Young-Laplace Research Articles

Flow modeling and experimental verification of flow resistors used in microfluidic chips driven by capillary force

A microfluidic chip driven by capillary force has the advantage of low cost and ease of manufacturing in batches, and its flow behavior is dominated by the geometry and surface characteristics of the microchannel. The design of mirochannel structures is very important for the microfluidic chips. This study presents a semi analytical method for the design of capillary microchannel. In this method, the quasi-steady state approximate solution method of the Young–Laplace equation is used to derive the capillary surface tension, and the parallel flow assumption based on the Reynolds equation is used to derive the resistance of the channel wall. A computational fluid dynamics simulation is used to provide the inlet effect coefficient and channel shape effect coefficient of this model. The availability of the semi analytical model is verified by the experiment. This model realizes the flow analysis of two-dimensional capillary flow channel with a continuous shape of the flow channel wall, providing a fast and accurate method for the structural design of the microfluidic chip driven by capillary force.

One-pot neutron imaging of surface phenomena, swelling and diffusion during methane absorption in ethanol and n-decane under high pressure.

We report a powerful method for capturing the time-resolved concentration profiles, liquid swelling and surface phenomena during the absorption of methane (CH4) in still liquid ethanol (C2D6O) and n-decane (n-C10D22) and at high spatial resolution (pixel size 21.07 μm) using neutron imaging. Absorption of supercritical methane was followed at two temperatures and two pressures of methane, namely 7.0, 37.8 °C and 80, 120 bar. Fick’s second law, which was used in the liquid-fixed coordinates, enabled for an adequate parameterization of the observed concentration profiles and liquid levels using simple analytical expressions. For both studied liquids, anomalously slow diffusion was observed in the initial stage of the absorption experiment. This was ascribed to the slow formation of the surface excess on the interface, time constant ranged 130–275 s. The axial symmetry of the cell allowed for the tomographic reconstructions of the profiles of the menisci. Based on these profiles, contact angle and surface tension were evaluated using the Young-Laplace equation. Overall, neutron imaging made it possible to capture time- and space-resolved information from which the methane concentration, liquid level and meniscus shape under high-pressure conditions inside a cylindrical titanium vessel were quantitatively derived. Multiple characteristics of ethanol, a methane hydrate inhibitor, and n-decane, a model constituent of crude oil, were thus measured for the first time under industrially relevant conditions in a one-pot experiment.

A theoretical study on three long-range interactions between two nanoparticles under the humid condition

At the micro/nanoscale under the humid condition, the competition among three long-range interactions of the electrostatic, cohesive, and capillary forces dominates the adhesive behavior between two nanoparticles. In this study, explicit solutions of the interfacial adhesive energy between two nanoparticles are obtained through continuum modeling by considering the three long-range interactions between them, where the Coulomb theorem, the Lennard–Jones potential, and the Young–Laplace equation are taken into consideration. The present theoretical results show that the interfacial adhesive forces strongly depend on the three interactions, where the cohesive force and capillary force play more important roles in the competition for a smaller distance h between two nanoparticles, while the electrostatic force dominates the interactions for a larger distance h. Checking against present molecular dynamics simulations shows that the present continuum solution has high accuracy. This study should be of great help for deeply understanding the aggregation and separation of nanoparticles under the humid condition.

Pendant drop tensiometry: A machine learning approach.

Modern pendant drop tensiometry relies on the numerical solution of the Young-Laplace equation and allows us to determine the surface tension from a single picture of a pendant drop with high precision. Most of these techniques solve the Young-Laplace equation many times over to find the material parameters that provide a fit to a supplied image of a real droplet. Here, we introduce a machine learning approach to solve this problem in a computationally more efficient way. We train a deep neural network to determine the surface tension of a given droplet shape using a large training set of numerically generated droplet shapes. We show that the deep learning approach is superior to the current state of the art shape fitting approach in speed and precision, in particular if shapes in the training set reflect the sensitivity of the droplet shape with respect to surface tension. In order to derive such an optimized training set, we clarify the role of the Worthington number as a quality indicator in conventional shape fitting and in the machine learning approach. Our approach demonstrates the capabilities of deep neural networks in the material parameter determination from rheological deformation experiments, in general.

Control of Void Formation in Adhesively Bonded Joints in the Presence of Filler

Abstract Adhesively bonded joints are ubiquitous in electronic assemblies that are used in a wide range of applications, which include automotive, medical, military, space and communications. The steady drive to reduce the size of assemblies in all of these applications, while providing increased functionality, generates a need for adhesive joints of higher strength, improved thermal and electrical conductivity and better dielectric isolation. All of these attributes of adhesive joints are degraded by the presence of voids in them. The quest to minimize voids in bonded structures motivated a previous study of their formation in a solvent cast, die bond epoxy film, which undergoes a liquid phase transition during cure. That work is extended in this study by including the effects of various filler morphologies in the adhesive. Fillers are added to adhesives to facilitate handling of thin sheet formats, control bond line thickness and reduce coefficient of thermal expansion. As such, fillers are selected to be inert with respect to the adhesive chemistry, while being readily wetted by it in the liquid state. Common filler morphologies include woven and molded open meshes, fibers chopped to uniform length, and spheres of uniform or distributed diameters. Void formation is influenced by a number factors, which include wettability of the bonded surfaces, adsorbed water, amount of solvent retained in the film, volume of entrapped air, thermal profile of the cure schedule, and clamping pressure during cure. The presence of fillers in the adhesive adds the additional factors of constrained diffusion paths and increased area for void nucleation. We have changed our approach to modeling the diffusion of volatile species in adhesive joints from a finite difference calculation in a uniform adhesive medium used previously, to a finite element model of a complex diffusion space. The open source program Gmsh is used to generate the diffusion space from a set of input parameters. The calculations of concentration profiles and diffusion fluxes of volatile species at the void interface are made using the open source finite element program elmer. As done previously, the position of the void interface is updated by integrating the product of time and flux of diffusing species over the area of the interface. The internal pressure of the void is determined by application of the Young-Laplace equation, while Henry’s law is used to estimate the concentration of diffusing species adjacent to the void interface. The calculation proceeds for a time equivalent to the integral of the time temperature product required to achieve a 70% cure state of the adhesive, at which point the void interface is immobile. The experimental approach is the same as used previously, with the filled adhesive sandwiched between glass slides and cured on a hot plate while imaged through a microscope. Images are automatically captured and analyzed by using the open source program imageJ, which allows us to track the evolution of individual voids as well as the time dependent distribution of the void population. We are working to correlate these experimental results with the predictions of our finite element calculations to allow us to make insightful choices of adhesives and optimize our bonding processes.

Shear-lag model for discontinuous fiber-reinforced composites with a membrane-type imperfect interface

A shear-lag model is developed for discontinuous fiber-reinforced composites with a membrane-type imperfect interface, across which the displacement vector is continuous but the traction vector suffers a jump that is governed by the generalized Young–Laplace equation. Closed-form expressions are obtained for the stress fields in both the fiber-reinforced region and the pure matrix regions and for the shear stress on the interface from both the fiber and matrix sides. To illustrate the newly developed analytical model, a numerical analysis is provided by directly using the general formulas derived. The numerical results reveal that the fiber aspect ratio and the interface parameter can both have significant effects on the stress distributions in the composite.

An Analytical Two-Dimensional Linearized Droplet Shape Model for Combined Tangential and Normal Body Forces

In view of emerging research on forced wetting under complex applied forces, a simple model for a droplet shape evolution is developed here. In particular, the model refers to droplet spreading under quasisteady conditions. The corresponding linearized two-dimensional Young–Laplace equation is solved analytically resulting in a system of two equations that relates the droplet shape features to each other. Despite its simplicity, the final model produces a wealth of droplet behaviors when combined with the physical requirement that the contact angle should be within a particular range of values. Indicative results of the droplet behavior under several forces scenarios are examined here exhibiting why the present model is useful for designing experimental campaigns on forced spreading.

Evaporation driven detachment of a liquid bridge from a syringe needle in repose

In this paper, a study of the stability of an evaporating semi-unbounded axisymmetric liquid bridge that forms between a syringe needle tip and a horizontal interface by using both theory and experiments is presented. Here, the evaporation produces slow quasistatic motion such that it allows one to use hydrostatics to analyze interface profiles via solutions to the Young–Laplace equation. The two main parameters, in the hydrostatic limit, are the familiar Bond number and a slenderness parameter that often appears in the literature that studies liquid bridge stability. The axisymmetric Young–Laplace equation yields a semi-analytical solution for capillary pressure at zero Bond number using boundary conditions appropriate for this study. At finite Bond numbers, computation of interface profiles is used to estimate the maximum slenderness. Experiments using water for Bond numbers 0.01 < Bo < 0.1 show good agreement for the maximum slenderness when comparing those results with predictions based on solutions to the Young–Laplace equation.

Method based on parallel‐wire conductivity probe for measuring water hold‐up in near‐horizontal oil–water two‐phase flow pipes

On the basis of a quick-closing valve technology, parallel-wire conductivity probes were designed to measure water hold-up of oil-water two-phase flow in near-horizontal pipe. First, the electric-field distribution characteristics of the parallel-wire conductivity probe and its response to the change of the water layer height were calculated by using finite-element method. Then, for the oil-water stratified distribution in the near-horizontal pipe with a 5° inclined angle, 20 mm inner diameter, and 1050 mm length, a measurement model for water hold-up was established. After that, a static experiment was carried out to investigate the accuracy of water-hold-up measurement. The results show that errors occur when the set water hold-up is with high values. The measurement errors were analysed based on curved oil-water interface predicted by Young-Laplace equation model, which are significantly related to the curvature of oil-water interface. It provides an effective experimental method for the measurement of water hold-up in a near-horizontal oil-water two-phase flow pipes. On the basis of this, the dynamic experiment of oil-water two-phase flow was carried out, and the slippage of oil-water two-phase flow was preliminarily revealed.

The Latest Method for Surface Tension Determination: Experimental Validation

The highest effectiveness of heat exchange is under boiling; hence, surface tension is an important parameter and should be determined when new liquid substances are created. The most popular methods are based on numerically solving the Young–Laplace equation by applying the Bashforth and Adams algorithm, which fails at the poles and at the inflection points. The newest algorithm is based on the closed-form expressions that define a drop or bubble. It gives the accurate solutions for the fully created drops or bubbles. To validate it, the surface tension value is determined for the air bubbles in water and compared with the reference data. Because the relative discrepancies are extremely small, the new method may be thought of as positively validated.

Two-phase electrohydrodynamics along a grooved flat heat pipe

The present communication reports on the investigation of the effect of an electric field on the performance of a flat plate heat pipe (FPHP). In the studied configuration, an electric stress is imposed on the liquid–vapor interface, which adds to the capillary force. The ability of the electric field to change the shape of the liquid–vapor interface is investigated by means of both a numerical and an experimental approach. The numerical approach consists in solving two strongly-coupled equations: the Laplace–Young equation and the Laplace equation for the electric potential; the latter being required to get the distribution of the normal electric stress along the meniscus, while the former is used to calculate the meniscus shape. The Laplace–Youngequation is modified accordingly to take into account the added contribution of the normal electric stress. The results of the numerical study for an application inside an FPHP are discussed. A possible enhancement of the capillary pumping is highlighted for a specific geometry of the electrode. The experimental approach is based on a test bench that consists in a tilted grooved aluminum plate equipped with a pair of horizontal electrodes filled with Novec HFE-7100 in liquid and vapor states. The effect of the electric field on the liquid distribution is observed by confocal microscopy. A good agreement is found between the experimental result and the numerical expectations. The experimental results highlight important effects of the electric field on the liquid distribution inside an FPHP, which could be ultimately used to enhance its thermal performance.

Using the universal phase diagrams to describe pore shape development in solid for different solidification rates

This study shows that there exist the universal three phase diagrams to describe general development of the pore shape in solid, resulting from a bubble captured by a solidification front with different solidification rates. Pore formation and its shape strongly determine microstructural quality of materials, functional materials encountered in biology, chemistry, engineering, foods, and phenomena of geophysics and climate change, and so on. The solidification rate plays an important role in solute transport and gas pressure, contact angle of the bubble cap, and pore shape in solid. Three universal phase diagrams are under dimensionless coordinate systems of (1) solidification rate, temperature gradients in solid and liquid at the solidification front, (2) solidification rate, contact angle and growth rate of base radius of the cap, and (3) apex radius, contact angle and base radius of the cap. Solidification rate is determined by temperature gradients in liquid and solid at the solid-liquid interface governed by the Stefan boundary condition, whereas apex radius is determined by solute gas pressure in the pore governed by the Young-Laplace equation, equation of state, and different cases governing directions of mass transfer in the pore. Extending previous analysis, phase diagrams in this study confirm that the bubble cannot be completely entrapped in Case 2b, which represents a stronger effect of pore volume expansion on solute gas pressure than solute transport from the surrounding liquid to pore in the early stage. The computed and measured results of development of the pore shape are in good agreement.

Capillary continuity in fractured porous media; part II: Evaluation of fracture capillary pressure in the presence of liquid bridges using a novel microfluidic approach

Fracture capillary pressure plays a major role in many aspects of fluid flow in fractured rocks, including physical interpretation, mathematical modeling, and simulation of various mechanisms. The 2D microfluidic devices are a ubiquitous tool to study the multiphase behavior of fractures. However, these devices still suffer from two essential limitations: 1) narrow-etched depth of the middle fracture, producing an undesirable effect on the fracture capillary pressure and 2) undesired deformation of the liquid bridge curvature. In this work, a novel technique is developed for fabricating microfluidic devices where the 2D domain is attached to a 3D open medium that is realistic enough to capture the essential physics underlying the mechanisms of multiphase flow and liquid bridge evolution in fractures.The developed “3D fracture-2D matrix” microfluidic device is utilized to study the mechanism of gas gravity drainage in fractured rocks and evaluate the available models that describe the fracture capillary pressure. The reasonable agreement between experimental results and theoretical calculations reveal that the Young-Laplace equation can be used as a framework for the fracture capillary pressure. This result is in contrast with the previous experimental results in the literature that rejected the validity of the Young-Laplace equation for evaluating fracture capillary pressure. Furthermore, the capillary bridge description is a key parameter in evaluating the fracture capillary pressure and estimating the recovery profile of matrix blocks through the capillary continuity phenomenon. The visual analysis shows that the circle approximation can describe the shape of the bridge and the dynamic bridge curvature is almost constant during the fracture desaturation under the gravity drainage mechanism. These findings can improve our understanding of fracture capillary pressure models that not only affect the ultimate recovery but also are required to design enhanced oil recovery in fractured reservoirs.

Phase-Behavior Modeling of Hydrocarbon Fluids in Nanopores Using PR-EOS Coupled with a Modified Young-Laplace Equation.

The effect of capillary pressure on the vapor–liquid two-phase equilibrium calculation has been extensively studied for the past two decades. However, the calculation accuracy is often weakened by the false assumptions and inherent flaws present in the modeling process. In this work, a modified Young–Laplace equation proposed by Tan and Piri [Tan, S.; Piri, M. Equation-of-State Modeling of Confined-Fluid Phase Equilibria in Nanopores. Fluid Phase Equilibr. 2015,393, 48–63.] is coupled with volume-translated Peng–Robinson equation of state to study the effect of capillary pressure on the two-phase equilibrium calculation in confined nanopores. In order to successfully apply the modified Young–Laplace equation during the vapor–liquid equilibrium calculation process, this study models the tuning parameter λ in the modified Young–Laplace equation (as proposed by Tan and Piri for perturbed-chain statistical associating fluid theory equation of state) for several pure hydrocarbons and their mixtures by matching experimental data collected from the literature. The tuning parameter λ can be expressed as a unique function for each pure substance or mixture. It is found that the tuning parameter λ shows a quadratic polynomial relationship with temperature, and the value of λ is always less than one. The λ can become negative under certain circumstances, which adjusts the capillary pressure to a lower value. It increases with an increasing pore radius; this is different from the results obtained by Tan and Piri which showed that the tuning parameter λ decreases with an increasing pore radius. The above rules apply to the tuning parameter λ obtained for both pure substances and mixtures. Using the two-phase equilibrium calculation coupled with the modified Young–Laplace equation, the calculated vapor pressures for pure substances and two-phase boundaries for mixtures match very well with the experimental data. Implementation of the modified Young–Laplace equation greatly improves the accuracy of the two-phase equilibrium calculation considering the capillarity effect. Such a modeling strategy could be integrated into a reservoir simulator to conduct more accurate flow simulations for tight/shale reservoirs.

An explicitly multi-component arterial gas embolus dissolves much more slowly than its one-component approximation

We worked out the growth and dissolution rates of an arterial gas embolism (AGE), to illustrate the evolution over time of its size and composition, and the time required for its total dissolution. We did this for a variety of breathing gases including air, pure oxygen, Nitrox and Heliox (each over a range of oxygen mole fractions), in order to assess how the breathing gas influenced the evolution of the AGE. The calculations were done by numerically integrating the underlying rate equations for explicitly multi-component AGEs, that contained a minimum of three (water, carbon dioxide and oxygen) and a maximum of five components (water, carbon dioxide, oxygen, nitrogen and helium). The rate equations were straight-forward extensions of those for a one-component gas bubble. They were derived by using the Young–Laplace equation and Dalton’s law for the pressure in the AGE, the Laplace equation for the dissolved solute concentration gradients in solution, Henry’s law for gas solubilities, and Fick’s law for diffusion rates across the AGE/arterial blood interface. We found that the 1-component approximation, under which the contents of the AGE are approximated by its dominant component, greatly overestimates the dissolution rate and underestimates the total dissolution time of an AGE. This is because the 1-component approximation manifestly precludes equilibration between the AGE and arterial blood of the inspired volatile solutes (O2, N2, He) in arterial blood. Our calculations uncovered an important practical result, namely that the administration of Heliox, as an adjunct to recompression therapy for treating a suspected N2-rich AGE must be done with care. While Helium is useful for preventing nitrogen narcosis which can arise in aggressive recompression therapy wherein the N2 partial pressure can be quite high (e.g.∼5 atm), it also temporarily expands the AGE, beyond the expansion arising from the use of Oxygen-rich Nitrox. For less aggressive recompression therapy wherein nitrogen narcosis is not a significant concern, Oxygen-rich Nitrox is to be preferred, both because it does not temporarily expand the AGE as much as Heliox, and because it is much cheaper and more conservation-minded.

Bond Number Revisited: Axisymmetric Macroscopic Pendant Drop.

The numbers Rbθ and Rbr introduced recently (Berim, G.O.; Ruckenstein, E. J. Phys. Chem. 2019, 123, 10294-10300) to characterize the cylindrical pendant drops hanging from the solid surface are modified for characterization of axisymmetric pendant drops which are more common in experiment. Similar to the case of cylindrical drops, Rbθ and Rbr are defined on the basis of rigorous solution of Young-Laplace equation for the drop profile. As a consequence, they contain only the input parameters of the drop-solid system such as the volume of the drop, gravitational acceleration, fluid densities, surface tension, and contact angle. This constitutes the main difference between Rb numbers and traditional Bond and Bond-like numbers which involve the dimensions of the drop unknown prior to the experiment (e.g., height of the drop or radius of curvature at the drop apex). It is shown, that the new numbers can be used, for example, for predicting the breakup conditions of the drop, determining the surface tension, and estimating the deviation of drop shape from the circular one. A good agreement between theoretical predictions and experimental results known from the literature was demonstrated.

Experimental evaluation and analytical model of the pressure generated by elastic compression garments on a deformable human limb analogue

Compression garments are extensively used for various therapeutic treatments and are expected to deliver accurate and reproducible compression pressures. This study focuses on developing an analytical model to predict the pressure generation by compression garments on human limb analogues. The analogues consisted of non-compressible and compressible cylinders that were chosen as the first step towards evaluating pressure generation on real human limbs. An experimental platform was developed to quantify the relationship between material properties, initial garment extension and pressure. A mathematical model was presented that provided greater accuracy in predicting the pressure generated by compression garments than the existing Young-Laplace equation for compressible limb analogues.

Fiber bundle topology optimization of hierarchical microtextures for wetting behavior in Cassie-Baxter mode

This paper presents the topology optimization of hierarchical microtextures for wetting behavior in the Cassie-Baxter mode, considering a structural unit of the hierarchical microtexture composed of base and secondary structures. The geometrical configuration of the considered structural unit can be described as a fiber bundle composed of an external surface of the base structure and the pattern of the secondary structures. Thus, two design variables are defined, one for the external surface of the base structure, and the other for the pattern of the secondary structures. The Young-Laplace equation, including a term depending on the mean curvature of the external surface, is used to describe the liquid/vapor interface imposed with a surface tension in the Cassie-Baxter mode. To overcome the difficulty of numerically computing the second-order derivative of the external surface, two partial differential equation filters are sequentially applied to the design variable of the base structure to ensure the numerical accuracy and feasibility of using an efficient linear-element-based finite element method to solve the Young-Laplace equation. To improve the performance of the hierarchical microtextures, the volume of the liquid bulges suspended at the liquid/vapor interface in the Cassie-Baxter mode, before the transition into the Wenzel mode, is minimized to optimize the match between the external surface of the base structure and the pattern of the secondary structures. In the topology optimization process, penalization of the material density of the surface tension is achieved by an artificial Marangoni phenomenon. In numerical examples, solid surfaces are tiled into textures with axial symmetry, radial symmetry, chirality, and quasiperiodicity; and structural units are derived consisting of base structures with peak shapes and dense secondary structures surrounding the crests of the peaks. The optimized performance of the derived structural units has been confirmed by comparisons.

Active control of the freezing process of a ferrofluid droplet with magnetic fields

Most existing studies of droplet freezing on cold solid surfaces focus on the use of different surface wettability and roughness which may be considered as passive methods. Here we report an active method using an applied magnetic field to control the deformation and freezing process of a sessile ferrofluid droplet on a cold surface. By changing the direction and magnitude of the magnetic field, we can elongate or squeeze the shape of ferrofluid droplets. Consequently, the droplet freezing time can be extended or shortened under the magnetic lift or squeezing conditions, respectively. Additionally, we use the modified Young-Laplace equation with consideration of an additional magnetic force effect to analyze the shape variation of a ferrofluid droplet with magnetic field, and also present a scaling analysis for the freezing time.

Steady-State Water Drainage by Oxygen in Anodic Porous Transport Layer of Electrolyzers: A 2D Pore Network Study

Recently, pore network modelling has been attracting attention in the investigation of electrolysis. This study focuses on a 2D pore network model with the purpose to study the drainage of water by oxygen in anodic porous transport layers (PTL). The oxygen gas produced at the anode catalyst layer by the oxidation of water flows counter currently to the educt through the PTL. When it invades the water-filled pores of the PTL, the liquid is drained from the porous medium. For the pore network model presented here, we assume that this process occurs in distinct steps and applies classical rules of invasion percolation with quasi-static drainage. As the invasion occurs in the capillary-dominated regime, it is dictated by the pore structure and the pore size distribution. Viscous and liquid film flows are neglected and gravity forces are disregarded. The curvature of the two-phase interface within the pores, which essentially dictates the invasion process, is computed from the Young Laplace equation. We show and discuss results from Monte Carlo pore network simulations and compare them qualitatively to microfluidic experiments from literature. The invasion patterns of different types of PTLs, i.e., felt, foam, sintered, are compared with pore network simulations. In addition to this, we study the impact of pore size distribution on the phase patterns of oxygen and water inside the pore network. Based on these results, it can be recommended that pore network modeling is a valuable tool to study the correlation between kinetic losses of water electrolysis processes and current density.