Young-Laplace Research Articles

Immiscible viscous fingering in time-dependent fluids: A linear stability analysis

When a less viscous fluid displaces a more viscous fluid, the interface between the two fluids becomes unstable. The instability exhibits itself as a large number of fingers of the displacing fluid penetrating the displaced fluid. This phenomenon is called viscous fingering or Saffman–Taylor instability, and plays a key role in oil industry, among others. The present study aims at investigating the immiscible viscous fingering of inelastic time-dependent fluids (i.e., fluids for which viscosity varies with time even at a fixed shear rate) in a homogeneous saturated porous medium. To represent such fluids, in the present work, use is made of the Quemada model. As an inelastic structural-kinetic rheological model, it can capture both thixotropy and anti-thixotropy through proper setting of model parameters. The model incorporates a natural time, which, in dimensionless form, is represented by a nominal Deborah number. Using this rheological model, the generalized Darcy’s law is derived, which is used to derive the basic flow. The interfacial instability is investigated by using the linear temporal stability analysis; that is, infinitesimally-small, normal-mode perturbations are introduced to the basic flow and their evolution in time is monitored. Using the Young–Laplace equation, the generalized dispersion relation is derived, which is solved numerically. The results show that the thixotropy and anti-thixotropy stabilize the Newtonian/time-dependent and time-dependent/Newtonian displacements, respectively. On the other hand, the Newtonian/time-dependent and time-dependent/Newtonian displacements are destabilized by the anti-thixotropy and thixotropy, respectively.

Modelling and model validation of particle stability and detachment from the particle-laden surface

Particle-bubble aggregates in flotation are characteristic of particle-laden bubbles and surfaces, but the available theories focus on the stability and detachment of single particle that resides lonely at the free surface. There is no modelling attempt to quantify the particle stability and detachment from the laden surfaces that can be relevant to flotation. Here, we developed a model that considers the particle tenacity (maximum adhesion force) at the particle-laden surface by solving the Young-Laplace equation (YLE) using the superposition approximation method. The vertical position of the target particle was calculated by considering the additive effect on the position by other nearby particles at the laden surface, based on the linearised YLE. Using the numerical results, a semi-empirical model for the particle tenacity was developed for engineering calculation exercises and assessed against the data of film flotation experiments. Application of the model to the case of changing contact angle was also established. The tenacity of particles at the laden surface was shown to be higher than at the free surface due to the lateral capillary attraction. This is the first model to quantify the particle stability and detachment from the particle-laden surface that can be useful for flotation.

Rupture distances and capillary forces of liquid bridges: Closed-form expressions and ANNs-trained prediction models

Accurate prediction of rupture distances and capillary forces of liquid bridges is crucial for studying the behaviour of wet granular materials. However, the validity of existing analytical expressions is limited to small liquid volumes, whereas current closed-form expressions require numerous calibrated coefficients, making them cumbersome. To overcome these limitations, this study employs Particle Swarm Optimization (PSO), a metaheuristic algorithm, to enhance closed-form expressions. This approach allows tuning the balance between accuracy and complexity, resulting in simplified yet accurate closed-form expressions for liquid bridges with varying volumes and contact angles between unequal-sized particles, under both volume and suction control conditions.Additionally, Artificial Neural Networks (ANNs) are used as an alternative approach. All network architectures up to three hidden layers are systematically explored, and prediction models for rupture distances and capillary forces of liquid bridges are trained using a database of numerical solutions of the Young–Laplace equation. The resulting models provide accurate predictions across a wide range of liquid volumes and contact angles.

Osmotically Rupturing Phagosomes in Macrophages Using PNIPAM Microparticles.

The rupture of macrophage phagosomes has been implicated in various human diseases and plays a critical role in immunity. However, the mechanisms underlying this process are complex and not yet fully understood. This study describes the development of a robust engineering method for rupturing phagosomes based on a well-defined mechanism. The method utilizes microfabricated microparticles composed of uncrosslinked linear poly(N-isopropylacrylamide) (PNIPAM) as phagocytic objects. These microparticles are internalized into phagosomes at 37 °C. By exposing the cells to a cold shock at 0 °C, the vast majority of the microparticle-containing phagosomes rupture. The percentage of phagosomal rupture decreases with the increase of the cold-shock temperature. The osmotic pressure in the phagosomes and the tension in the phagosomal membrane are calculated using the Flory-Huggins theory and the Young-Laplace equation. The modeling results indicate that the osmotic pressure generated by dissolved microparticles is probably responsible for phagosomal rupture, are consistent with the experimentally observed dependence of phagosomal rupture on the cold-shock temperature, and suggest the existence of a cellular mechanism for resisting phagosomal rupture. Moreover, the effects of various factors including hypotonic shock, chloroquine, tetrandrine, colchicine, and l-leucyl-l-leucine O-methyl ester (LLOMe) on phagosomal rupture have been studied with this method. The results further support that the osmotic pressure generated by the dissolved microparticles causes phagosomal rupture and demonstrated usefulness of this method for studying phagosomal rupture. This method can be further developed, ultimately leading to a deeper understanding of phagosomal rupture.

Experimental and theoretical investigation of the impact of crude-oil on the wettability behavior of calcite and silicate due to low salinity effect

Wettability alteration is recognized as the main responsible mechanism for enhanced oil recovery during low salinity water flooding (LSWF) in both carbonates and sandstones. However, there is still a lack of understanding about the possible role of oil type on rock wettability alteration during LSWF. In the current study, contact angle (CA), interfacial tension (IFT), and zeta potentials for both oil/brine and rock/brine interfaces are measured for rock/brine/crude oil systems in a wide range of salinity of seawater. Two different crude oil samples and both calcite and silicate as good end-members of carbonate and sandstones are investigated. For oil A, the CA decreases with brine dilution; however, for oil B, the CA showed almost the opposite trend vs. salinity. The increased water-wetness of silicate compared to calcite surface was more highlighted in lower salinity. The results of zeta potentials showed that diluting seawater (SW) reduced the zeta potentials of rock/brine and oil/brine in all systems. The changes in zeta potential suggest that more dilution shall lead to more water-wetness, which is not in agreement with the CA behavior of two minerals in the case of crude oil B. Based on the augmented Young-Laplace equation, it was demonstrated that there is a good correlation between the IFT and the wettability, especially for calcite minerals. To shed light on the competition between the IFT and the EDL force, a comprehensive model was created to predict the CA results by coupling the surface complexation model (SCM), the DLVO theory, and the Young-Laplace equation. The coupled model successfully predicted the experimental contact angle for both crude oil and rock samples. Analyzing the disjoining pressure curves showed that due to the attractive EDL forces of calcite rocks, the oil/brine IFT solely controls the calcite wettability behavior with salinity. However, for silicate substrates, the high repulsive EDL forces are the main reason for the rock water-wetness at low salinity brines.

A New Method for Calculating Reservoir Core-Bound Water Saturation Using the Cast Thin Section

The rock coring of the reservoir in the Bohai A field is difficult. The cores of the target section in the study area are loose, making it difficult to accurately measure the core-bound water saturation. The purpose of this research was to develop and validate a method for calculating a reservoir core-bound water saturation ratio using the cast thin section. First, pepper noise denoising and image enhancement were performed on the thin section by median filtering and gamma variation. Based on this, the enhanced sheet images were thresholded for segmentation by the two-dimensional OTSU algorithm, which automatically picked up the thin section pore-specific parameters. Then, the thin section image was equivalent to a capillary cross-section, while the thin film water fused to the pore surface was observed as bound water. For hydrophilic rocks with a strong homogeneity, the area of thin film water in the pore space of the sheet was divided by the total area of the pore space, which produced the bound water saturation. Next, the theoretical relationship between the film water thickness and the critical pore throat radius was derived based on the Young–Laplace equation. The bound water saturation of the rock was calculated by combining the pore perimeter and the area that was automatically picked up from the thin film for a given critical pore throat radius of the rock. Finally, 22 images of thin sections of sparse sandstone from the coring well section of the study area were image processed using the new method proposed in this paper, and the bound water saturation was calculated. The calculated results were compared with 22 NMR-bound water saturations and 11 semi-permeable baffle plate-bound water saturations in the same layer section. The results showed that the bound water saturation values calculated by the three methods produced consistent trends with absolute errors within 5%. The calculated results confirm the reliability of the method proposed in this paper. This method can effectively avoid the problem of the inaccurate results of core experiments due to the easy damage of sparse sandstone and provides a new idea for the accurate determination of the bound water saturation of sparse sandstone.

The bounce behavior of a freely rising oil droplet in water under the horizontal wall constraint

The interaction problem of a freely-rising oil droplet in water due to the horizontal wall constraint is solved numerically. The motion equation, water film drainage equation, and Young-Laplace equation are coupled to establish a dimensionless mathematical model for describing the bounce behavior of oil droplets in water. In addition to buoyancy and flow resistance, the motion equation also introduces added mass force and film induced force caused by interaction with the wall. Further analysis shows that the coupling model conforms to the dynamics characteristics of a damped vibration system from the perspective of vibration. Based on the analysis of vibration parameters, We found that the bounce behavior of oil droplets is directly related to the oil-water system's Eo number and Oh number, in addition to the size dependence. Moreover, the bounce pattern diagram with (G, Oh) as the control parameter provides a suitable identification for the transition law of the bounce number of oil droplets under the horizontal wall constraint. The findings of this study facilitate quantifying the processes of oil droplet adhesion, coalescence, and spreading and provide a sub-model reference for the description of complex oil-water systems.

A New Immersed Finite Element Method for Two-Phase Stokes Problems Having Discontinuous Pressure

Abstract In this paper, we develop a new immersed finite element method (IFEM) for two-phase incompressible Stokes flows. We allow the interface to cut the finite elements. On the noninterface element, the standard Crouzeix–Raviart element and the P 0 {P_{0}} element pair is used. On the interface element, the basis functions developed for scalar interface problems (Kwak et al., An analysis of a broken P 1 {P_{1}} -nonconforming finite element method for interface problems, SIAM J. Numer. Anal. (2010)) are modified in such a way that the coupling between the velocity and pressure variable is different. There are two kinds of basis functions. The first kind of basis satisfies the Laplace–Young condition under the assumption of the continuity of the pressure variable. In the second kind, the velocity is of bubble type and is coupled with the discontinuous pressure, still satisfying the Laplace–Young condition. We remark that in the second kind the pressure variable has two degrees of freedom on each interface element. Therefore, our methods can handle the discontinuous pressure case. Numerical results including the case of the discontinuous pressure variable are provided. We see optimal convergence orders for all examples.

Bézier Curve Method to Compute Various Meniscus Shapes.

This paper is an extension of our earlier paper in which it was shown that the meniscus shape in a cylindrical capillary could be computed by solving the Young-Laplace equation via optimization of a Bézier curve. This work extends the previous work by demonstrating that the method is applicable to predict the meniscus shape not only in a cylindrical capillary but also in other cases, such as at a tilted plate, between two plates, and for a sessile drop. Numerous works have attempted previously to solve the Young-Laplace equation, and their results all agree with this paper's validating its method. All the preceding approaches, however, used special techniques to solve the differential equation, while the Bézier curve method proposed in this work is more simple, which allows it to maintain greater computational simplicity. Moreover, the Bézier curve method can be applied to solve many other different differential equations in the same way as shown in this work. The effect of the Bézier curve degree on the precision of prediction was also thoroughly investigated. It was found that the 4th degree Bézier curve was required to predict the meniscus shape precisely in a cylindrical capillary, against a tilted plate, and between two plates, while the 5th degree was required for the shape of the sessile drop.

A Fast Prediction Model for Liquid Metal Transfer Modes during the Wire Arc Additive Manufacturing Process

The liquid metal transfer mode in wire arc additive manufacturing (WAAM), plays an important role in determining the build quality. In this study, a fast prediction model based on the Young-Laplace equation, momentum equation, and energy conservation, is proposed, to identify the metal transfer modes, including droplet, liquid bridge, and wire stubbing, for a given combination of process parameters. To close the proposed model, high-fidelity numerical simulations are applied, to obtain the necessary inputs required by the former. The proposed model's accuracy and effectiveness are validated by using experimental data and high-fidelity simulation results. It is proved that the model can effectively predict the transition from liquid bridge, to droplet and wire stubbing modes. In addition, its errors in dripping frequency and liquid bridge height range from 6% to 18%. Moreover, the process parameter windows about transitions of liquid transfer modes have been established based on the model, considering wire feed speed, travel speed, heat source power, and material parameters. The proposed model is expected to serve as a powerful tool for the guidance of process parameter optimization, to achieve high-quality builds.

Bubbling in carbon dioxide aqueous solutions containing fine air bubbles

Bubbling in carbon dioxide (CO2) aqueous solutions initiated by pre-existing fine air bubbles, rather than CO2 gas cavities, has been theoretically investigated. As the bubbling of CO2 gas progressed more rapidly than the dissolution of air in the solutions, the CO2 bubbles were assumed to be at thermodynamic partial equilibrium, in which the equilibria with respect to the pressure (Young–Laplace equation) and chemical potential of CO2 (Henry’s law) were attained, but the equilibrium with respect to the chemical potential of air was not attained between the bubbles and the aqueous solution. It has been shown that the radii of CO2 bubbles in unsaturated CO2 solutions are in stable equilibrium, whereas they have two equilibrium states in weakly supersaturated CO2 solutions: a stable state with small bubble radii and an unstable state with large bubble radii. In highly supersaturated CO2 solutions, CO2 bubbles cannot satisfy the equilibrium of the chemical potential of CO2, and they assume a growing state that satisfies only the pressure equilibrium.

Dynamic analysis of small droplets at constant pressure and analytical model for drip systems and very low pressure drop-on-demand applications

We study the evolution of the growing volume of a droplet formed out of a capillary tube driven at a constant applied pressure by optical volume detection. A particular application aims at modeling the dynamic of the drop in the case of the injection of drugs in the middle-ear cavity using a small target drug delivery system. Various dispense tips such as a steel needle or silicone catheters and different t-BuOH aqueous solutions were used. A physical model based on the simplified Laplace–Young equation for a spherical droplet was developed to interpret the experimental results and model the observed deviation of the mean flow rate from the Poiseuille law when the drop radius is smaller than the capillary length. We emphasize the large influence of the surface tension which introduces a highly nonlinear effect at low applied pressure just above the capillary threshold pressure. The model fits well the evolution of the growing volume at various applied pressure up to a maximum diameter corresponding to the drop size close to the capillary length of the fluid, lc=γ/ρg, based on the liquid density ρ, gravity g and surface tension γ. We demonstrate that the model can also be applied to non spherical pendant droplets providing the apex elongation over the drop height of a spherical cap of the same volume is kept in a 30% range.

A Predictive Model of Capillary Forces and Contact Diameters between Two Plates Based on Artificial Neural Network.

Many efforts have been devoted to the forecasting of the capillary force generated by capillary adsorption between solids, which is fundamental and essential in the fields of micro-object manipulation and particle wetting. In this paper, an artificial neural network (ANN) model optimized by a genetic algorithm (GA-ANN) was proposed to predict the capillary force and contact diameter of the liquid bridge between two plates. The mean square error (MSE) and correlation coefficient (R2) were employed to evaluate the prediction accuracy of the GA-ANN model, theoretical solution method of the Young-Laplace equation and simulation approach based on the minimum energy method. The results showed that the values of MSE of capillary force and contact diameter using GA-ANN were 10.3 and 0.0001, respectively. The values of R2 were 0.9989 and 0.9977 for capillary force and contact diameter in regression analysis, respectively, demonstrating the accuracy of the proposed predictive model. The sensitivity analysis was conducted to investigate the influence of input parameters, including liquid volume and separation distance, on the capillary force and contact diameter. The liquid volume and separation distance played dominant roles in affecting the capillary force and contact diameter.

Stability and critical volume of a suspended pendant drop in air via experiments and eigenvalue analysis

In this paper, we study the stability of pendant drops suspended from a syringe needle tip using theory and experiments. We apply an eigenvalue analysis to the Young-Laplace equation for pendant drops to predict the instability type and critical drop volume that detaches and falls from a syringe needle tip due to gravity. We performed pendant drop experiments using different liquids and syringe needle sizes for a wide range of Bond numbers, 0.2<Bo∗<1.2. Experimental results that included pinched-off drop volumes were compared with values computed at their stability limit from the eigenvalue analysis. The stability analysis was capable of predicting axisymmetric instabilities, and the agreement between volumes at pinch-off found through numerical and experimental analysis depended on the Bond number.

Freestanding lipid bilayer tensiometer for the study of mechanosensitive ion channels

Mechanical forces modify the cell membrane potential by opening mechanosensitive ion channels. We report the design and construction of a lipid bilayer tensiometer to study channels that respond to lateral membrane tension, [Formula: see text] , in the range 0.2 to 1.4 [Formula: see text] (0.8 to 5.7 [Formula: see text] ). The instrument consists of a black-lipid-membrane bilayer, a custom-built microscope, and a high-resolution manometer. Values of [Formula: see text] are obtained from the determination of the bilayer curvature as a function of applied pressure by means of the Young-Laplace equation. We demonstrate that [Formula: see text] can be determined by calculating the bilayer radius of curvature from fluorescence microscopy imaging or from measurements of the bilayer's electrical capacitance, both yielding similar results. Using electrical capacitance, we show that the mechanosensitive potassium channel TRAAK responds to [Formula: see text] , not curvature. TRAAK channel open probability increases as [Formula: see text] is increased from 0.2 to 1.4 [Formula: see text] but open probability never reaches 0.5. Thus, TRAAK opens over a wide range of [Formula: see text] , but with a tension sensitivity about one-fifth that of the bacterial mechanosensitive channel MscL.

Numerical Study of Gas Breakthrough in Preferential Rocks for Underground Nuclear Waste Repositories

During the long-term storage of radioactive waste, the continuous generation of gas in the disposal area may influence the integrity of host rock. Thus, the investigation of gas migration and breakthrough in low-permeability rock is indispensable for the stability assessment. In this work, the pore space models of four potential host rocks (Boom clay, COx argillite, Opalinus clay, and Beishan granite) were generated via the binarization of the Gaussian random field. This method provides a randomly formed pore network that does rely on an initial definition of pore shape. The constructed models were analyzed and validated by using the mathematical morphology. A numerical calculation scenario of gas breakthrough on the basis of the Young–Laplace equation was proposed and applied. Results show that the gas breakthrough pressures are 2.62–4.11 MPa in Boom clay and 3.72–4.27 MPa in COx argillite. It enhances the idea that the capillary-induced gas breakthrough is possible at pressures lower than the fracture threshold. For Opalinus clay and Beishan granite, no connected pathway exists, and the breakthrough is more likely to occur through pathway dilation or fractures. The presented method has the advantage of experimental reproducibility and brings a new idea for the investigation of fluid migration in low-permeability rocks.

Freezing characters study of the sessile seawater drop on a cold substrate

Sea spray icing poses risks to vessels and offshore structures in cold ocean regions. Compared to many research works dealing with the freezing of fresh water, the freezing process of sessile seawater drop was less discussed. The coupled level set and volume of fluid method combined with the enthalpy–porosity method is used to solve the Stefan problem. A two-dimensional (2D) axis-symmetric model is adopted to describe the freezing and temperature variation process. Numerical results were verified by our experiment results. The initial geometric profile of sessile drops was characterized by the Young–Laplace equation. Various salinities within the oceanographic range (10–40 g/kg) were adopted, and results showed that the freezing time increases dramatically with increasing salinity. The influence of the contact angle and substrate temperature in the freezing process was also concentrated. All these results contributed to a better understanding of the icing mechanism on marine surfaces.

Interaction between the oil droplet in water and wetted wall: Force model and motion law

To investigate the force model and motion law of oil droplets in water near the wetted wall, oil droplets with R1 = 0.29–0.62 mm and oil films with R2 = 1–6 mm are solved numerically. In addition to buoyancy, flow resistance, and added mass force, the film-induced force triggered by the wetted wall constraint is also introduced into the force model. The drainage process is described using the Stokes–Reynolds equation, and the Young–Laplace equation is used to calculate the pressure within the water film. The results show that the force model can be coupled with the Stokes–Reynolds–Young–Laplace model equation to better describe the drainage dynamics near the wetted wall. The pressure distribution law is closely related to the shape of the water film, especially when the oil–water interface is in the shape of a dimple, which can lead to the formation of negative pressure zones within the water film. The maximum pressure first grows in an exponential, then logarithmic pattern and eventually approaches the equivalent Laplace pressure. Around the critical size, the direction of the film-induced force changes and the form of action switches between driving and drag forces. The film-induced force's dominant effect is strongest when the curvature radius of the oil film is comparable to the droplet size.

Pattern formation on dynamic membranes.

Pattern formation defines cell identities and plays a crucial role in arguably all membrane functionality such are cell division, motility, communication, adhesion, etc. Cell often evolves by changing their shape, which translates to membrane dynamics, hence leading to pattern formation on dynamic surfaces. While pattern formation on static shapes has been intensively studied both theoretically and experimentally, the understanding of patterning on moving shapes remains largely elusive. We study force distribution on dynamic but initially spherical or cylindrical shapes by our surface dynamics equations. For simplicity, we consider small deformation of incompressible sphere and cylinder and show that shape dynamics induce nonuniform force distributions, therefore clarifying spontaneous polarisation, symmetry breaking, and rich static and moving pattern formations. Based on surface dynamics equations we derive a generic Young-Laplace equation which indicates that practically any static and dynamic patterns are possible in incompressible systems and if so, the question is what is the underlying mechanism that controls cell identity? The answer to the problem is again a surface dynamics equation that guarantees mass conservation. In other words, dynamic surfaces induce dynamic surface mass density that is governed by a generic mass balance equation and the last one controls the identity. While mass balance itself is regulated by an active or passive influx of material particles on the surface. The last statement for cell membrane means that membrane mass balance is in full correlation with cell-governed reaction, synthesis, and diffusion. The same statement can be reached for the charge balance equation which is also part of surface dynamics equations.

Generalization of Young-Laplace, Kelvin, and Gibbs-Thomson equations for arbitrarily curved surfaces

The Young-Laplace, Kelvin, and Gibbs-Thomson equations form a cornerstone of colloidal and surface sciences and have found successful applications in many subfields of physics, chemistry, and biology. The Gibbs-Thomson effect, for example, predicts that small crystals are in equilibrium with their liquid melt at a lower temperature than large crystals and the positive interfacial energy increases the energy required to form small particles with a high curvature interface. In cases of liquids contained within porous media (confined geometry), the effect indicates decreasing the freezing/melting temperatures and the increment of the temperature is inversely proportional to the pore size. These phenomena can be reformulated for Gaussian maps of macromolecules and can be asked the following question: can one use the equations for predicting the melting temperature and shape of polymer chains in confined geometries? The answer is no, mainly because macromolecules form highly curved surfaces (Gaussian maps), and the equations hold only for simple geometries (sphere, plane, or cylinder). Here, we present general Young-Laplace, Kelvin, and Gibbs-Thomson equations for arbitrarily curved surfaces and apply them to predict temperature distribution on a few protein surfaces. Also, after increased interest toward liquid/liquid phase separation in biology, we derive generic Ostwald ripening and show that for shape-changing condensates, instead of a monotonic growing mechanism, a variety of processes are possible. Due to the generality of equations, we clarify that at appropriate internal/external pressure conditions systems, bounded by surfaces, may adopt any shape and thermal stability is strongly influenced by the geometries of confined spaces.