Showing papers on "Marangoni effect published in 2012"

Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications

Abstract: This article presents a comprehensive review of numerical methods and models for interface resolving simulations of multiphase flows in microfluidics and micro process engineering. The focus of the paper is on continuum methods where it covers the three common approaches in the sharp interface limit, namely the volume-of-fluid method with interface reconstruction, the level set method and the front tracking method, as well as methods with finite interface thickness such as color-function based methods and the phase-field method. Variants of the mesoscopic lattice Boltzmann method for two-fluid flows are also discussed, as well as various hybrid approaches. The mathematical foundation of each method is given and its specific advantages and limitations are highlighted. For continuum methods, the coupling of the interface evolution equation with the single-field Navier–Stokes equations and related issues are discussed. Methods and models for surface tension forces, contact lines, heat and mass transfer and phase change are presented. In the second part of this article applications of the methods in microfluidics and micro process engineering are reviewed, including flow hydrodynamics (separated and segmented flow, bubble and drop formation, breakup and coalescence), heat and mass transfer (with and without chemical reactions), mixing and dispersion, Marangoni flows and surfactants, and boiling.

Surfactant-Induced Marangoni Eddies Alter the Coffee-Rings of Evaporating Colloidal Drops

Abstract: The influence of the small ionic surfactant sodium dodecyl sulfate (SDS) on the evaporation of drying colloidal droplets is quantitatively investigated. The addition of SDS leads to a significantly more uniform deposition of colloidal particles after evaporation (i.e., the so-called “coffee-ring effect” is dramatically altered). We understand this phenomenon in the context of circulating radial Marangoni flows induced by the variation of SDS concentration along the air–water interface. Video microscopy permits the direct visualization of the colloidal particles involved in these flows, revealing a surprisingly stable “Marangoni eddy” that prevents particle deposition at the drop perimeter.

Overcoming the "coffee-stain" effect by compositional Marangoni-flow-assisted drop-drying.

Abstract: Attempts at depositing uniform films of nanoparticles by drop-drying have been frustrated by the "coffee-stain" effect due to convective macroscopic flow into the contact line. Here, we show that uniform deposition of nanoparticles in aqueous suspensions can be attained easily by drying the droplet in an ethanol vapor atmosphere. This technique allows the particle-laden water droplets to spread on a variety of surfaces such as glass, silicon, mica, PDMS, and even Teflon. Visualization of droplet shape and internal flow shows initial droplet spreading and strong recirculating flow during spreading and shrinkage. The initial spreading is due to a diminishing contact angle from the absorption of ethanol from the vapor at the contact line. During the drying phase, the vapor is saturated in ethanol, leading to preferential evaporation of water at the contact line. This generates a surface tension gradient that drives a strong recirculating flow and homogenizes the nanoparticle concentration. We show that this method can be used for depositing catalyst nanoparticles for the growth of single-walled carbon nanotubes as well as to manufacture plasmonic films of well-spaced, unaggregated gold nanoparticles.

Suppression of the coffee ring effect by hydrosoluble polymer additives.

Abstract: A simple and novel method has been demonstrated for avoiding coffee ring structure based on hydrosoluble polymer additives during droplet evaporation. The polymer additives lead to the motion of the contact line (CL) resulted from the viscosity and Marangoni effect. The viscosity provides a large resistance to the radially outward flow. It results in a small amount of spheres deposited at droplet edge, which do not facilitate the pinning of the CL. The Marangoni effect resulted from the variation of polymer concentration at droplet edge during droplet evaporation contributes to the motion of the CL. Thus, uniform and ordered macroscale SiO2 microspheres deposition is achieved. What’s more, the coffee ring effect can be eliminated by different hydrosoluble polymer. This method will be applicable to a wide of aqueous system and will be of great significance for extensive applications of droplet deposition in biochemical assays and material deposition.

Viscous Marangoni propulsion

Abstract: Marangoni propulsion is a form of locomotion wherein an asymmetric release of surfactant by a body located at the surface of a liquid leads to its directed motion. We present in this paper a mathematical model for Marangoni propulsion in the viscous regime. We consider the case of a thin rigid circular disk placed at the surface of a viscous fluid and whose perimeter has a prescribed concentration of an insoluble surfactant, to which the rest of its surface is impenetrable. Assuming a linearized equation of state between surface tension and surfactant concentration, we derive analytically the surfactant, velocity and pressure fields in the asymptotic limit of low capillary, Peclet and Reynolds numbers. We then exploit these results to calculate the Marangoni propulsion speed of the disk. Neglecting the stress contribution from Marangoni flows is seen to over-predict the propulsion speed by 50 %.

Viscous Marangoni propulsion

Abstract: Marangoni propulsion is a form of locomotion wherein an asymmetric release of surfactant by a body located at the surface of a liquid leads to its directed motion. We present in this paper a mathematical model for Marangoni propulsion in the viscous regime. We consider the case of a thin rigid circular disk placed at the surface of a viscous fluid and whose perimeter has a prescribed concentration of an insoluble surfactant, to which the rest of its surface is impenetrable. Assuming a linearized equation of state between surface tension and surfactant concentration, we derive analytically the surfactant, velocity and pressure fields in the asymptotic limit of low Capillary, Peclet and Reynolds numbers. We then exploit these results to calculate the Marangoni propulsion speed of the disk. Neglecting the stress contribution from Marangoni flows is seen to over-predict the propulsion speed by 50%.

Vapour-driven Marangoni propulsion: continuous, prolonged and tunable motion

Abstract: We show the vapour-driven Marangoni effect as a new paradigm for the continuous self-propulsion of floating soft machines by transduction of chemical energy to motility, featuring a prolonged locomotion at steady velocity with a small amount of on-board fuel. The propulsion is induced by modification of the liquid surface using organic vapour transported through a nanocellulose aerogel membrane. The steady velocity is achieved through a continuous supply of fuel vapour that lowers the surface tension of the liquid, combined with the spontaneous recovery of the surface tension after the floating machine has passed. The membranes are gas permeable from their open-porous nanofibrillar structure and float on water and oils due to their superhydrophobic and superoleophobic nature. The velocity is tunable by selecting solvents with different vapour pressure.

Swimming active droplet: A theoretical analysis

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.

Drift instability in the motion of a fluid droplet with a chemically reactive surface driven by Marangoni flow.

Abstract: We theoretically derive the amplitude equations for a self-propelled droplet driven by Marangoni flow. As advective flow driven by surface tension gradient is enhanced, the stationary state becomes unstable and the droplet starts to move. The velocity of the droplet is determined from a cubic nonlinear term in the amplitude equations. The obtained critical point and the characteristic velocity are well supported by numerical simulations.

Noncoalescence of sessile drops from different but miscible liquids: hydrodynamic analysis of the twin drop contour as a self-stabilizing traveling wave.

Abstract: Capillarity always favors drop fusion. Nevertheless, sessile drops from different but completely miscible liquids often do not fuse instantaneously upon contact. Rather, intermediate noncoalescence is observed. Two separate drop bodies, connected by a thin liquid neck, move over the substrate. Supported by new experimental data, a thin film hydrodynamic analysis of this state is presented. Presumably advective and diffusive volume fluxes in the neck region establish a localized and temporarily stable surface tension gradient. This induces a local surface (Marangoni) flow that stabilizes a traveling wave, i.e., the observed moving twin drop configuration. The theoretical predictions are in excellent agreement with the experimental findings.

Landau-Levich flow visualization: Revealing the flow topology responsible for the film thickening phenomena

Abstract: An extensive body of experimental work has proven the validity of the analysis of Landau and Levich, who were the first to determine theoretically the thickness of the film deposited by the withdrawal of a flat substrate from a bath of liquid with a clean interface. However, there are a number of experimental investigations that have shown that surfactants in the liquid may result in a thickening of the deposited film. Marangoni phenomena have usually been considered responsible for this effect. However, some careful experiments and numerical simulations reported in the literature seemed to rule out this view as the cause of the observed behavior. Despite all these studies and the number of reports of film thickening, an experimental study of the flow field close to the coated substrate in the presence of surfactants has never been undertaken. In this paper we will present a set of flow visualization experiments on coating of a planar substrate in the range of capillary numbers 10−4 ≲ Ca ≲ 10−3 for sodium dodecyl sulfate solutions with bulk concentrations of 0.25 CMC ⩽ C ⩽ 5.0 CMC (critical micelle concentration). It was evident during experiments that the flow field near the meniscus region exhibits patterns that can only be explained with a stagnation point residing in the bulk and not at the interface. As opposed to patterns with an interfacial stagnation point, the observed flow fields allow for the increase in film thickness due to the presence of surfactants compared to the clean interface case.

Gel-based self-propelling particles get programmed to dance.

Abstract: We present a class of gel-based self-propelling particles moving by the Marangoni effect in an oscillatory mode. The particles are made of an ethanol-infused polyacrylamide hydrogel contained in plastic tubing. These gel boats floating on the water surface exhibit periodic propulsion for several hours. The release of ethanol from the hydrogel takes place beneath the liquid surface. The released ethanol rises to the air–water interface by buoyancy and generates a self-sustained cycle of surface tension gradient driven motion. The disruption of the ethanol flux to the surface by the bulk flows around the moving particle results in their pulsating motion. The pulse interval and the distance propelled in a pulse by these gel floaters were measured and approximated by simple expressions based on the rate of ethanol mass-transfer through and out of the hydrogel. This allowed us to design a multitude of particles performing periodic steps in different directions or at different angles of rotation, traveling in c...

Self-propelled motion of a fluid droplet under chemical reaction.

Abstract: We study self-propelled dynamics of a droplet due to a Marangoni effect and chemical reactions in a binary fluid with a dilute third component of chemical product which affects the interfacial energy of a droplet. The equation for the migration velocity of the center of mass of a droplet is derived in the limit of an infinitesimally thin interface. We found that there is a bifurcation from a motionless state to a propagating state of droplet by changing the strength of the Marangoni effect.

Evolution of surface topography in one-dimensional laser machining of structural alumina

Abstract: High energy lasers are an emerging industrial tool to fabricate complex shapes on hard and brittle structural ceramics such as alumina. The selection of laser processing parameters and the prediction of material removal rates during the laser machining are the critical issues. This paper was attempted to present the state of the art of laser machining of alumina using an integrated experimental and computational approach. A multistep computational model based on COMSOL™ Multiphysics was developed to study the influence of various single-pulse laser energy densities and associated physical phenomena (recoil pressure, Marangoni convection, and surface tension) on the temperature history, fluid velocity, crater size, and surface topography. A pulsed Nd:YAG laser was employed to machine alumina under different processing conditions. The surface topography of laser machined alumina was measured by an optical profilometer and the results were compared with the computationally predicted topographic parameters with reasonably close agreement.

Marangoni driven free surface flows in liquid weld pools

Abstract: Extending the weldability of novel materials, and improving the weld quality by tailoring weld microstructures are key factors to obtain the welding techniques demanded in the modern manufacturing industries. This can be done, for example, by feeding chemical elements from a consumable wire into the weld pool during welding. The mixing of chemical components in the weld pool and the resulting post-solidification weld microstructures are influenced by weld pool hydrodynamics. Weld pool hydrodynamics is known to be primarily driven by Marangoni forces acting at the free liquid surface, i.e by tangential gradients in surface tension along the liquid surface due to pronounced lateral gradients in temperature and surface active element concentration. In this research, we develop a Computational Fluid Dynamics model to study steel weld pool hydrodynamics during conduction mode laser spot welding. It is concluded that free surface deformations and instabilities have a strong impact on the fluid flow and heat transfer in weld pools, and should therefore be accounted for in weld pool simulations. With increasing the surface active element concentration and laser power, the weld pool flow becomes highly unstable and can no longer be accurately modeled with a flat surface assumption. More accurate predictions of weld pool physics can be made if the free surface, solidification stage, and three-dimensionality are taken into account. This reduces the need for the use of unphysical parameter fittings widely reported in literature.

Patterning by Photochemically Directing the Marangoni Effect

Abstract: Polystyrene (PS) that has been exposed to ultraviolet light (UV) undergoes partial dehydrogenation of the alkane polymer backbone which increases its surface energy. Exploiting this photochemistry, we exposed polystyrene films to UV light using a photomask to induce a patterned photochemical reaction producing regions in the film with differing surface energy. Upon heating the solid polymer film with the preprogrammed surface energy pattern to a liquid state, the polymer flows from the low surface energy unexposed regions to high surface energy exposed regions. This flow creates three-dimensional topography by the Marangoni Effect, which describes convective mass transfer due to surface energy gradients. The topographical features can be permanently preserved by quenching the film below its glass to liquid transition temperature. Their shape and organization are only limited by the pattern on the photomask.

TIG and A-TIG welding experimental investigations and comparison to simulation: Part 1: Identification of Marangoni effect

Abstract: In the present work, the chemical mechanism was shown for tungsten inert gas (TIG) and active TIG (A-TIG) welding. The results obtained with a two-dimensional axial symmetric model developed to simulate the flow behaviour in the meting pool on a stainless steel disc (304L) melted by a stationary heat source were presented to show the influence of Marangoni convection combined with Lorentz forces. This study shows the influence of the addition of an activating flux on the geometric characteristics of the weld beads in A-TIG welding.

Nanometer-scale flow of molten polyethylene from a heated atomic force microscope tip

Abstract: We investigate the nanometer-scale flow of molten polyethylene from a heated atomic force microscope (AFM) cantilever tip during thermal dip-pen nanolithography (tDPN). Polymer nanostructures were written for cantilever tip temperatures and substrate temperatures controlled over the range 100–260 °C and while the tip was either moving with speed 0.5–2.0 µm s−1 or stationary and heated for 0.1–100 s. We find that polymer flow depends on surface capillary forces and not on shear between tip and substrate. The polymer mass flow rate is sensitive to the temperature-dependent polymer viscosity. The polymer flow is governed by thermal Marangoni forces and non-equilibrium wetting dynamics caused by a solidification front within the feature.

Marangoni convection of power law fluids driven by power-law temperature gradient

Abstract: This paper presents a research for Marangoni convection driven by a power-law temperature gradient. It is assumed that the surface tension is quadratic functions of the temperature and the effects of power law viscosity on temperature field into account by assuming that the temperature field is similar to the velocity field. The Navier–Stokes equations and the heat equation with modified Fourier's law heat conduction (Zheng's Model) for power law fluid media are reduced to two nonlinear ordinary differential equations and the solutions are presented numerically. The effects of the Power-law Number and the Marangoni Number on the interfacial velocity and the interfacial temperature gradient are presented in tabular form and the effects of various parameters on the velocity and temperature fields are analyzed and discussed in detail.

Segmented waves in a reaction-diffusion-convection system

Abstract: The interaction of traveling waves, with both Marangoni and buoyancy driven flows, can generate an extraordinary rich array of patterns ranging from stationary structures to chaotic waves. However, the inherent complexity of reaction-diffusion-convection (RDC) systems makes the explanation of the patterning mechanisms very difficult, both numerically and experimentally. In this paper, we describe the appearance of segmented waves in a shallow layer of an excitable Belousov-Zhabotinsky solution. The segmentation process was found to be dependent both on the depth of the solution and on the excitability of the reaction. We caught the essential features of the system through a RDC model, where the chemical waves were coupled both with surface and bulk fluid motions and we found that by varying the excitability of the reaction, and in turn the wavelength of the chemical fronts, it is possible to create a sort of hydrodynamic resonance structures (corridors), which are responsible for the segmentation process.

Investigation on the phase separation in undercooled Cu–Fe melts

Abstract: On the basis of the gravity difference and the temperature dependence of the interfacial energy of the separated phases, the amalgamation of the droplets of minor phase was affected by Stokes sedimentation and Marangoni motion during the liquid-phase separation. Moreover, the velocity of Stokes motion increased distinctly with the undercooling, while the velocity of Marangoni motion was slightly impacted. At the beginning of the liquid-phase separation, the droplets of minor phase were dominated by Marangoni motion when the droplets radius was small. As the droplets radius increased by combination, the effect of Stokes sedimentation strengthened gradually. Additionally, the coagulation process was mainly controlled by Stokes sedimentation when a critical radius rd was far exceeded.

Long-wave Marangoni convection in a thin film heated from below.

Abstract: We consider long-wave Marangoni convection in a liquid layer atop a substrate of low thermal conductivity, heated from below.We demonstrate that the critical perturbations are materialized at the wave number K ∼ √Bi, where Bi is the Biot number which characterizes the weak heat flux from the free surface. In addition to the conventional monotonic mode, a novel oscillatory mode is found. Applying the K ∼ √Bi scaling, we derivea new set of amplitude equations. Pattern selection on square and hexagonal lattices shows that supercritical branching is possible. A large variety of stable patterns is found for both modes of instability. Finite-amplitude one-dimensional solutions of the set, corresponding to either steady or traveling rolls, are studied numerically; a complicated sequence of bifurcations is found in the former case. The emergence of an oscillatory mode in the case of heating from below and stable patterns with finite-amplitude surface deformation are shown in this system for the first time.