Surface Tension Gradient Research Articles

Effect of surfactant redistribution on the flow and stability of foam films.

The viscous froth model for two-dimensional (2D) dissipative foam rheology is combined with Marangoni-driven surfactant redistribution on a foam film. The model is used to study the flow of a 2D foam system consisting of one bubble partially filling a constricted channel and a single spanning film connecting it to the opposite channel wall. Gradients of surface tension arising from film deformation induce tangential flow that redistributes surfactant along the film. This redistribution, and the consequent changes in film tension, inhibit the structure from undergoing a foam-destroying topological change in which the spanning film leaves the bubble behind; foam stability is thereby increased. The system's behaviour is categorized by a Gibbs-Marangoni parameter, representing the ratio between the rate of motion in tangential and normal directions. Larger values of the Gibbs-Marangoni parameter induce greater variation in surface tension, increase the rate of surfactant redistribution and reduce the likelihood of topological changes. An intermediate regime is, however, identified in which the Gibbs-Marangoni parameter is large enough to create a significant gradient of surface tension but is not great enough to smooth out the flow-induced redistribution of surfactant entirely, resulting in non-monotonic variation in the bubble height, and hence in foam stability.

An Incompressible Smoothed Particle Hydrodynamics (ISPH) Model of Direct Laser Interference Patterning

Functional surfaces characterised by periodic microstructures are sought in numerous technological applications. Direct laser interference patterning (DLIP) is a technique that allows the fabrication of microscopic periodic features on different materials, e.g., metals. The mechanisms effective during nanosecond pulsed DLIP of metal surfaces are not yet fully understood. In the present investigation, the heat transfer and fluid flow occurring in the metal substrate during the DLIP process are simulated using a smoothed particle hydrodynamics (SPH) methodology. The melt pool convection, driven by surface tension gradients constituting shear stresses according to the Marangoni boundary condition, is solved by an incompressible SPH (ISPH) method. The DLIP simulations reveal a distinct behaviour of the considered substrate materials stainless steel and high-purity aluminium. In particular, the aluminium substrate exhibits a considerably deeper melt pool and remarkable velocity magnitudes of the thermocapillary flow during the patterning process. On the other hand, convection is less pronounced in the processing of stainless steel, whereas the surface temperature is consistently higher. Marangoni convection is therefore a conceivable effective mechanism in the structuring of aluminium at moderate fluences. The different character of the melt pool flow during DLIP of stainless steel and aluminium is confirmed by experimental observations.

Marangoni-driven film climbing on a draining pre-wetted film

Marangoni flow is the motion induced by a surface tension gradient along a fluid–fluid interface. In this study, we report a Marangoni flow generated when a bath of surfactant contacts a pre-wetted film of deionized water on a vertical substrate. The thickness profile of the pre-wetted film is set by gravitational drainage and so varies with the drainage time. The surface tension is lower in the bath due to the surfactant, and thus a liquid film climbs upwards along the vertical substrate due to the surface tension difference. Particle tracking velocimetry is performed to measure the dynamics in the film, where the mean fluid velocity reverses direction as the draining film encounters the front of the climbing film. The effect of the surfactant concentration and the pre-wetted film thickness on the film climbing is then studied. High-speed interferometry is used to measure the front position of the climbing film and the film thickness profile. As a result, higher surfactant concentration induces a faster and thicker climbing film. Also, for high surfactant concentrations, where Marangoni driving dominates, increasing the film thickness increases the rise speed of the climbing front, since viscous resistance is less important. In contrast, for low surfactant concentrations, where Marangoni driving balances gravitational drainage, increasing the film thickness decreases the rise speed of the climbing front while enhancing gravitational drainage. We rationalize these observations by utilizing a dimensionless parameter that compares the magnitudes of the Marangoni stress and gravitational drainage. A model is established to analyse the climbing front, either in the Marangoni-driving-dominated region or in the Marangoni-balanced drainage region. Our work highlights the effects of the gravitational drainage on the Marangoni flow, both by setting the thickness of a pre-wetted film and by resisting the film climbing.

Experiments and analytical solutions of light driven flow in nanofluid droplets

Adding nanoparticles with high light response characteristics to a light-transmitting fluid medium can form a light-driven nanofluid and achieve efficient use of light energy. This paper conducts the experimental observation and theoretical analysis of the light driven nanofluid flow behavior, which is the theoretical basis for achieving the precise control of optical drive nanofluid. To realize the efficient conversion of light energy into kinetic energy, here, the motion of Fe<sub>3</sub>O<sub>4</sub> particles with a diameter of 300 nm in droplets induced by the Marangoni effect is studied under different light sources by using the particle image velocimetry (PIV). The experimental results show that when the number density of particles is higher than the critical value, the vertical vortices with symmetrical structure can be induced. At the bottom of the droplet, the particles move from the periphery to the center of droplet, and at the top of the droplet, the particles move from the center to the periphery of droplet. In addition, the frequency of light source and the number density of particles are the dominant factors in this process. Subsequently, for the light driven nanofluid experiment in this paper, the analytical solution of the flow field distribution is achieved by using the Stokes equation and the surface tension gradient boundary condition. The analytical solution of the flow field distribution obtained here is consistent with the experimental results, confirming the validity of the quantitative theory. Finally, the correlation between various driving modes, including surface tension at the top surface, surface pressure at the bottom surface or concentrated light radiation force in bulk phase, is discussed. This research provides theoretical support for the precise regulation of flow behavior and efficient conversion of light energy in the optical microfluidic system.

Modelling on space-domain surface waves of vertical low-Re falling film and the enhancement on mass transfer in halide-solution/air absorption

Vertical falling film with low Reynolds number (Re) is widely used, but the influence of surface waves on mass transfer is still unclear. This paper theoretically described the wave structure along the flow direction, and evaluating the enhancement on mass transfer during halide-solution/air absorption. The effects of flow viscosity, surface tension gradient, liquid/air convective heat transfer, film thickness and flow distance are considered. Model validation were performed by comparing with the data from literatures and our experiments. For practical use, empirical correlations of wavelength and amplitude are provided, using Re, Marangoni and Nusselt numbers as variables. Wavelength increases proportionally with liquid Re, and amplitude mainly increases with the flow distance. When Re increases from 20 to 60, wave amplitude and wavelength increase by 10% and 40%. The enhancement effect is determined by the wavelength and frequency, and is more obvious under conditions of large liquid concentration or small liquid Re.

Bayesian optimization for a high- and uniform-crystal growth rate in the top-seeded solution growth process of silicon carbide under applied magnetic field and seed rotation

Abstract The Top-Seeded Solution Growth (TSSG) method is a promising technique for the production of high-quality SiC single crystal. To achieve a high- and uniform-growth rate in the TSSG process of SiC, the fluid flows developing in the growth solution (melt), due to the applied and induced electromagnetic fields, buoyancy, seed rotation, and free surface tension gradient, need to be controlled. Previous numerical analysis has shown that such complex flows in the TSSG melt can be controlled by the applications of a static magnetic field and seed rotation. However, the requirement of significant computational resources prevented us from carrying out the needed optimization for the process parameters involved. In order to resolve the computational demand issue, in this study, we utilized the Bayesian optimization algorithm for an efficient optimization of the associated control parameters of the TSSG process of SiC. It was shown that the Bayesian algorithm determines the optimal state at about roughly 1/4 of the computational cost of a conventional optimization, and accurately predicts the growth-rate evaluation function around the optimal state. The optimal state obtained by the present optimization process predicts a high- and uniform-growth rate in the TSSG system of SiC considered in this work.

Bubble Rise Velocity and Surface Mobility in Aqueous Solutions of Sodium Dodecyl Sulphate and n-Propanol

Aqueous solutions of simple alcohols exhibit many anomalies, one of which is a change in the mobility of the bubble surface. This work aimed to determine the effect of the presence of another surface-active agent on bubble rise velocity and bubble surface mobility. The motion of the spherical bubble in an aqueous solution of n-propanol and sodium dodecyl sulphate (SDS) was monitored by a high-speed camera. At low alcohol concentrations (xP < 0.01), both the propanol and SDS molecules behaved as surfactants, the surface tension decreased and the bubble surface was immobile. The effect of the SDS diminished with increasing alcohol concentrations. In solutions with a high propanol content (xP > 0.1), the SDS molecules did not adsorb to the phase interface and thus, the surface tension of the solution was not reduced with the addition of SDS. Due to the rapid desorption of propanol molecules from the bottom of the bubble, a surface tension gradient was not formed. The drag coefficient can be calculated using formulas for the mobile surface of a spherical bubble.

Dynamics of Thin Film Under a Volatile Solvent Source Driven by a Constant Pressure Gradient Flow

The evolution of a thin liquid film subject to a volatile solvent source and an air-blow effect which modifies locally the surface tension and leads to Marangoni-induced flow is shown to be governed by a degenerate fourth order nonlinear parabolic h-evolution equation of the type given by ∂ t h = − div x M 1 h ∂ x 3 h + M 2 h ∂ x h + M 3 h , where the mobility terms M 1 h and M 2 h result from the presence of the source and M 3 h results from the air-blow effect. Various authors assume M 2 h ≈ 0 and exclude the air-blow effect into M 3 h . In this paper, the authors show that such assumption is not necessarily correct, and the inclusion of such effect does disturb the dynamics of the thin film. These emphasize the importance of the full definition t → · grad γ = grad x γ + ∂ x h grad y γ of the surface tension gradient at the free surface in contrast to the truncated expression t → · grad γ ≈ grad x γ employed by those authors and the effect of the air-blow flowing over the surface.

Evaporation of saline colloidal droplet and deposition pattern**Project supported by the National Natural Science Foundation of China (Grant Nos. 11472275 and U1738118), the Chinese Academy of Sciences Key Technology Talent Program, and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB22040301).

The dynamic process of the evaporation and the desiccation of sessile saline colloidal droplets, and their final deposition are investigated. During the evaporation, the movement of the colloidal particles shows a strong dependence on the salt concentration and the droplet shape. The final deposition pattern indicates a weakened coffee-ring effect in this mixed droplet system. The microscopic observation reveals that as evaporation proceeds, the particle motion trail is affected by the salt concentration of the droplet boundary. The Marangoni flow, which is induced by surface tension gradient originating from the local evaporative peripheral salt enrichment, suppresses the compensation flow towards the contact line of the droplet. The inhomogeneous density and concentration field induced by evaporation or crystallization can be the major reason for various micro-flows. At last stage, the distribution and crystallization of NaCl are affected by the colloidal particles during the drying of the residual liquid film.

Formation, growth, and saturation of dry holes in thick liquid films under vapor-mediated Marangoni effect

Films and drops of liquids can change their shapes and move under the spatial gradient of surface tension. A remote volatile liquid of relatively low surface tension can induce such flows because its vapor locally lowers the surface tension of the films and drops. Here, we show that aqueous liquid films thicker than approximately 100 µm can be punctured to immediately expose a dry hole by an overhanging isopropyl alcohol drop, which is attributed to the vapor-mediated Marangoni effect. We construct and corroborate scaling laws to predict the film dynamics, considering the balance of the driving capillary force and resisting viscous and hydrostatic forces as well as the contact angle of the alcohol-adsorbed solid surface. This remote scheme to induce and sustain changes of liquid morphology can be applied for fluid sculpture and patterning for industrial and artistic practices.

Electrorheology of a dilute emulsion of surfactant-covered drops

We investigate the effects of surfactant coating on a deformable viscous drop under the combined action of shear flow and a uniform electric field. Employing a comprehensive three-dimensional approach, we analyse the non-Newtonian shearing response of the bulk emulsion in the dilute suspension regime. Our results reveal that the location of the peak surfactant accumulation on the drop surface may get shifted from the plane of shear to a plane orthogonal to it, depending on the tilt angle of the applied electric field and strength of the electrical stresses relative to their hydrodynamic counterparts. The surfactant non-uniformity creates significant alterations in the flow perturbation around the drop, triggering modulations in the bulk shear viscosity. Overall, the shear-thinning or shear-thickening behaviour of the emulsion appears to be greatly influenced by the interplay of surface charge convection and Marangoni stresses. We show that the balance between electrical and hydrodynamic stresses renders a vanishing surface tension gradient on the drop surface for some specific shear rates, rendering negligible alterations in the bulk viscosity. This critical condition largely depends on the electrical permittivity and conductivity ratios of the two fluids and orientation of the applied electric field. Also, the physical mechanisms of charge convection and surface deformation play their roles in determining this critical shear rate. As a consequence, we obtain new discriminating factors, involving electrical property ratios and the electric field configuration, which govern the same. Consequently, the surfactant-induced enhancement or attenuation of the bulk emulsion viscosity depends on the electrical conductivity and permittivity ratios. The concerned description of the drop-level flow physics and its connection to the bulk rheology of a dilute emulsion may provide a fundamental understanding of a more complex emulsion system encountered in industrial practice.

Interactions of Oil Drops Induced by the Lateral Capillary Force and Surface Tension Gradients.

The interacting forces on the objects at the air-liquid interface are important for researching self-assembly of objects. Due to the interacting forces among objects, the objects self-assemble at the air-liquid interface and organize into ordered structures. In general, for the interacting of oil drops, they can attract coalescence or repel dispersion. However, according to our former research, we find that interactions of oil drops can be motion like interactions of gas atoms. The oil drops cannot coalesce to form a big oil drop or separate to form ordered structures. They attract at a long distance but repel when they almost contact. In this study, according to our simulation, we demonstrate that the atomic-like motion of oil drops is mainly caused by the surface tension gradient and the lateral capillary force. Based on the results, our research will facilitate the fundamental understanding about interactions among oil drops. Apart from giving detailed demonstration about the interacting forces among oil drops, our research may also put forward research about self-assembly, oil emulsification, and microfluidics.

Translational and rotational motion of disk-shaped Marangoni surfers

In this paper, we study the Marangoni propulsion of a neutrally buoyant disk-shaped object at the air-water interface. Self-propulsion was achieved by coating the back of the disk with either soap or isopropyl alcohol in order to generate and then maintain a surface tension gradient across the surfer. As the propulsion strength and the resulting disk velocity were increased, a transition from a straight-line translational motion to a rotational motion was observed. Although spinning had been observed before for asymmetric objects, these are the first observations of spinning of a geometrically axisymmetric Marangoni surfer. Particle tracking and particle image velocimetry measurements were used to interrogate the resulting flow field and understand the origin of the rotational motion of the disk. These measurements showed that as the Reynolds number was increased, interfacial vortices attached to sides of the disk were formed and intensified. Beyond a critical Reynolds number of Re > 120, a vortex was observed to shed resulting in an unbalanced torque on the disk that caused it to rotate. The interaction between the disk and the confining wall of the Petri dish was also studied. Upon approaching the bounding wall, a transition from straight-line motion to rotational motion was observed at significantly lower Reynolds numbers than on an unconfined interface. Interfacial curvature was found to either enhance or eliminate rotational motion depending on whether the curvature was repulsive (concave) or attractive (convex).

A-TIG welding process for enhanced-penetration in Duplex stainless-steel: effect of activated fluxes

ABSTRACTWeldability of duplex stainless steel (DSS) is an important issue in fabrication of pipes at petrochemical industries. Well-established tungsten inert gas (TIG) welding process has the limitations of lesser penetration; however, process parameters (such as current and voltage) need to increase to attain deeper penetration, which, in turn, affects the material’s property owing to increased heat energy. Use of activated fluxes generate the extra heat energy with same process parameters and causes the deeper penetration and increased dilution. The aim of the present study is to investigate the effect of activated fluxes on penetration, dilution, weld chemistry, weld microstructure, gas and slag metal reactions which has resulted from extra heat energy produced. Different activated fluxes were investigated in context of heat energy, associated penetration, dilution and weld pool properties. The oxygen content in activated flux has played significant role in hot cracking and void formations in the weld. Similarly, it also changes the surface tension gradient of weld pool considerably. Dendrite growth is predominant in oxide-based fluxes and this growth in austenite and ferrite dendrite has been evidenced as a function of oxygen content. The process with relevant mechanisms is elaborated in the present study.

Collection of nanoparticles at the air-liquid interface by surface tension gradients

Particles such as nano-plastics at the air-liquid interface is harmful to the environment. Due to small size of the nanoparticles, expensive materials are needed to collect them such as ultrafiltration membranes. In our study, we propose an easy method to collect the nanoparticles at the air-liquid interface. Because surface tension of contaminated water is lower than that of deionized water, the surface tension gradient is used to transport the nanoparticles. In our study, we wet a strip with deionized water and then immerse one end of the wetting strip into contaminated water. Due to the surface tension gradient between the contaminated water and the deionized water, the nanoparticles at the surface of the contaminated water are transported to the surface of the strip. In addition, by adding a small amount of deionized water at the other end of the strip, the nanoparticles can be constantly collected. Furthermore, many materials can be used as the hydrophilic strip, such as glass, paper, and steel mesh.

Liquid Metal Gallium Micromachines Speed Up in Confining Channels

One of the great challenges in the field of tiny machines is the capability of engineering liquid metal micromachines to autonomously move within confining channels to perform various complex tasks. Herein, liquid metal gallium micromachines that significantly increase their velocity in confining channels with adaptive deformation under exposure to an electric field are presented. The liquid metal gallium micromachines move toward the negative electrode under the propulsion of hydrogen bubbles, which is obviously different from the previous report that liquid metal gallium alloy (i.e., Galinstan) micromachines move to the positive electrode, owing to the surface tension gradient. More importantly, the liquid metal gallium micromachine can adaptively deform and accelerate in confined channels. The velocity of liquid metal gallium micromachines increases with the decrease in the width of channels. It is found that the speed‐up motion of liquid metal gallium micromachines is caused by the enhanced electro‐osmosis effect in confining channels. The findings not only help understand the role of the confinement effect on the motion of liquid metal micromachines but also provide a novel strategy to manipulate the motion velocity of liquid metal micromachines for specific applications.

Surfactant-induced spreading of nanoparticles is inhibited on mucus mimetic surfaces that model native lung conditions

We investigated the ability of surfactant-induced spreading to promote nanoparticle distribution on model mucus hydrogels. The hydrogels were formulated with viscoelastic properties and surface tensions that match those of native lung mucus. Nanoparticle-containing droplets with or without surfactant were deposited on the mucus surface and spreading patterns were monitored by time-course fluorescence imaging. Overall, surfactant-induced spreading of nanoparticles required an appropriate balance between Marangoni forces and viscoelastic subphase resistance. Spreading was enhanced on bare gels by increasing the concentration of surfactant in the droplets or reducing the viscoelastic properties of the subphase. However, with a pre-existing film of pulmonary surfactant on the mucus surface, spreading was dramatically inhibited as the surface tension gradient between the droplets and the surrounding subphase decreased. A complete lack of spreading was observed at surface tensions that matched those in the tracheobronchial region of the lungs, even with full-concentration Infasurf. These studies demonstrate that the magnitude of spreading on lung mucus-like surfaces is limited by native mucosal properties.

Aerodynamically stabilized Taylor cone jets.

We introduce a way to stabilize steady micro/nanoliquid jets issuing from Taylor cones together with coflowing gas streams. We study the dripping-jetting transition of this configuration theoretically through a global stability analysis as a function of the governing parameters involved. A balance between the local radial acceleration to the surface tension gradient, the mass conservation, and the energy balance equations enable us to derive two coupled scaling laws that predict both the minimum jet diameter and its maximum velocity. The theoretical prediction provides a single curve that describes not only the numerical computations but also experimental data from the literature for cone jets assisted with gas coflow. Additionally, we performed a set of experiments to verify what parameters influence the jet length. We adopt a very recent model for capillary jet length to our configuration by combining electrohydrodynamic effects with the gas flow through an equivalent liquid pressure. Due to diameters below 1 μm and high speeds attainable in excess of 100 m/s, this concept has the potential to be utilized for structural biology analyses with x-ray free-electron lasers at megahertz repetition rates as well as other applications.

A New Approach to Tackle Wafer Contact Mark Contamination Issues in Marangoni Drying

Introduction Wafer drying is the last and critical step in wet wafer surface preparation processes for a product finished with clean and dry surfaces (1). Among various wafer drying technologies, Marangoni drying has been the most commonly used application nowadays due to its advantages in many aspects (1-3). However, surface tension gradients generated by Marangoni effect might not be able to fully overcome the capillary force existing at the tight geometry of the contact area between wafers and a wafer holder, resulting in contact mark contamination issues, especially under an inspection condition with reduced wafer edge exclusion (Figure 1). In this paper, we demonstrate the application of a technological approach to enhance a complete drainage of water droplets at the wafer/holder contact points to significantly mitigate the contact mark contamination issue. Experimental Experiments were conducted on a GAMATM wafer cleaning station in NAURA-Akrion’s Applications Lab, in which a LuCIDTM dryer is used for the wafer drying process. The dryer was set to run a typical Marangoni process at fixed parameters, with the in-tank wafer holder as the only variable. Various numbers of 200mm bare Si test wafers, sandwiched with clean dummy wafers to serve a full loading condition, were placed to various slots of a full pitch process carrier for a test batch. To ensure a consistent degree of hydrophilic state of Si surfaces during the drying process, each wafer batch was processed with an SC1/QDR/Dry instead of a Dry Only recipe. Before and after a process run, test wafers were inspected with a KLA-Tencor SP1 at ≥100nm particle threshold with 2mm edge exclusion. Results Wafer contact mark incidence was evaluated by overlapping the “pre” and “post” wafer map of each test wafer to identify the specific contact mark signature. Figure 2 highlights the incidence with respect to frequency and severity of contact mark occurrence. The former indicates how many test wafers in a testing batch show contact mark contamination, while the latter presents the extent of particle clustering in a contact mark. It can be seen from Fig.2 that both the frequency and severity of contact mark contamination were significantly reduced with appropriate liquid drainage at the contact area between the test wafers and a modified in-tank holder. Conclusion Experiments were conducted to tackle the wafer contact mark issue in a Marangoni drying process. The capillary effect holding liquid droplets at wafer/holder contact points can be overcome by a drainage technology to significantly reduce the contact mark incidence. With the technological solution, the Marangoni process window can be broadened and, in turn, the robustness and performance of the drying process are enhanced. References D.C. Burkman, et. al., in Handbook of Semiconductor Wafer Cleaning Technology (ed.. W. Kern), Noyes Publications, Westwood, NJ, 1993, pp. 131-134.A.F.M. Leenaars, et. al., Marangoni Drying: A New Extremely Clean Drying Process, Langmuir, 1990, 6 (11), pp. 1701-1703.T. Vukosav, Substrate Drying Using Surface Tension Gradient Technology, R&D Magazine, 7/16/2013. https://www.rdmag.com/article/2013/07/substrate-drying-using-surface-tension-gradient-technology Figure 1

Marangoni-Convection-Driven Bubble Behavior and Microstructural Evolution of Sn-3.5Ag/Sn-17Bi-0.5Cu (Wt Pct) Alloy Solidified on Cu Substrate Under Space Microgravity Condition

Marangoni convection significantly affects the solidification structure as it controls the bubble behavior and mass transfer in the melt. Sn-3.5Ag/Sn-17Bi-0.5Cu (wt pct) alloy with different surface tension gradients was fabricated and solidified on a Cu ring substrate under space microgravity condition (SJ-10 satellite) to study the Marangoni convection formation mechanism. The pore and element distributions in the solidified alloy and surface tension gradient in the melt were analyzed. The differences between the microstructures of alloys solidified under microgravity and normal gravity conditions were also investigated. The surface tension gradient induced by Bi concentration difference resulted in the formation of Marangoni convection from the right to left of the melt under the microgravity condition. In the left (Bi-scarce) part of the melt, Marangoni convection induced by the Cu concentration difference flowed from outside to inside. Driven by bubble-agitation convection, Cu mainly migrated from the substrate to the right part of the melt. Therefore, dendrite-like CuxSny was distributed along a gradient. Under the normal gravity condition, significant gravity-induced convection resulted in an even distribution of Bi and Cu, which decreased the contact angle and reduced the surface tension, thus promoting nucleation of the alloy. Therefore, fine dendrite-like CuxSny with larger number density were uniformly distributed in the melt.