, whereas computed clay-brine interfacial tension was lower in presence of hydrogen compared to carbon dioxide and nitrogen. These results suggest that nitrogen and carbon dioxide could be used as favorable cushion gas for maintaining formation pressure during underground hydrogen storage. We also demonstrated a remarkable relationship between clay/gas IFT and gas density that could serve as a helpful tool for quick estimation of rock-fluid interfacial tension.

Dynamic interfacial tension and adsorption kinetics of nonionic surfactants during microfluidic droplet formation process

Surfactant adsorption plays an important role in the microfluidic droplet formation process, which manifested as dynamic interfacial tension phenomenon. Due to rapid droplet expansion and convection flow around the droplet, traditional methods of interfacial tension measurement are difficult to investigate the surfactant adsorption kinetics in microfluidic process. We thus developed a differential pressure based microfluidic platform and proposed an in-situ method to determine time-evolving interfacial tension during microfluidic droplet formation according to Young-Laplace equation in this research. Four classical nonionic surfactants: Triton X-100, Tween 20, Brij 56, and Brij 58 were tested with classical n-octant/water as the working system. The concentrations of these surfactants at interface were further determined from the measured interfacial tension based on Frumkin adsorption model. The adsorption rates of surfactant showed that increasing surfactant concentration in the bulk solution and flow rate of continuous phase both promoted surfactant adsorption in the cases of Tween 20, Brij 56, and Brij 58, indicating the mass transfer-controlled mechanism of adsorption kinetics. The average thickness of mass transfer boundary layer ranged from 0.1 to 5 μm was determined from the mass transfer rate and a correlation equation was proposed to predict the thickness. However, the adsorption mechanism of Triton X-100 turned to be kinetics-controlled for its high critical micelle concentration, which helped to determine the adsorption and desorption rate constants.

In English

Wettability is of pivotal importance in many areas of science and technology, ranging from the extractive industry to development of advanced functional materials and biomedicine problems. An increasing interest to wetting-related phenomena stimulates impetuous growth of research activity in this field. The presented review is aimed at the cumulative coverage of issues related to wettability and its investigation. It outlines basic concepts of wetting as a physical phenomenon, methods for its characterisation (with the emphasis on sessile drop techniques), and performances of contemporary instrumentation for wettability measurements. In the first section, physics of wettability is considered. The intermolecular interactions related to wetting are classified as dependent on their nature. Thus, discussion of interactions involving polar molecules covers permanent dipole - permanent dipole interactions and freely rotating permanent dipoles. Consideration of interactions resulting from the polarization of molecules includes interactions between ions and uncharged molecules, Debye interactions, and London dispersion interactions. Hydrogen bonds are discussed separately. The second section deals with the issues related to surface tension and its effect on shaping the surface of a liquid brought in contact with a solid body. The relationship between the surface tension and the contact angle as well as equations that quantify this relationship are discussed. The Young–Laplace equation governing the shape of the drop resting on the surface is analysed. The third section is devoted to the experimental characterization of surface wettability and the underlying theoretical analysis. Particular attention is paid to the method known as the Axisymmetric Drop Shape Analysis (ADSA). Principles of automated determination of relevant physical values from experimental data are briefly discussed. Basics of numerical techniques intended for analysing the digitized image of the drop and extracting information on surface tension and contact angle are outlined. In the fourth section, an overview of commercially available instrumentation for studying wettability and the contact angle measurements is presented. The prototype contact angle analyser designed and manufactured at the ISP NASU is introduced.

Change of the form of the vertical elastic tank with a liquid

The kind of a hydrostatic equation for the vertical elastic tank, for example, a fuel tank of a rocket on a starting table is proved. The hydrostatic equation is received on the basis of specified Bernoullis equation. The substantiation is lead with the help of Laplaces formula for pressure under an elastic surface of a liquid which can arise both due to forces of a superficial tension, and due to an elastic thin-walled shell as in the present task. The form of the vertical elastic tank with a rigid bottom and the rigid top band, filled with a lied liquid is received. It is shown that it is necessary to use special record of the Gooks law for reception of the form of the tank. The analysis of this form is carried out. Distribution on height of the tank of hydrostatic pressure, volumetric density of energy of the stretched elastic wall, and also the sum of these sizes is shown. Hydrostatic pressure at which level there is a maximal increase in the area of the elastic tank is found.

Numerical simulation of the evaporation process of pinned urea-water droplets in cavities

Modeling the evaporation process of pinned urea-water solution (UWS) droplets sitting on a heated surface is of large interest for reducing the deposit formation in Selective Catalytic Reduction (SCR) systems, which can lead to a significant loss in efficiency. The kinetics of diffusion-governed evaporation of sessile droplets having the shape of a spherical cap in an infinitely extended geometry has been extensively studied in the past. The present work is focused on modelling of the heat and mass transport in the gas phase during evaporation of drops with a size comparable with a capillary length. The model is valid for the wall temperatures below the saturation temperature, and the Rayleigh number is of order of 10. The influence of gravity on both the droplet shape and on the gas flow is taken into account. The droplet shape is determined by solving the Laplace-Young equation in cylindrical coordinates. The evaporation of droplets within a constrained surrounding geometry is considered. The domain geometry is close to the geometry of an experimental cell, in which validation tests have been performed. The simulations show that the influence of the droplet shape deviation from a spherical cap on the evaporation rate is negligible. The evolution of the droplet height and contact angle however are affected by the gravity. Furthermore, the evaporation rate is strongly affected by the natural convection and by the constrained geometry of the domain.

Dynamics of two-dimensional liquid bridges

We have simulated the motion of a single vertical, two-dimensional liquid bridge spanning the gap between two flat, horizontal solid substrates of given wettabilities, using a multicomponent pseudopotential lattice Boltzmann method. For this simple geometry, the Young–Laplace equation can be solved (quasi-)analytically to yield the equilibrium bridge shape under gravity, which provides a check on the validity of the numerical method. In steady-state conditions, we calculate the drag force exerted by the moving bridge on the confining substrates as a function of its velocity, for different contact angles and Bond numbers. We also study how the bridge deforms as it moves, as parametrized by the changes in the advancing and receding contact angles at the substrates relative to their equilibrium values. Finally, starting from a bridge within the range of contact angles and Bond numbers in which it can exist at equilibrium, we investigate how fast it must move in order to break up.

Thermal analysis of water-filled micro heat pipes of natural-convection water heat sink

Based on the principles of mass, momentum, and energy conservations as well as the Young-Laplace capillary equation, a one-dimensional steady-state model of micro heat pipes (MHPs) of equilateral-triangle cross section has been constructed, with the incorporation of a natural convection heat sink surrounding the condenser section. Subsequently, the model is utilized to address some of the issues associated with a copper-water MHP whose condenser section is immersed in a nominally quiescent cooling water. The heat transport capacity derived in this study agrees well with existing experimental results. Moreover, four parameters – the heat load, the operating temperature, the temperature of the condenser coolant, and the average temperature of the evaporator section – have been identified as the key factors associated with the performance of an MHP, and a detailed investigation on their relationships has been carried out. For an MHP filled with a fixed amount of working fluid, an operation chart relating these parameters has been constructed. Moreover, it is shown that these parameters are not totally independent of each other, since, given any two of them, the remaining two can be determined using a set of two coupled, approximately linear algebraic equations.

Determination of Time-Evolving interfacial tension and ionic surfactant adsorption kinetics in microfluidic droplet formation process

Surfactant adsorption plays an important role in microfluidics, which can be investigated by the dynamic evolution of interfacial tension. A differential pressure-based method is proposed to understand the basic laws of time-evolving interfacial tension and adsorption kinetics of ionic surfactants during the microfluidic droplet formation processes. Instantaneous flow rates and flow resistances are precisely analyzed based on auto-recognized microscopic images and the waveform of differential pressure, and the interfacial tension is determined from the Young-Laplace equation with a time resolution of 1/60 s. The concentration of surfactant at the liquid–liquid interface is obtained according to the Frumkin adsorption model, leading to an in-depth understanding of the adsorption rates and the apparent mass transfer rates of surfactants. The surfactant adsorption is demonstrated to obey the kinetic-controlled adsorption mechanism and therefore a measurement method for the adsorption rate constant is created to understand the kinetic characteristics of small-molecule ionic surfactants.

Young and Young-Laplace equations for a static ridge of nematic liquid crystal, and transitions between equilibrium states.

Motivated by the need for greater understanding of systems that involve interfaces between a nematic liquid crystal, a solid substrate and a passive gas that include nematic–substrate–gas three-phase contact lines, we analyse a two-dimensional static ridge of nematic resting on a solid substrate in an atmosphere of passive gas. Specifically, we obtain the first complete theoretical description for this system, including nematic Young and Young–Laplace equations, and then, making the assumption that anchoring breaking occurs in regions adjacent to the contact lines, we use the nematic Young equations to determine the continuous and discontinuous transitions that occur between the equilibrium states of complete wetting, partial wetting and complete dewetting. In particular, in addition to continuous transitions analogous to those that occur in the classical case of an isotropic liquid, we find a variety of discontinuous transitions, as well as contact-angle hysteresis, and regions of parameter space in which there exist multiple partial wetting states that do not occur in the classical case.

Investigation of interface profiles in meshed wicks and related evaporation characteristics

The porous wick in a heat pipe determines the working fluid capillary replenishment ability and heat transfer process. To study the evaporation characteristics of meshed wicks fabricated with wires of micron-scale, a mathematical model based on the augmented Young-Laplace equation and molecular kinetic theory to predict the evaporation interface profile is developed, and the Marangoni effect and slip velocity in the boundary are considered. The evaporation interface can be divided into the thin-film region and intrinsic meniscus region according to the ratio of capillary pressure and disjoining pressure. A new solution method considering the constraints at the intersection of the two regions to obtain the interface profile is proposed and validated. Based on the two-dimensional results, the area and heat transfer rates of the two regions formed in the meshed wicks are calculated by integrating along the four side wires. Then, the evaporation characteristics of the thin-film region, including the pressure and thermal resistance distribution, are studied. Finally, the influence of the Marangoni effect, superheat, wire spacing, interface pressure difference and slip velocity on the interface profile and heat transfer of these two regions are discussed.