Showing papers on "Marangoni effect published in 2013"
TL;DR: An improved lattice Boltzmann equation (LBE) method is presented to capture the interface between different phases and solve the pressure and velocity fields, which can recover the correct Cahn-Hilliard equation (CHE) and Navier-Stokes equations.
Abstract: A phase-field-based hybrid model that combines the lattice Boltzmann method with the finite difference method is proposed for simulating immiscible thermocapillary flows with variable fluid-property ratios. Using a phase field methodology, an interfacial force formula is analytically derived to model the interfacial tension force and the Marangoni stress. We present an improved lattice Boltzmann equation (LBE) method to capture the interface between different phases and solve the pressure and velocity fields, which can recover the correct Cahn-Hilliard equation (CHE) and Navier-Stokes equations. The LBE method allows not only use of variable mobility in the CHE, but also simulation of multiphase flows with high density ratio because a stable discretization scheme is used for calculating the derivative terms in forcing terms. An additional convection-diffusion equation is solved by the finite difference method for spatial discretization and the Runge-Kutta method for time marching to obtain the temperature field, which is coupled to the interfacial tension through an equation of state. The model is first validated against analytical solutions for the thermocapillary driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then used to simulate thermocapillary migration of a three-dimensional deformable droplet and bubble at various Marangoni numbers and density ratios, and satisfactory agreement is obtained between numerical results and theoretical predictions.
100 citations
TL;DR: In this paper, an active microswimmer was constructed where a micron-sized droplet of bromine water was placed into a surfactant-laden oil phase.
Abstract: Recently, an active microswimmer was constructed where a micron-sized droplet of bromine water was placed into a surfactant-laden oil phase. Due to a bromination reaction of the surfactant at the interface, the surface tension locally increases and becomes non-uniform. This drives a Marangoni flow which propels the squirming droplet forward. We develop a diffusion-advection-reaction equation for the order parameter of the surfactant mixture at the droplet interface using a mixing free energy. Numerical solutions reveal a stable swimming regime above a critical Marangoni number M but also stopping and oscillating states when M is increased further. The swimming droplet is identified as a pusher whereas in the oscillating state it oscillates between being a puller and a pusher.
92 citations
TL;DR: Oil droplets loaded with surfactant propel themselves with a velocity up to 6 mm s(-1) when they are placed in an aqueous phase of NaOH solution or buffer solution when the initial value of pH is adjusted such that the pH exceeds the threshold at the equilibrium state, the droplets move spontaneously.
Abstract: Oil droplets loaded with surfactant propel themselves with a velocity up to 6 mm s–1 when they are placed in an aqueous phase of NaOH solution or buffer solution. The required driving force for such motion is generated on the interface of the droplets by the change in interfacial tension, due to deprotonation of the surfactant. This force induces Marangoni convection, which gives rise to a circulating flow inside the droplets. The droplets begin to move when the axis of this circulation deviates from the vertical line. This motion depends on the pH condition of the aqueous phase. When the initial value of pH is adjusted such that the pH exceeds the threshold at the equilibrium state, the droplets move spontaneously. It was seen that the droplets were independent of the material of the solid substrates because the droplets were not directly in contact with the surface of the substrate. The condition for the onset of this spontaneous motion was verified by comparing the prediction from the linear stability ...
75 citations
TL;DR: It is shown that fingering emerges during evaporation inside the coffee ring, resulting from a bidispersed colloidal mixture of micro- and nanoparticles, which could help to understand the variety of the final deposition patterns of colloidal droplets.
Abstract: Colloidal droplets including micro- and nanoparticles generally leave a ringlike stain, called the ``coffee ring,'' after evaporation. We show that fingering emerges during evaporation inside the coffee ring, resulting from a bidispersed colloidal mixture of micro- and nanoparticles. Microscopic observations suggest that finger formation is driven by competition between the coffee-ring and Marangoni effects, especially when the inward Marangoni flow is overwhelmed by the outward coffee-ring flow. This finding could help to understand the variety of the final deposition patterns of colloidal droplets.
75 citations
TL;DR: It is demonstrated that temperature-induced variations of the equilibrium contact angle give rise to complex dynamics, which includes enhanced spreading rates, nonmonotonic dependence of the contact line speed on the applied substrate temperature gradient, as well as "stick-slip" behavior.
Abstract: We study the two-dimensional dynamics of a droplet on an inclined, nonisothermal solid substrate. We use lubrication theory to obtain a single evolution equation for the interface, which accounts for gravity, capillarity, and thermo- capillarity, brought about by the dependence of the surface tension on temperature. The contact line motion is modeled using a relation that couples the contact line speed to the difference between the dynamic and equilibrium contact angles. The latter are allowed to vary dynamically during the droplet motion through the dependence of the liquid−gas, liquid−solid, and solid−gas surface tensions on the local contact line temperature, thereby altering the local substrate wettability at the two edges of the drop. This is an important feature of our model, which distinguishes it from previous work wherein the contact angle was kept constant. We use finite-elements for the discretization of all spatial derivatives and the implicit Euler method to advance the solution in time. A full parametric study is carried out in order to investigate the interplay between Marangoni stresses, induced by thermo-capillarity, gravity, and contact line dynamics in the presence of local wettability variations. Our results, which are generated for constant substrate temperature gradients, demonstrate that temperature-induced variations of the equilibrium contact angle give rise to complex dynamics. This includes enhanced spreading rates, nonmonotonic dependence of the contact line speed on the applied substrate temperature gradient, as well as "stick−slip" behavior. The mechanisms underlying this dynamics are elucidated herein.
67 citations
TL;DR: The perturbation analysis allows for a simple rubric to be laid out for cosolvent additions that can reduce the Marangoni effect during the later stages of coating deposition and drying when the thin film limit applies.
Abstract: Striation defects in spin-coated thin films are a result of unfavorable capillary forces that develop due to the physical processes commonly involved in the spin-coating technique. Solvent evaporation during spinning causes slight compositional changes in the coating during drying, and these changes lead to instability in the surface tension, which causes lateral motions of the drying fluid up to the point where it gels and freezes in the thickness variations. In an earlier publication, we looked at the case where evaporation happens fast enough that the compositional depletion is mostly a surface effect. In terms of the mass transport rate competition within the coating solution, that work covered the thick film limit of this instability problem. However, in many cases, the coatings are thin enough or diffusion of solvent within the coating is fast enough to require a different solvent mixing strategy, which is developed here. A simple perturbation analysis of surface roughness is developed, and evaporation is allowed in the thin film limit. The perturbation analysis allows for a simple rubric to be laid out for cosolvent additions that can reduce the Marangoni effect during the later stages of coating deposition and drying when the thin film limit applies.
49 citations
TL;DR: It is found that turbulence driven redistribution of surfactant on the interface inhibited the Marangoni effect that is otherwise induced by film draining during coalescence in more quiescent flow, showing that the maximum stable droplet diameter is proportional to the Kolmogorov scale when viscous stresses are important.
Abstract: Lattice Boltzmann simulations of water-in-oil (W/O) type emulsions of moderate viscosity ratio (≃1/3) and with oil soluble amphiphilic surfactant were used to study the droplet size distribution in forced, steady, homogeneous turbulence, at a water volume fraction of 20%. The viscous stresses internal to the droplets were comparable to the interfacial stress (interfacial tension), and the droplet size distribution (DSD) equilibrated near the Kolmogorov scale with droplet populations in both the viscous and inertial subranges. These results were consistent with known breakup criteria for W/O and oil-in-water emulsions, showing that the maximum stable droplet diameter is proportional to the Kolmogorov scale when viscous stresses are important (in contrast to the inviscid Hinze-limit where energy loss by viscous deformation in the droplet is negligible). The droplet size distribution in the inertial subrange scaled with the known power law ∼d −10/3, as a consequence of breakup by turbulent stress fluctuations external to the droplets. When the turbulent kinetic energy was sufficiently large (with interfacial Peclet numbers above unity), we found that turbulence driven redistribution of surfactant on the interface inhibited the Marangoni effect that is otherwise induced by film draining during coalescence in more quiescent flow. The coalescence rates were therefore not sensitive to varying surfactant activity in the range we considered, and for the given turbulent kinetic energies. Furthermore, internal viscous stresses strongly influenced the breakup rates. These two effects resulted in a DSD that was insensitive to varying surfactant activity.
47 citations
TL;DR: In this article, an investigation for magnetohydrodynamics (MHD) thermocapillary Marangoni convection heat transfer of an electrically conducting power-law fluid driven by temperature gradient is presented.
Abstract: This paper presents an investigation for magnetohydrodynamics (MHD) thermocapillary Marangoni convection heat transfer of an electrically conducting power-law fluid driven by temperature gradient. The surface tension is assumed to vary linearly with temperature and the effects of power-law viscosity on temperature fields are taken into account by modified Fourier law for power-law fluids (proposed by Pop). The governing partial differential equations are converted into ordinary differential equations and numerical solutions are presented. The effects of the Hartmann number, the power-law index and the Marangoni number on the velocity and temperature fields are discussed and analyzed in detail.
44 citations
TL;DR: In this paper, the authors provided evidence that when the so-called phenomenon of particle accumulation structure (PAS) occurs, extended regions exist where ½ of the axial component of vorticity matches the angular frequency of the traveling wave produced by the instability of the Marangoni flow.
Abstract: Evidence is provided that when the so-called phenomenon of particle accumulation structure (PAS) occurs, extended regions exist where ½ of the axial component of vorticity matches the angular frequency of the traveling wave produced by the instability of the Marangoni flow. Several cases are considered in which such axial component is varied by “injecting” vorticity into the system via rotation of one of its endwalls. The results show that both the resulting PAS lines and the trajectories of related solid particles undergo significant changes under the influence of imposed rotation. By analysis of such findings, a validation and a generalization/extension of the so-called “phase-locking” model are provided.
43 citations
TL;DR: In this article, a 3D transient model of a transferred argon arc in interaction with an anode material is presented and the results discussed using the open software @Saturne distributed by Electricite de France.
Abstract: A three-dimensional (3D) transient model of a transferred argon arc in interaction with an anode material is presented and the results discussed. The model based on a finite volume method is developed using the open software @Saturne distributed by Electricite de France. The 3D model includes the characterization of the plasma gas and of the work piece with a current continuity resolution in the whole domain. Transport and thermodynamic properties are dependent on the local temperature and on the vapours emitted by the eroded material due to the heat flux transferred by the plasma. Drag force, Marangoni force, Laplace and gravity forces are taken into account on the weld pool description. The plasma and the weld pool characteristics are presented and compared with experimental and theoretical results from the literature. For a distance between the two electrodes of d = 5 mm and an applied current intensity of I = 200 A, the vapour concentration is weak. The influence of the parameters used in the Marangoni formulation is highlighted. Finally, in agreement with some authors, we show with this global transient 3D model that it is not necessary to include the voltage drop in the energy balance.
41 citations
TL;DR: In this paper, the authors present the results of a numerical study of the thermocapillary convection in a liquid bridge of (decane) and (5 cSt silicone oil) when the interface is subjected to an axial gas stream.
Abstract: We present the results of a numerical study of the thermocapillary (Marangoni) convection in a liquid bridge of ( -decane) and (5 cSt silicone oil) when the interface is subjected to an axial gas stream. The gas flow is co- or counter-directed with respect to the Marangoni flow. In the case when the gas stream comes from the cold side, it cools down the interface to a temperature lower than that of the liquid beneath and in a certain region of the parameter space that cooling causes an instability due to a temperature difference in the direction perpendicular to the interface. The disturbances are swept by the thermocapillary flow to the cold side, which leads to the appearance of axisymmetric waves propagating in the axial direction from the hot to cold side. The mechanism of this new two-dimensional oscillatory instability is similar to that of the Pearson’s instability of the rest state in a thin layer heated from below (Pearson, J. Fluid Mech., vol. 4, 1958, p. 489), and it appears at the value of the transverse Marangoni number lower than that of the Pearson’s instability in a horizontal layer ( , depending on the Biot number). The generality of the instability mechanism indicates that it is not limited to cylindrical geometry and might be observed in a liquid layer with cold gas stream.
TL;DR: Rueger and Calabrese as mentioned in this paper measured the drop size for water dispersed into viscous food grade mineral oils in a batch Silverson L4R rotor-stator mixer.
Abstract: Most previous studies of liquid–liquid dispersion in complex geometry are limited to turbulent flow at low continuous phase viscosity. In this study, a viscous continuous phase was employed over a range of flow conditions including both the laminar and turbulent regimes. Equilibrium drop size was measured for water dispersed into viscous food grade mineral oils in a batch Silverson L4R rotor–stator mixer. The influence of fluid viscosities and interfacial tension (by adding an oil-soluble surfactant) were examined. In order to isolate the effect of drop breakage from coalescence, Part 1 is limited to dilute conditions (water phase fraction, ϕ = 0.001). In the laminar regime, drop breakup was more likely due to a simple shear breakage mechanism than one for extension. Following Grace (1982) , a semi-empirical drop size correlation was developed. For turbulent flow, the validity of the sub-Kolmogorov inertial stress model for correlating equilibrium mean drop size was verified. Surfactants were found to mostly decrease drop size by lowering interfacial tension. Except for laminar systems near the critical micelle concentration, where Marangoni stresses appear to play some role, the effect of surfactants on the drop size could be correlated using the equilibrium or static interfacial tension. The influence of water phase fraction and coalescence is considered in Part 2 ( Rueger and Calabrese, 2013 ) of this paper.
TL;DR: In this paper, the influence of UV light on the drainage flows of foams and thin-liquid films stabilized by photoswitchable azobenzene surfactants, whose shape and hydrophobicity can be modified using UV illumination, was investigated.
Abstract: We study the influence of UV light on the drainage flows of foams and thin-liquid films stabilized by photoswitchable azobenzene surfactants, whose shape and hydrophobicity can be modified using UV illumination. This model system, the dynamics of which was well characterized in a previous study, enables us to trigger a controlled variation of the surface excess and surface tension. In both geometries we observe light-induced flows which are able to suppress the drainage flow induced by gravity. However, we show that the physical origin of the flows is different in both geometries. At the scale of a few films in the so-called ‘two-bubble’ experiment the comparisons of the physical length scales, i.e. the radius of the meniscus and the film thickness, to the chemical “reservoir length” (Γ/c) show that the flux of the surfactant at the interface in the presence of UV light is different in the films and in the meniscus, inducing a Marangoni flow from the meniscus to the film, which is stronger than gravity and capillary suction. The velocity of this flow can be tuned by the light intensity and the surfactant concentration. In the real foams, however, we show that the above mechanism is not relevant because the radii of curvature of the Plateau borders are orders of magnitude lower than in the two-bubble experiment, thus the capillary suction prevents such transfer between the films and the Plateau borders. Instead, the decrease of the drainage velocity is shown to be due to a gradient of the surface tension in the illuminated zone hence to a local variation of the capillary pressure. This study underlines the importance of characterizing the radius of the Plateau borders for the understanding of foams, as this key parameter sets the order of magnitude of capillary pressure, film thickness and amount of available surfactant. We also show that this photosurfactant is a new toolbox for the understanding of foam stability.
TL;DR: In this article, the impact of a solutal Marangoni effect on the deposit obtained from a polymer solution was examined through numerical simulations, and a hydrodynamical model with lubrication approximation was used to describe the liquid phase in a dip-coating-like configuration.
Abstract: This paper examines through numerical simulations the impact of a solutal Marangoni effect on the deposit obtained from a polymer solution. A hydrodynamical model with lubrication approximation is used to describe the liquid phase in a dip-coating–like configuration. The studied case considers evaporation in stagnant air (diffusion-limited evaporation), which results in a coupling between the liquid and gas phases. Viscosity, surface tension, and saturated vapor pressure depend on the solute concentration. In the evaporative regime, when the surface tension increases with the polymer concentration, the Marangoni effect induces a periodic regime. This results in a self-organized periodic patterning of the dried film in certain control parameter ranges. A morphological phase diagram as well as meniscus and dry-deposit shapes are provided as a function of the substrate velocity and bulk solute concentration.
TL;DR: In this paper, it is shown that a thin layer of silica flux leads to an increased depth of weld penetration during activated TIG (=A-TIG) welding of Armco iron.
Abstract: It is experimentally shown that a thin layer of silica flux leads to an increased depth of weld penetration during activated TIG (=A-TIG) welding of Armco iron. The oxygen-content is found higher in the solidified weld metal and it is linked to the increased depth of penetration through the reversed Marangoni convection. It is theoretically shown for the first time that the basic reason of the reversed Marangoni convection is the phenomenon called “surface phase transition” (SPT), leading to the formation of a nano-thin FeO layer on the surface of liquid iron. It is shown that the ratio of dissolved oxygen in liquid iron to the O-content of the silica flux is determined by the wettability of silica particles by liquid iron. It is theoretically shown that when the silica flux surface density is higher than 15 µg/mm2, reversed Marangoni flow will take place along more than 50 pct of the melted surface. Comparing the SPT line with the dissociation curves of a number of oxides, they can be positioned in the following order of their ability to serve as a flux for A-TIG welding of steel: anatase-TiO2 (best)-rutile-TiO2 (very good)-silica-SiO2 (good)-alumina-Al2O3 (does not work). Anatase (and partly rutile) are self-regulating fluxes, as they provide at any temperature just as much dissolved oxygen as needed for the reversed Marangoni convection, and not more. On the other hand, oxygen can be over-dosed if silica, and other, less stable oxides (such as iron oxides) are used.
TL;DR: In this article, the effects of insoluble and soluble surfactant on the motion of a long bubble propagating through a capillary tube are investigated computationally using a finite-difference/front-tracking method.
TL;DR: Gao et al. as mentioned in this paper used a temperature-responsive wettability of a surface made of a block copolymer (BCP) to show the temperature-controlled directional spreading of water droplets.
Abstract: The actuation of microscale liquid droplets is a key point in the lab-on-chip field. Marangoni force actuation resulting from a temperature gradient has remarkable advantages. However, high hysteresis between the droplet and the surface is an obstacle to this motion. Here, we take advantage of the temperature-responsive wettability of a surface made of a block copolymer (BCP) to show the temperature-controlled directional spreading of water droplets. By applying a temperature gradient on the BCP surface, both the topologies and chemical components in the nanodomains could be changed gradually. As a result, a wettability gradient force would form with the same direction as the Marangoni force, which could also be formed due to the same temperature gradient, and the collaborative effect of these forces could help overcome the high hysteresis. This was confirmed theoretically by calculating the total force acting on the droplet. The liquid droplet was observed to move by forces of non-mechanical origin in experiments conducted using a thermal gradient on the BCP films. Furthermore, two water droplets were observed to merge into one when they were placed in a V-shaped temperature field. These results help us understand the motion of droplets on a surface with high hysteresis and provide potential applications in microfluidic devices. Directing the manner in which a liquid spreads across a surface — through patterns, for example — is important in a variety of fields ranging from printing to microfluidic device fabrication. Longcheng Gao and colleagues from Beihang University, China, have now achieved such control over a liquid through temperature variations. The researchers prepared a material with a temperature-dependent surface wettability by combining the polymers poly(methyl methylacrylate) (PMMA) and poly(N-isopropylacrylamide) (PNIPPAAm). The resulting PMMA-b-PNIPPAAm block copolymer is hydrophobic at high temperatures yet hydrophilic at low temperatures. Under a temperature gradient, the consequent difference in wettability causes a liquid drop to flow along the surface. Furthermore, as the surface tension of a liquid varies according to its temperature, an additional ‘Marangoni’ flow is induced. Since the directions of the Marangoni effect and the wettability gradient are the same, they work in concert to promote the movement of the droplet along the block copolymer. By applying temperature gradient on the temperature-responsive wettablitity surface of block copolymer, water droplet movement by the nonmechanical origin forces is realized on the surface with high hysteresis, due to the binary collaboration effect of wettability gradient force and Marangoni force. The results help to understand the motion of droplets on the surface with high hysteresis and also provide potential application in microfluidic devices.
TL;DR: In this article, the Navier-Stokes-Boussinesq equations with an undeformable interface were solved using the linear Henry relation for the partition of the weakly surface-active butanol.
Abstract: Transient solutal Marangoni convection in a closed two-layer system is studied by a combination of numerical simulations and supplementary validation experiments. The initially quiescent, equally sized liquid layers are the phases of a cyclohexanol/water mixture. Butanol is additionally dissolved in the upper organic layer. Its diffusion across the interface is sensitive to the Marangoni instability. Complex convective patterns emerge that develop a hierarchical cellular structure in the course of the mass transfer. Our highly resolved simulations based on a pseudospectral method are the first to successfully reproduce the multiscale flow observed in the experiments. We solve the three-dimensional Navier-Stokes-Boussinesq equations with an undeformable interface, which is modeled using the linear Henry relation for the partition of the weakly surface-active butanol. Length scales in the concentration and velocity fields associated with the small and large-scale cells agree well with our experimental data from shadowgraph images. Moreover, the simulations provide detailed information on the local properties of the flow by which the evolution of the patterns and their vertical structure are analyzed. Apart from relatively weak influences due to buoyancy, the evolution of the convective structures is self-similar between different initial butanol concentrations when length and time are appropriately rescaled.
TL;DR: In this paper, the stability of a gravity-driven film flow on a porous inclined substrate is considered, when the film is contaminated by an insoluble surfactant, in the frame work of Orr-Sommerfeld analysis.
Abstract: The stability of a gravity-driven film flow on a porous inclined substrate is considered, when the film is contaminated by an insoluble surfactant, in the frame work of Orr-Sommerfeld analysis. The classical long-wave asymptotic expansion for small wave numbers reveals the occurrence of two modes, the Yih mode and the Marangoni mode for a clean/a contaminated film over a porous substrate and this is confirmed by the numerical solution of the Orr-Sommerfeld system using the spectral-Tau collocation method. The results show that the Marangoni mode is always stable and dominates the Yih mode for small Reynolds numbers; as the Reynolds number increases, the growth rate of the Yih mode increases, until, an exchange of stability occurs, and after that the Yih mode dominates. The role of the surfactant is to increase the critical Reynolds number, indicating its stabilizing effect. The growth rate increases with an increase in permeability, in the region where the Yih mode dominates the Marangoni mode. Also, the growth rate is more for a film (both clean and contaminated) over a thicker porous layer than over a thinner one. From the neutral stability maps, it is observed that the critical Reynolds number decreases with an increase in permeability in the case of a thicker porous layer, both for a clean and a contaminated film over it. Further, the range of unstable wave number increases with an increase in the thickness of the porous layer. The film flow system is more unstable for a film over a thicker porous layer than over a thinner one. However, for small wave numbers, it is possible to find the range of values of the parameters characterizing the porous medium for which the film flow can be stabilized for both a clean film/a contaminated film as compared to such a film over an impermeable substrate; further, it is possible to enhance the instability of such a film flow system outside of this stability window, for appropriate choices of the porous substrate characteristics.
TL;DR: In this paper, an experimental apparatus was designed and fabricated to visually investigate microbubble emission boiling (MEB) phenomena characterized by its extremely high heat dissipation capacity and potential application in the field of thermal engineering.
TL;DR: In this paper, hollow glass cenospheres of various diameters ranging from 5 to 200µm are sorted according to size by evaporation of isopropyl alcohol droplets on an unpatterned glass substrate.
Abstract: The high throughput size sorting of particles in liquid suspensions is of interest for a variety of microanalytical and micromanufacturing applications. Hollow glass cenospheres of various diameters ranging from 5 to 200 µm are sorted according to size by evaporation of isopropyl alcohol droplets on an unpatterned glass substrate. By raising the temperature of the glass substrate, a stable Marangoni convection is developed inside the droplet. At a substrate temperature of 55 °C, more of the larger spheres (150–200 µm) are deposited near the droplet center, but smaller spheres 150 µm diameter outnumber those with <50 µm diameter by 6×. The deposited spheres remain attached to the substrate surface when dry. The self-assembled nature of this drying pattern results in size sorting.
TL;DR: In this paper, a momentum jump condition is derived which models the influence of surface active agents at fluid interfaces due to Marangoni stresses, underlying assumptions are quasi-stationary shape and surfactant distribution.
TL;DR: In this article, the level-set method coupled with mass-transfer equation is used to simulate the mass transfer induced Marangoni effect during drop formation, and the simulated drop volume, shape, and extraction fraction are in good accordance with experimental data.
Abstract: Marangoni effect induced by interphase mass transfer plays an important role in liquid-liquid extraction and reaction processes. The interaction of Marangoni effect and interphase mass transfer during drop formation at different injection rates and different initial solute concentrations was investigated by experimental and numerical simulation. The extraction fraction was measured and the corresponding correlation was proposed. The level-set method coupled with mass-transfer equation is for the first time used to simulate the mass-transfer induced Marangoni effect during drop formation. The simulated drop volume, shape, and extraction fraction are in good accordance with experimental data. Through the numerical simulation, it is found that the mass transfer in the first mass-transfer period is the most efficient during drop formation when Marangoni convection occurs. (c) 2013 American Institute of Chemical Engineers AIChE J, 59: 4424-4439, 2013
TL;DR: In this article, a modelling study of surfactant evolution on a film surface coupled to lamellar film drainage has been carried out, and numerical simulation was carried out using a material point method followed by a bookkeeping operation to regrid the film.
TL;DR: In this paper, the authors investigated ring formation from drying sessile colloidal droplets (∼1.0 mm in size) containing microparticles of silicon or polystyrene.
Abstract: Ring formation from drying sessile colloidal droplets (∼1.0 mm in size) containing microparticles of silicon or polystyrene was investigated with video microscopy. Results show that ring formation begins at the pinned contact line with the growth of an annular nucleus in a line by line way, which recedes inward albeit only slightly, followed by stacking of particles when the flow velocity becomes sufficiently large. The central height of the droplet decreases linearly with evaporation time, which implies that in the early stage, the number of particles arriving at contact line increases with time in a power law N∝t3/(1 + λ), where the parameter λ, according to Deegan's evaporation model, is related to the contact angle via λ=π−2θc2π−2θc. Experimental values of λ agree well with model calculation for small contact angles, but are relatively smaller in the case of large contact angles. ‘Amorphization’ mechanism for the deposit at different stages of evaporation is discussed. Marangoni flow in a droplet on h...
TL;DR: In this article, different methods (frozen time, non-normal, nonlinear methods) are proposed to predict critical times for convection onset and threshold values for free convection occuring during the drying of plane layers of polymer solutions may be due to various mechanisms, based on buoyancy or Marangoni effect.
TL;DR: Results of a pioneering study are presented, in which for the first time, crystallization, phase separation and Marangoni instabilities occurring during the spin-coating of polymer blends are directly visualized, in real-space and real-time.
Abstract: Results of a pioneering study are presented in which for the first time, crystallization, phase separation and Marangoni instabilities occurring during the spin-coating of polymer blends are directly visualized, in real-space and real-time. The results provide exciting new insights into the process of self-assembly, taking place during spin-coating, paving the way for the rational design of processing conditions, to allow desired morphologies to be obtained.
TL;DR: In this paper, the authors measured the heat transfer coefficient of steam-ethanol mixtures flowing vertically downward over a horizontal, water-cooled tube at pressures ranging from around atmospheric down to 14kPa.
Abstract: Careful heat-transfer measurements have been conducted for condensation of steamethanol mixtures flowing vertically downward over a horizontal, water-cooled tube at pressures ranging from around atmospheric down to 14kPa. Care was taken to avoid error due to the presence of air in the vapor. The surface temperature was accurately measured by embedded thermocouples. The maximum vapor velocity obtainable was limited by the maximum electrical power input to the boiler. At atmospheric pressure this was 7.5m/s while at the lowest pressure a velocity of 15.0m/s could be achieved. Concentrations of ethanol by mass in the boiler when cold prior to start up were 0.025%, 0.05%, 0.1%, 0.5%, and 1.0%. Tests were conducted for a range of coolant flow rates. Enhancement of the heat-transfer coefficient over pure steam values was found by a factor up to around 5, showing that the decrease in thermal resistance of the condensate due to Marangoni condensation outweighed diffusion resistance in the vapor. The best performing compositions (in the liquid when cold) depended on vapor velocity but were in the range 0.025‐0.1% ethanol in all cases. For the atmospheric pressure tests the heat-transfer coefficient for optimum composition, and at a vapor-to-surface temperature difference of around 15K, increased from around 55kW/m 2 K to around 110kW/m 2 K as the vapor velocity increased from around 0.8 to 7.5m/s. For a pressure of 14kPa the heat-transfer coefficient for optimum composition, and at a vapor-to-surface temperature difference of around 9K, increased from around 70kW/m 2 K to around 90kW/m 2 K as the vapor velocity increased from around 5.0 to 15.0m/s. Photographs showing the appearance of Marangoni condensation on the tube surface under different conditions are included in the paper. [DOI: 10.1115/1.4007893]
TL;DR: In this article, the authors investigate the influence of individual effects (kinetic effects, latent heat of vaporization, Marangoni convection, Stefan flow, droplet's surface curvature) on the rate of evaporation of a water droplet placed on a highly heat conductive substrate for different sizes of the droplet (down to submicron sizes).
Abstract: The aim of the current numerical study is to investigate the influence of individual effects (kinetic effects, latent heat of vaporization, Marangoni convection, Stefan flow, droplet’s surface curvature) on the rate of evaporation of a water droplet placed on a highly heat conductive substrate for different sizes of the droplet (down to submicron sizes). We performed simulations for one particular set of parameters: the ambient relative air humidity is set to 70%, the ambient temperature is 20 ∘C, the contact angle is 90∘, and the substrate material is copper. The Suggested model combines both diffusive and kinetic models of evaporation. The obtained results allow estimation of the characteristic droplet sizes where each of the mentioned above phenomena becomes important or can be neglected.
TL;DR: In this article, the authors used the Volume of Fluid (VOF) method to track the liquid/gas interface in 2D and 3D domains and found that the inherent velocity of bubbles decreases with an increase of the Marangoni number, a result that is in line with the results of previous space experiments.