Surface Tension Gradient Research Articles

Influence of Seawater on the Degree of Entrainment in the Flotation of a Synthetic Copper Ore

Froth flotation is a process in which hydrophobic particles attach to bubbles forming particle–bubble aggregates, which are transported to the top section of the cell where they overflow to form the concentrate. Particles also reach the concentrate by entrainment, which is a non-selective process that leads to low concentrate grades. The objective of this work was to study and compare the degree of entrainment measured using three methods, in fresh and seawater, and using methyl isobutyl carbinol (MIBC) and DF-250 as frothers. The experimental results indicated that the degree of entrainment decreased in seawater. Besides, water recovery was lower in the experiments with seawater regardless of the frother that was used in the experiments, which correlated with the observed low degrees of entrainment. It is proposed that the reduction of entrainment and water recovery in seawater can be explained by a reduction of air recovery and/or more bubble coalescence in the froth. It is also proposed that surfactant diffusion/convection from the lamellae to the Plateau borders in the froth is reduced in seawater, which reduces the surface tension gradients, and thus the restoring liquid flow from the Plateau borders to the lamellae.

Bubble behaviors during subcooled pool boiling in water and nonionic surfactant aqueous solution

A visualization study of the bubble behavior in pool boiling of ultra-pure water and surfactant aqueous solution (Triton X-114) under different heat fluxes was performed, using a narrow transparent bare FTO heating surface with various subcooling degrees of 5°C, 25°C and 35°C, respectively. It is shown that with the decrease of liquid subcooling, bubble coalescence in ultra-pure water becomes obvious. Whilst with the increase of liquid subcooling, the bubble surface gets rough and unstable. In contrast, a newly discovered phenomenon of bubble-bubble (BB) penetration occurs in the surfactant solution under the same working condition as that in water. BB penetration behavior is a bubble interaction without coalescence. This bubble behavior is believed to be the results of micro-convection due to the shrinkage of the bubble root, and the Marangoni effect due to the surface tension gradient. Combination of Marangoni effect and bubble surface movement causes the surfactant molecules to aggregate toward the bubble root, and it effectively promotes the nucleation of the next bubble. Owe to the rapid growth of newly nucleated bubbles, the bubble-bubble penetration and piercing behaviors happen during the growth stage. The newly nucleated bubble partially accelerates the first bubble departure, also interacts with the first bubble by forming a tiny vapor channel. This phenomenon should be one of the reasons of enhanced heat transfer using surfactant solutions.

Directional autonomous water flow in laser-engineered microfluidic gradient structures on polymethylmetacrylate-coated steel surface

Autonomous directional water flow was demonstrated on a laser-microstructured steel-supported polymethylmetacrylate (PMMA) film with a surface tension gradient. For this purpose, a 4 μm-thick PMMA layer on AISI 304 steel surface was raster-scanned in air in ablative mode by a 1064 nm, 100 ns laser beam in a number of lines, with the amount and topography of ablated PMMA analyzed by optical microscopy, profilometry and IR spectroscopy. Such scanning, performed at increasing incident fluences, produced a series of chemically and topographically modified, differently water-wet neighbouring mm-sized spots, autonomously driving single-droplet water flow along the surface tension (contact angle) gradient.

Physicochemical Studies of Al–Cu Alloy Powder and Material on Its Basis Produced under Nonoptimal Conditions of 3D Printing

The surface structure and volume of a 3D article produced by the method of selective laser melting from a powder of the D-16 alloy has been studied. Using the XPS method, it has been determined that there is an Al2O3 layer on its surface and a metal alloy Al–Cu with a copper content of ~5% under it, which coincides with the data of energy dispersive X-ray analysis conducted on the initial powder by the method of scanning electron microscopy. Local areas with an increased copper content (up to 13 at %) were revealed at the boundaries of the crystal grains. A high porosity of the obtained material has been established, which resulted from the specifics of crystallization of the Al–Cu system’s alloys related to the transfer of substance along the interfaces, as a consequence of the presence of concentration, temperature and, surface tension gradients along with nonoptimal 3D printing conditions.

Flow boiling characteristics in different configurations of stepped microchannels

Geometrical modifications in microchannel geometry intended towards mitigation of flow instabilities generally results in increased pressure drop across the microchannel heat sink. To overcome this, stepped microchannels configurations with combination of narrow bottom (aspect ratio: AR = depth/width > 1) and wider top (AR < 1) part are investigated and their flow boiling performances have been compared with rectangular cross-section microchannels (RMC) having same hydraulic diameter (350 μm). The effect of varying wider cross-section on flow boiling instability and heat transfer performance have been explored for three configurations of stepped microchannels namely: stepped straight microchannels (SMC), stepped converging microchannels (SCMC) and stepped diverging microchannels (SDMC). These geometrical variants are fabricated on a 10 × 10 mm2 copper block having nine parallel microchannels. Flow boiling experiments have been conducted using de-ionized (DI) water as coolant for an inlet subcooling of 20 °C, coolant mass fluxes ranging from 327.6 to 777.54 kg/m2s and for wide range of heat fluxes. Combination of narrow and wider converging/diverging flow passage improves flow stability by allowing bubbles in the confined narrow bottom to grow and expand in the wider top section thus reducing their evaporative momentum. Different flow regimes govern the heat transfer and pressure drop mechanisms while the compressible volume-liquid interaction dictates flow instability. Favorable surface tension gradient in SDMC alleviates flow instability whereas reduced flow resistance at the inlet in SCMC resulted in smooth rewetting during dry out. Amplitude and fluctuation of pressure drop is found to be minimum in SCMC among all geometric configurations, while better heat transfer performance has been observed in SDMC configuration.

Melt pool morphology and surface roughness relationship for direct metal laser solidification of Hastelloy X

PurposeLimited research has attempted to reveal the different modes of the melt pool formation in additive manufacturing. This paper aims to study the mechanisms of surface roughness formation, especially on the aspect of melt pool formation which determine the surface profile and consequently significantly influence the surface roughness.Design/methodology/approachIn this study, the conditions under which different modes of melt pool formation (conduction mode and keyhole mode) occur for the case of as-fabricated Hastelloy X using direct metal laser solidification (DMLS) are derived and validated experimentally. Top surfaces of uni-directionally built samples under various processing conditions are cut, grinded, polished and etched to reveal their individual melt pool morphologies. Similarly, up-skin (slope angle < 90°) and down-skin (slope angle > 90°) melt pool morphologies are also investigated to compare the differences. Surface tension gradients and resultant Marangoni flow, which dominate the melt flow in the melt pool, is also calculated to help better evaluate the melt pool shape forming.FindingsTwo types of melt pool formation modes are dominating in DMLS: conduction mode and keyhole mode. Melt pool formed by conduction mode generally has an aspect ratio of 1:2 (depth vs width) and is in elliptical shape. Appropriate selection of scanning laser power and speed are required to maintain a low characteristic length and width ratio to prevent ballings. Melt pool formed by keyhole mode has an aspect ratio of 1:1 or less. High-energy contour promotes formation of key-hole-shaped melt pool which fills the gaps between layers and smoothens the up-skin surface roughness. Low-energy contour scan is necessary for down-skin surface to form small melt pool profiles and achieve low Ra.Originality/valueThis paper provides valuable insight into the origins of surface quality problem of DMLS, which is a very critical issue for upgrading the process for manufacturing real components. This paper helps promote the understanding of the attributes and capabilities of this rapidly evolving three-dimensional printing technology and allow appropriate control of processing parameters for successful fabrication of components with sound surface quality.

Fundamental limits of Marangoni-driven patterning

We predict the maximum aspect ratio and minimum feature pitch for equal line-space Marangoni-driven patterning (MDP) using analytical and numerical techniques and compare the predicted upper/lower bounds to prior experimental results. MDP is a novel technique that harnesses surface tension gradients to apply topography to thin polymer films. MDP operates by first exposing a polymer film to UV light though a photomask, causing a chemical reaction and a change in surface energy in the exposed regions. By heating the film above its glass transition temperature, surface tension gradients give rise to Marangoni forces, which cause the polymer to flow into the higher surface tension regions and form hill-and-valley topography. This topography could be used either as an etch mask for traditional device fabrication or as a functional coating for improved optical performance, improved adhesion, or antifouling purposes. To understand the full scope of applications for MDP, it is necessary to know the maximum aspect ratio (AR) and minimum feature pitch achievable by this technique, as densely packed, high aspect ratio features are often desirable. To determine these previously unknown limits for equal line-space patterning, we present a model for MDP and solve it analytically and numerically. Using limiting values of physical parameters and engineering constraints, we determine an upper bound for feature aspect ratio and a lower bound on feature pitch. These results are then compared to prior experimental results, showing that the AR can be significantly increased and the pitch can be significantly decreased for MDP. We conclude on the barriers and potential strategies for improving MDP.

CFD study of Marangoni condensation heat transfer of vapor mixture on a horizontal tube

Over the past few decades, experimental studies have been conducted on the condensation heat transfer of vapor mixtures. However, the local heat transfer characteristics of vapor mixture affected by surface tension have not been fully investigated. The present work, for the first time, suggested the CFD simulation method for the Marangoni condensation of ethanol-vapor mixture and analyzed the calculated result with flow structure. A CFD study has been performed for the condensation heat transfer of steam–ethanol mixtures on a horizontal tube to elucidate the Marangoni condensation phenomenon and the consequent heat transfer mechanism, which are difficult to fully obtain experimentally. In the present study, the numerical predictions of condensation heat transfer using a liquid film model agree well with those of the experimental results. The CFD analysis of steam–ethanol mixture compares with pure steam to clearly show the influence of surface tension on the heat transfer. In particular, when a small amount of ethanol is added to pure steam, the condensation heat transfer is enhanced because the local liquid film thickness is changed because of the surface tension gradient on the gas–liquid interface, which is caused by a concentration difference.

Droplet motion on contrasting striated surfaces

Liquid droplets move readily under the influence of surface tension gradients on their substrates. Substrates decorated with parallel microgrooves, or striations, presenting the advantage of homogeneous chemical properties yet varying the topological characteristics on either side of a straight-line boundary, are considered in this study. The basic type of geometry consists of hydrophobic micro-striations/rails perpendicular to the boundary, with the systematic variation of the width to spacing ratio, thus changing the solid–liquid contact fraction and inducing a well-defined wettability contrast across the boundary. Droplets in the Cassie–Baxter state, straddling the boundary, move along the wettability contrast in order to reduce the overall surface free energy. The results show the importance of the average solid fraction and contrasting fraction in a wide range of given geometries across the boundary on droplet motion. A unified criterion for contrasting striated surfaces, which describes the displacement and the velocity of the droplets, is suggested, providing guidelines for droplet manipulation on micro-striated/railed surfaces.

Liquid metal droplet-enabled electrocapillary flow in biased alternating electric fields: a theoretical analysis from the perspective of induced-charge electrokinetics

The phenomenon of Marangoni chaotic electroconvection of electrolytes induced by liquid metal droplets has been serving as a method of choice for pumping of microfluidics in the past ten years. Although an external additional alternating voltage, usually being sufficiently small, was invariably employed in practical experiments for stabilizing the unidirectional liquid motion caused by a preexisted direct-current electric field, its subtle effect on the superimposed non-uniform surface tension and the final fluid transport state is still theoretically unclear. From the physical perspective of induced-charge electrokinetics, we present herein an analytical criteria for the conditions under which a sessile metal drop can actuate unidirectional liquid motion passing across it affected by a biased alternating voltage signal, wherein a mechanical balance between the linear pump pressure and nonlinear bipolar stress components exerted on the conducting drop surface has been taken into account. For accuracy validation, a numerical model was developed, in which multiple frequency electrochemical polarization was calculated under the Debye–Huckel limit, and coupled to the mechanical problem via inserting the resultant surface tension gradient as a source term of electrocapillary stress at the droplet–medium interface. The analytical solution accords well with the simulation results, in terms of the threshold voltage amplitude for effective liquid transport along the static potential gradient. At last, we demonstrate that the effect of continuous electrowetting can be fully exploited for simultaneous pumping and extraction of microscale impurities in closed fluid loops embedding a network of three-dimensional floating electrode plates for invoking auxiliary dielectrophoretic attraction. These results prove invaluable for achieving a high degree of freedom manipulation of particle and liquid contents in modern microfluidic systems with flexible conducting microdroplets.

Uniform and Gaussian Ultraviolet Light Intensity Distribution on Droplet for Selective Area Deposition of Particles

Abstract Particle transport through Marangoni convection inside a sessile droplet can be controlled by the ultraviolet (UV) light distribution on the surface. The photosensitive solution changes the surface tension gradient on the droplet surface and can induce clockwise and counterclockwise circulations depending on the incident light distribution. In this paper, the stream function in the sessile drop has been evaluated in toroidal coordinates by solving the biharmonic equation. Multiple primary clockwise and counterclockwise circulations are observed in the droplet under various concentric UV light profiles. The downward dividing streamlines are expected to deposit the particles on the substrate, thus matching the number of deposited rings on the substrate with the number of UV light rings. Moffatt eddies appear near the contact line or centerline of the droplet depending on the UV light profile and its distance from the contact line.

The study of effects of surface tension, magnetic field and non-uniform salinity gradients on the onset of double diffusive convection in composite system

The study of effects of surface tension, magnetic field and non-uniform salinity gradients on the onset of double diffusive convection in composite system

Effect of shielding conditions on bead profile and melting behaviour in laser powder bed fusion additive manufacturing

A series of experiments were performed using a 500 W continuous wave fibre laser on a single powder bed layer using different processing variables. The aim was to investigate the effect of different shielding conditions on melting behaviour and bead profile in laser powder bed fusion (PBF). Through high-speed imaging, it was found that under an argon atmosphere a strong plasma plume is generated from the meltpool. Laser beam-plasma plume interactions caused strong instabilities during melting, including laser wandering, track instability and continuous fluctuations between melting regimes (conduction and keyhole). Hence, it was not possible to control the profile of the melted tracks under this condition. By using a helium atmosphere, a smaller plasma was obtained, reducing the disruptions caused by laser-plasma interactions. This led to a stable melting regime that allowed control of the melt bead profile. This condition was used to study the effect of laser-material fundamental interaction parameters on the bead geometry in powder bed melting. It was found that during melting of single tracks, the dominant regime of melting is conduction for the range of parameters tested. Penetration and melt width were found to increase with increasing energy density. For longer interaction times, melt widths were found to be up to ten times the size of the beam diameter used. Fluid flow modelling showed that this is due to strong melt flow as consequence of surface tension gradients generated by very high temperature gradients.

Leveling of a model paint film with a yield stress

The coating dynamics of a drying paint film with a yield stress is studied. The liquid is modeled as a binary mixture with one volatile component, solvent, and one nonvolatile component, resin. When the solvent has a different surface tension than the resin, solvent evaporation can lead to the creation of surface tension gradients which can potentially overcome the yield stress and dramatically affect the flow history. Using the lubrication approximations to derive the flux of the liquid film parallel to the substrate, we find that the presence of the yield stress causes several distinct flow regimes. The total flux of each of these regimes is summed, and using the continuity equation we derive an evolution equation giving the height of the free surface as a function of the distance along the substrate and time. The resulting equations are discretized and solved numerically using finite differences. High order derivative is treated implicitly, allowing for large time steps and reducing the computational requirements. We find that the presence of a yield stress greatly affects the leveling behavior of the coating. Critical yield stresses exist that can cause maximal leveling of the coating film.

Rotational synchronization of camphor ribbons in different geometries.

We present experiments on multiple pinned self-propelled camphor ribbons, which is a rectangular piece of paper with camphor infused in its matrix. Experiments were performed on three, four, and five ribbons placed in linear and polygonal geometries. The pinned ribbons rotate on the surface of water, due to the surface tension gradient introduced by the camphor layer in the neighborhood of the ribbon. This camphor layer leads to a chemical coupling between the ribbons. In different geometries, the ribbons have been observed to rotationally synchronize in all the possible configurations. A numerical model, emulating the interactions between the ribbons as Yukawa interaction was studied, which was qualitatively able to reproduce the experimental findings.

Closed-form theoretical model of the secondary drop size in partial coalescence—Capturing pertinent timescales and viscous forces

One of the most important outcomes of partial drop coalescence is the ratio of the secondary drop radius to the primary drop radius, known as the drop ratio, ri. This ratio is thought to be approximately constant and independent of physical parameters of the fluids involved. However, this study reveals that ambient fluid viscosity can alter the size of the secondary drop and the drop ratio consequently. Using scaling analysis, we derive a model that predicts the behavior of the drop ratio as a function of the Ohnesorge number, a dimensionless ratio of viscous to inertial forces. In addition, we present our experimental results of coalescing drops on a planar interface under the influence of surface tension gradients. A high-speed digital camera is used to observe the evolution of drops as they coalesce with a bulk liquid. We show that this process is influenced by the surface tension gradient between the drop and the bulk liquid. The ratio of the secondary drop to the primary drop in partial coalescence is smaller than the reported values for coalescence without a surface tension gradient. The analytical model derived through this study is based on a new modified Ohnesorge number that includes surface tension gradients. Our analytical model is compared against other models and the results illustrate good agreement with our experimental findings and experimental data in the literature.

A flow velocity dependence of dynamic surface tension in Plateau borders of foam

HypothesisLiquid drainage through foams is a multiscale process, that primarily occurs through channels known as Plateau borders (PBs). Recent experimental studies of isolated PBs have observed variations in channel surface tension, γ, with liquid flow rate, Q, for systems containing soluble low molecular weight surfactant (LMWS). The current study proposes that the dynamic surface tension (DST) could be responsible for this effect, where the residence time of surfactant molecules in the PB is similar to the time required for their adsorption to the channel interface. ExperimentsProfile geometries of isolated ‘ideal’ PB’s were created in a bespoke experimental setup at controlled forced liquid flow rates. Average surfactant residence times, τRes, were calculated for solutions of Sodium dodecylsulfate (SDS), Tween 20 (T20) and Tween 80 (T80), and used to calculate corresponding average DST values in discrete regions of measured PB profiles. DST values were combined with microscale drainage theory to assess the potential physical implications on liquid flow. FindingsSignificant variations in the magnitude of γ were calculated based on surfactant characteristics, where only the rapid adsorption of SDS was sufficient to produce DST values approaching equilibrium. These findings seriously question assumptions of near equilibrium surface tension in LMWS foam systems above their critical micelle concentration (CMC). Furthermore, the presence of surface tension gradients identified using this discrete approach, highlights the need to further refine the current theory to a continuous approach incorporating Marangoni effects.

Evaluation of the Effect of Cooling Conditions and Heat Transfer Coefficients on Solidification of Al-Cu Binary Alloy in Static Casting Process

Source-based method for modelling solidification problems have been modified and presented in the current work. It coupled the effect of thermal radiation to macro-transport codes and was solved using finite volume method. The problem was formulated based on the classic continuum energy conservation equation for transient conduction controlled solidification system. Radiation heat transfer and latent heat evolution were added as source terms and solved with appropriate numerical treatments to obtain a system of linearized source terms. This circumvented the need for the application of any analytical solution to the intricate heat transfer regimes included in the model. The effect of cooling was carried out under various cooling conditions imposed on different surfaces of the mould for the solidifying metal. The resultant influence of cooling on the solid fraction evolution during static casting was then evaluated. The simulated cooling curves show that thermal radiation have no influence on the rate of heat extraction and the results show that the predicted cooling curves and solid fraction updates are similar to the results of previous models. The predicted curves at the top section of the open mould however show a little deviation due to effect of surface tension gradient forces. It was further revealed that heat transfer coefficients has more effect cooling curves and temperature contours at the lateral mould surfaces than the interior of the casting which is in agreement with theory of Newtonian cooling.

A coupled immersed interface and level set method for simulation of interfacial flows steered by surface tension

This work presents a methodology to address the problems of bubbles and drops evolving in incompressible, viscous flows due to the effect of surface tension. It is based on the combination of a recently developed immersed interface method to resolve discontinuities, with the level set (LS) method to reproduce the evolving interfaces. The paramount feature of this immersed interface method is the use of Lagrange interpolation enclosing grid points positioned in the vicinity of the interface and few exceptional grid points positioned on the interface. Different problems are considered to assert the accurateness of the proposed methodology, involving both simple and complex interface geometries. Precisely, the following problems are addressed: circular flow with a fixed interface, the dispersion of capillary waves, initially circular, ellipse, star shaped bubbles oscillating to an equilibrium state, and circular drops deforming in shear flows. The transient evolution of bubbles/drops in terms of their shapes, pressure profiles, velocity vectors, deformation ratios of major and minor axis is analyzed to observe the effect of surface tension. The proposed methodology is seen to recover the exact numerical equilibrium between the surface tension and pressure gradient in the vicinity of complex interface geometries as well, while recreating the flow physics with an adequate level of accuracy with well representation of overall trends. Moreover, the numerical results yield a good level of agreement with the reference data.

Electric field control of propulsion force of a boat driven by chemical Marangoni effect

Chemical Marangoni propulsion (CMP) is a driving on fluid by surface tension imbalance around object caused by anisotropic distribution of surfactant or by the reaction of Marangoni convection caused by the surface tension gradient. The purpose of the study is a remote control of the propulsion force in CMP. Electrostatic interaction of ionic surfactants as propellant with external electric field (EF) is expected to modify the surfactant distribution and modulate the surface tension gradient. We selected surface active imidazolium-based ionic liquids (ILs) as propellants. Effects of the application of the EF (667 kV/m) to the IL layer emitted from the object on the propulsion force and the accompanying Marangoni convection were evaluated on aqueous surface. When hydrophobic ILs with [PF6] anion were used, the application of the EF decreased the propulsion force and also decreased the flow velocity and flow width of Marangoni convection. The decreasing rate of the propulsion force increased with the alkyl-chain length of the IL cations. The maximum decreasing rate was 33 %. We considered that the main reason for the EF-induced reduction in the propulsion force is the decrease in the surface tension gradient due to the increases in the surface tension of the emitted IL layers caused by the rearrangement of the surface active IL molecules on aqueous surface. This is the first report about the EF control of the propulsion force in CMP.