Buoyancy-driven convection around chemical fronts traveling in covered horizontal solution layers

Density differences across an autocatalytic chemical front traveling horizontally in covered thin layers of solution trigger hydrodynamic flows which can alter the concentration profile. We theoretically investigate the spatiotemporal evolution and asymptotic dynamics resulting from such an interplay between isothermal chemical reactions, diffusion, and buoyancy-driven convection. The studied model couples the reaction-diffusion-convection evolution equation for the concentration of an autocatalytic species to the incompressible Stokes equations ruling the evolution of the flow velocity in a two-dimensional geometry. The dimensionless parameter of the problem is a solutal Rayleigh number constructed upon the characteristic reaction-diffusion length scale. We show numerically that the asymptotic dynamics is one steady vortex surrounding, deforming, and accelerating the chemical front. This chemohydrodynamic structure propagating at a constant speed is quite different from the one obtained in the case of a pure hydrodynamic flow resulting from the contact between two solutions of different density or from the pure reaction-diffusion planar traveling front. The dynamics is symmetric with regard to the middle of the layer thickness for positive and negative Rayleigh numbers corresponding to products, respectively, lighter or heavier than the reactants. A parametric study shows that the intensity of the flow, the propagation speed, and the deformation of the front are increasing functions of the Rayleigh number and of the layer thickness. In particular, the asymptotic mixing length and reaction-diffusion-convection speed both scale as square root Ra for Ra>5. The velocity and concentration fields in the asymptotic dynamics are also found to exhibit self-similar properties with Ra. A comparison of the dynamics in the case of a monostable versus bistable kinetics is provided. Good agreement is obtained with experimental data on the speed of iodate-arsenous acid fronts propagating in horizontal capillaries. We furthermore compare the buoyancy-driven dynamics studied here to Marangoni-driven deformation of traveling chemical fronts in solution open to the air in the absence of gravity previously studied in the same geometry [L. Rongy and A. De Wit, J. Chem. Phys. 124, 164705 (2006)].     

Flow development at the surfaces of bubbles and droplets in gradient solutions of a surfase-active liquid

The development of solutocapillary flows at the surfaces of air bubbles and chlorobenzene droplets was experimentally studied in nonuniform aqueous solutions of ethanol and isopropanol, which have a low surface tension and, hence, exhibit surface-active properties with respect to water. The experiments demonstrated the retardation of the onset of the development of the Marangoni concentration-induced convection relative to the moment of the contact between an inflowing surfactant (alcohol) and the surface. The critical concentration gradients (the Marangoni diffusion numbers) necessary for the initiation of mass transfer of a liquid along the interface were determined as dependent on the rate of inflow of a tongue of a more concentrated solution and the initial alcohol concentration around the bubble.     

Surfactant-Influenced Gas-Liquid Interfaces: Nonlinear Equation of State and Finite Surface Viscosities

A canonical flow geometry was utilized for a fundamental study of the coupling between bulk flow and a Newtonian gas-liquid interface in the presence of an insoluble surfactant. We develop a Navier-Stokes numerical model of the flow in the deep-channel surface viscometer geometry, which consists of stationary inner and outer cylinders, a floor rotating at a constant angular velocity, and an interface covered initially by a uniformly distributed surfactant. Here, the floor of the annular channel is rotated fast enough so the flow is nonlinear and drives the film toward the inner cylinder. The boundary conditions at the interface are functions of the surface tension, surface shear viscosity, and surface dilatational viscosity, as described by the Boussinesq-Scriven surface model. A physical surfactant system, namely hemicyanine, an insoluble monolayer on an air-water interface, with measured values of surface tension and surface shear viscosity versus concentration, was used in this study. We find that a surfactant front can form, depending on the Reynolds number and the initial surfactant concentration. The stress balance in the radial direction was found to be dominated by the Marangoni stress, but the azimuthal stress was only due to the surface shear viscosity. Numerical studies are presented comparing results of surfactant-influenced interface cases implementing the derived viscoelastic interfacial stress balance with those using a number of idealized stress balances, as well as a rigid no-slip surface, providing added insight into the altered dynamics that result from the presence of a surfactant monolayer. Copyright 2000 Academic Press.     

Superspreading driven by Marangoni flow

The spontaneous spreading (called superspreading) of aqueous trisiloxane ethoxylate surfactant solutions on hydrophobic solid surfaces is a fascinating phenomenon with several practical applications. For example, the ability of trisiloxane ethoxylate surfactants to enhance the spreading of spray solutions on waxy weed leaf surfaces, such as velvetleaf (Abutilion theophrasti), makes them excellent wetting agents for herbicide applications. The superspreading ability of silicone surfactants has been known for decades, but its mechanism is still not well understood. In this paper, we suggest that the spreading of trisiloxane ethoxylates is controlled by a surface tension gradient, which forms when a drop of surfactant solution is placed on a solid surface. The proposed model suggests that, as the spreading front stretches, the surface tension increases (the surfactant concentration becomes lower) at the front relative to the top of the droplet, thereby establishing a dynamic surface tension gradient. The driving force for spreading is due to the Marangoni effect, and our experiments showed that the higher the gradient, the faster the spreading. A simple model describing the phenomenon of superspreading is presented. We also suggest that the superspreading behavior of trisiloxane ethoxylates is a consequence of the molecular configuration at the air/water surface (i.e. small and compact hydrophobic part), as shown by molecular dynamics modeling. We also found that the aggregates and vesicles formed in trisiloxane solutions do not initiate the spreading process and therefore these structures are not a requirement for the superspreading process.     

Interfacial forces and Marangoni flow on a nematic drop retracting in an isotropic fluid

Nematic-isotropic interfaces exhibit novel dynamics due to anchoring of the liquid crystal molecules on the interface. The objective of this study is to demonstrate the consequences of such dynamics in the flow field created by an elongated nematic drop retracting in an isotropic matrix. This is accomplished by two-dimensional flow simulations using a diffuse-interface model. By exploring the coupling among bulk liquid crystal orientation, surface anchoring and the flow field, we show that the anchoring energy plays a fundamental role in the interfacial dynamics of nematic liquids. In particular, it gives rise to a dynamic interfacial tension that depends on the bulk orientation. Tangential gradient of the interfacial tension drives a Marangoni flow near the nematic-isotropic interface. Besides, the anchoring energy produces an additional normal force on the interface that, together with the interfacial tension, determines the movement of the interface. Consequently, a nematic drop with planar anchoring retracts more slowly than a Newtonian drop, while one with homeotropic anchoring retracts faster than a Newtonian drop. The numerical results are consistent with prior theories for interfacial rheology and experimental observations.     

Marangoni flow of Ag nanoparticles from the fluid-fluid interface

Fluid flow is observed when a volume of passivated Ag nanoparticles suspended in chloroform is mixed with a water/ethanol (v/v) mixture containing acidified 11-mercaptoundecanoic acid. Following mechanical agitation, Ag nanoparticles embedded in a film are driven from the organic-aqueous interface. A reddish-brown colored film, verified by transmission electron microscopy to contain uniformly dispersed Ag nanoparticles, is observed to spontaneously climb the interior surface of an ordinary, laboratory glass vial. This phenomenon is recorded by a digital video recorder, and a measurement of the distance traveled by the film front versus time is extracted. Surface (interfacial) tension gradients due to surfactant concentration, temperature, and electrostatic potential across immiscible fluids are known to drive interface motion; this well-known phenomenon is termed Marangoni flow or the Marangoni effect. Experimental results are presented that show the observed mass transfer is dependent on an acid surfactant concentration and on the volume fraction of water in the aqueous phase, consistent with fluid flow induced by interfacial tension gradients. In addition, an effective desorption rate constant for the Marangoni flow is measured in the range of approximately 0.01 to approximately 1 s(-1) from a fit to the relative film front distance traveled versus time data. The fit is based on a time-dependent expression for the surface (interface) excess for desorption kinetics. Such flow suggests that purposeful creation of interfacial tension gradients may aid in the transfer of 2- and 3-dimensional assemblies, made with nanostructures at the liquid-liquid interface, to solid surfaces.     

Measurement of flow visualized on surface of bubble blown in air

Bubbles blown in surfactant (frother) solution reveal surface flows attributed to gravity drainage and opposing Marangoni Effect. A technique is introduced to visualize the flows and estimate trajectory velocity. The flow pattern and velocity depend on frother type (pentanol vs. a polyglycol) and concentration but no correlation with surface tension was found. The relevance of the observations to the action of frother in flotation is briefly discussed.     

Thermal Marangoni Convection of a Fluid Film Coating a Deformable Membrane

The thermal Marangoni instability of a fluid film coating a deformable membrane has been investigated by taking into account the deformation of the fluid free surface. Numerical calculations for different thermal boundary conditions are presented. The prestressed membrane is supposed to be very thin and therefore its behavior is similar to that of an isothermal fluid free surface with a surface tension but with a different mechanical boundary condition; that is, the fluid should stick on its surface and thus the fluid velocity is zero. An important assumption is that the membrane has no temperature dependence and therefore that only one Marangoni number exists for the free surface of the fluid. Numerical results are presented for stationary and oscillatory thermocapillary instability in both the sinuous and the varicose modes. It is shown that membrane deformation has important implications on the Marangoni instability of the fluid layer for positive and negative Marangoni numbers. Copyright 2001 Academic Press.     

Plane hydrodynamic flow in thin free suspended nematic liquid crystal films

Abstract

Radial hydrodynamic flows in free suspended films (with thickness h ≥ 20 μm) of some liquid crystal materials was observed in a narrow temperature range before the line nematic-smectic C transition. The observed flows are explained by a non-linear temperature dependence of the surface tension (Marangoni effect).

Upon thinning the liquid crystal films to a thickness 6 μ < h < 20 μm the hydrodynamic flow changes its character: instead of radial flow with sinking seeding particles we observe two circular plane hydrodynamic flows symmetrical to the film's diameter. The temperature distribution in the free film and the surface tension field are discussed. A model for the established circular flows in thin liquid crystal films is presented.     

Directional and path-finding motion of polymer hydrogels driven by liquid mixing

The spreading of a miscible liquid with a low surface tension on a water surface generates the directional motion of submerged polymer hydrogels, which could be attributed to convective flows resulting from the gradient of surface tension along the surface (Marangoni effect). The direction and velocity of this motion can be well controlled by altering the driving conditions. Furthermore, a spherical hydrogel can smartly find the path to walk through a microfluidic maze when liquid mixing occurs near the maze exit. This convenient chemical driving approach to transporting submerged objects in a desired way may be useful in microfluidics, micromechanics, and other applications.     

Droplet behavior on flat and textured surfaces: co-occurrence of Deegan outward flow with Marangoni solute instability

It is demonstrated experimentally that the solution droplet behavior is governed by the co-occurrence of outward hydrodynamic and surface tension (solute Marangoni) induced flows. Potassium ferrocyanide allows the effective visualization of the processes taking place in the droplet. Wetting properties of the substrate govern the shape evolution of the evaporated droplet. Quantitative estimation of the wetting properties of textured polymer surface is presented.     

Molecular dynamics simulation of nanodroplet spreading enhanced by linear surfactants

We utilize molecular dynamics simulations to probe the surfactant-mediated spreading of a Lennard-Jones liquid droplet on a solid surface. The surfactants are linear hexamers that are insoluble in the liquid and reduce the surface tension of the liquid-vapor interface. We study how the interaction of the surfactant hexamers with the solid substrate influences spreading, as well as the dependence of spreading on surfactant concentration. We find that the spreading speed is strongly influenced by the attraction of the hydrophobic surfactant tail to the solid surface. When this attraction is sufficiently strong, surfactant molecules partition to the liquid-solid interface and facilitate spreading. This partitioning can lead to an inhomogeneous distribution of surfactant over the liquid-vapor interface, which could drive the Marangoni convection. We also observe that the surfactant molecules can assemble into micelles on the solid surface. The repulsion between micelles at the liquid-solid interface can lead to break-off and migration of the micelles from the liquid-solid to the gas-solid interface and spreading is facilitated in this way. Our model system contains features that are believed to underlie superspreading in experimental studies of droplet spreading.     

Spontaneous oscillations due to solutal Marangoni instability: air/water interface

Systems far from equilibrium are able to self-organize and often demonstrate the formation of a large variety of dissipative structures. In systems with free liquid interfaces, self-organization is frequently associated with Marangoni instability. The development of solutal Marangoni instability can have specific features depending on the properties of adsorbed surfactant monolayer. Here we discuss a general approach to describe solutal Marangoni instability and review in details the recent experimental and theoretical results for a system where the specific properties of adsorbed layers are crucial for the observed dynamic regimes. In this system, Marangoni instability is a result of surfactant transfer from a small droplet located in the bulk of water to air/water interface. Various dynamic regimes, such as quasi-steady convection with a monotonous decrease of surface tension, spontaneous oscillations of surface tension, or their combination, are predicted by numerical simulations and observed experimentally. The particular dynamic regime and oscillation characteristics depend on the surfactant properties and the system aspect ratio.      

Marangoni effects on evaporative lithographic patterning of colloidal films

We investigate the effects of Marangoni stresses on the evaporative lithographic patterning of colloidal films (Harris, D. J.; Hu, H.; Conrad, J. C.; Lewis, J. A. Phys. Rev. Lett. 2007, 98 (14), 148301). Films are dried beneath a mask that induces periodically varying regions of free and hindered evaporation. Direct imaging reveals that silica microspheres suspended within an organic solvent exhibit recirculating flows induced by temperature and surface tension gradients that arise during drying. The films display remarkable pattern formation with a majority of the particles deposited in the masked regions. Above a critical colloid volume fraction, recirculating flows are suppressed, leading to particle deposition in unmasked regions of high evaporative flux.     

Immiscible surfactant droplets on thin liquid films: spreading dynamics, subphase expulsion and oscillatory instabilities

After deposition of immiscible, surface-active liquids on thin liquid films of higher surface tension, Marangoni stresses thin the liquid film around the surfactant droplet and induce a radially outward flow. We observed an oscillatory instability, caused by temporary trapping and subsequent release of subphase liquid from underneath the surfactant droplet. Height profiles of the thin liquid films were monitored using optical interferometry and fluorescence microscopy, both in the vicinity of the deposited surfactant droplet and at larger distances. Numerical calculations based on the lubrication approximation are compared to the experimental results. Good agreement between the experimental and calculated far-field dynamics and values of the spreading exponents was found.     

Orientation‐Induced Adsorption of Hydrated Protons at the Air–Water Interface

The surface tension of the air—water interface increases upon addition of inorganic salts, implying a negative surface excess of ionic species. Most acids, however, induce a decrease in surface tension, indicating a positive surface excess of hydrated protons. In combination with the apparent negative charge at pure air–water interfaces derived from electrokinetic experiments, this experimental observation has been a source of intense debate since the mid‐19th century. Herein, we calculate surface tensions and ionic surface propensities at air–water interfaces from classical, thermodynamically consistent molecular dynamics simulations. The surface tensions of NaOH, HCl, and NaCl solutions show outstanding quantitative agreement with experiment. Of the studied ions, only H₃O⁺ adsorbs to the air–water interface. The adsorption is explained by the deep potential well caused by the orientation of the H₃O⁺ dipole in the interfacial electric field, which is confirmed by ab initio simulations.     

Viscoelastic theory for nematic polymer interfaces

A macroscopic theory for the dynamics of compressible nematic polymer‐viscous fluid interfaces is developed from first principles. The theory is used to define and characterize the basic interfacial viscoelastic material properties of the ordered interfaces. The theory is based on a decomposition of the kinematic fields and nematic tensor order parameter that takes into account the symmetry breaking of the interface. The interfacial rate of entropy production used to identify the interfacial viscoelastic modes is given in terms of surface rate of deformation tensor and the surface Jaumann derivative of the tangential component nematic tensor order parameter. The derived surface viscous stress tensor is asymmetric and thus describes surface flow‐induced changes in the tensor order parameter. Consistency with the Boussinesq surface fluid appropriate for Newtonian interfaces is established. The interfacial material functions are identified as the dynamic surface tension, the interfacial dilational viscosities, and the interfacial shear viscosities. The interfacial material functions depend on the surface tensor order parameter and as a consequence anisotropy is their characteristic feature. Two characteristic interfacial tensions and two dilational viscosities are predicted depending on the director orientation. In addition six interfacial shear viscosities arise as the directors sample the velocity, velocity gradient, and vorticity directions. Finally the theory provides for the necessary theoretical tools needed to describe the interfacial dynamics of nematic polymer interfaces, such as capillary instabilities, Marangoni flows, and wetting phenomena.     

Spreading of Oil Droplets Containing Surfactants and Pesticides on Water Surface Based on the Marangoni Effect

Oil droplets containing surfactants and pesticides are expected to spread on a water surface, under the Marangoni effect, depending on the surfactant. Pesticides are transported into water through this phenomenon. A high-speed video camera was used to measure the movement of Marangoni ridges. Gas chromatography with an electron capture detector was used to analyze the concentration of the pesticide in water at different times. Oil droplets containing the surfactant and pesticide spread quickly on the water surface by Marangoni flow, forming an oil film and promoting emulsification of the oil–water interface, which enabled even transport of the pesticide into water, where it was then absorbed by weeds. Surfactants can decrease the surface tension of the water subphase after deposition, thereby enhancing the Marangoni effect in pesticide-containing oil droplets. The time and labor required for applying pesticides in rice fields can be greatly reduced by using the Marangoni effect to transport pesticides to the target.     

Propensity for the air/water interface and ion pairing in magnesium acetate vs magnesium nitrate solutions: molecular dynamics simulations and surface tension measurements

Molecular dynamics simulations in slab geometry and surface tension measurements were performed for aqueous solutions of magnesium acetate and magnesium nitrate at various concentrations. The simulations reveal a strong affinity of acetate anions for the surface, while nitrate exhibits only a very weak surface propensity, and magnesium is per se strongly repelled from the air/water interface. CH3COO- also exhibits a much stronger tendency than NO3- for ion pairing with Mg2+ in the bulk and particularly in the interfacial layer. The different interfacial behavior of the two anions is reflected by the opposite concentration dependence (beyond 0.5 M) of surface tension of the corresponding magnesium salts. Measurements, supported by simulations, show that the surface tension of Mg(NO3)2(aq) increases with concentration as for other inorganic salts. However, in the case of Mg(OAc)2(aq) the surface tension isotherm exhibits a turnover around 0.5 M, after which it starts to decrease, indicating a positive net solute excess in the interfacial layer at higher concentrations.     

A Hydrolyzable Supra-amphiphile as a Marangoni Self-Propulsion Fuel for Efficient Macroscopic Supramolecular Self-Assembly

Self-assembly of μm-to-mm components is important for achieving all-scale ordering with requirements of extra energy for motion and interaction of components. Marangoni flows caused by surfactants on water provide appropriate energy but have limited lifetimes because of the inevitable interfacial aggregation and difficult decomposition of aggregated covalent surfactants that inactivate Marangoni effects. Here we have synthesized a supra-amphiphile Marangoni “fuel”—sodium-4-(benzylideneamino) benzenesulfonate (SBBS)—that can be hydrolyzed in a timely manner to a species without surface activity to extend the motion time by 10-fold. The motion was optimized at pH=2 by a fine equilibrium between the releasing and removal of interfacial SBBS, leading to the self-assembly of millimeter-scaled ordered dimers. The underlying mechanism was interpreted by motion analyses and simulation. This strategy provides an active solution to self-assembly at the μm-to-mm scale, as well as interactive ideas between miniaturized chemical robots.