Solutal Marangoni Effect Research Articles

Marangoni Flow Induced Evaporation Enhancement on Binary Sessile Drops.

The evaporation processes of pure water, pure 1-butanol, and 5% 1-butanol aqueous solution drops on heated hydrophobic substrates are investigated to determine the effect of temperature on the drop evaporation behavior. The evolution of the parameters (contact angle, diameter, and volume) during evaporation measured using a drop shape analyzer and the infrared thermal mapping of the drop surface recorded by an infrared camera were used in investigating the evaporation process. The pure 1-butanol drop does not show any thermal instability at different substrate temperatures, while the convection cells created by the thermal Marangoni effect appear on the surface of the pure water drop from 50 °C. Because 1-butanol and water have different surface tensions, the infrared video of the 5% 1-butanol aqueous solution drop shows that the convection cells are generated by the solutal Marangoni effect at any substrate temperature. Furthermore, when the substrate temperature exceeds 50 °C, coexistence of the thermal and solutal Marangoni flows is observed. By analyzing the relation between the ratio of the evaporation rate of pure water and 1-butanol aqueous solution drops and the Marangoni number, a series of empirical equations for predicting the evaporation rates of pure water and 1-butanol aqueous solution drops at the initial time as well as the equations for the evaporation rate of 1-butanol aqueous solution drop before the depletion of alcohol are derived. The results of these equations correspond fairly well to the experimental data.

Influence of thermal and solutal Marangoni effects on free surface deformation in an open rectangular cavity

Steady thermo-solutocapillary convection in a rectangular cavity with deformable free surface under microgravity condition is numerically studied, where level set method is employed to capture the free surface deformation. Both the temperature and solute concentration gradients are applied horizontally. The computational results show that, as the thermal to solutal Marangoni number ratio varies between -10 and -1 (namely, -10 ≤ Rσ < -1), the flow field exists one anti-clockwise rotating convective cell driven by thermocapillary convection, and the free surface bulges out near the left end wall and bulges in near the right end wall. As -1 < Rσ < 0, the flow field exists one clockwise rotating convective cell driven by solutocapillary convection, and the free surface bulges out near the right end wall and bulges in near the left end wall. As Rσ = -1, the flow field consists of one clockwise and one anti-clockwise rotating convective cells, and the free surface bulges in at the central point and bulges out near the left and right end walls.

The eruptive regime of mass-transfer-driven Rayleigh–Marangoni convection

The transfer of an alcohol, 2-propanol, from an aqueous to an organic phase causes convection due to density differences (Rayleigh convection) and interfacial tension gradients (Marangoni convection). The coupling of the two types of convection leads to short-lived flow structures called eruptions, which were reported in several previous experimental studies. To unravel the mechanism underlying these patterns, three-dimensional direct numerical simulations and corresponding validation experiments were carried out and compared with each other. In the simulations, the Navier–Stokes–Boussinesq equations were solved with a plane interface that couples the two layers including solutal Marangoni effects. Our simulations show excellent agreement with the experimentally observed patterns. On this basis, the origin of the eruptions is explained by a two-step process in which Rayleigh convection continuously produces a concentration distribution that triggers an opposing Marangoni flow.

Numerical simulation of dip-coating in the evaporative regime.

A hydrodynamic model is used for numerical simulations of a polymer solution in a dip-coating-like experiment. We focus on the regime of small capillary numbers where the liquid flow is driven by evaporation, in contrast to the well-known Landau-Levich regime dominated by viscous forces. Lubrication approximation is used to describe the flow in the liquid phase. Evaporation in stagnant air is considered (diffusion-limited evaporation), which results in a coupling between liquid and gas phases. Self-patterning due to the solutal Marangoni effect is observed for some ranges of the control parameters. We first investigate the effect of evaporation rate on the deposit morphology. Then the role of the spatial variations in the evaporative flux on the wavelength and mean thickness of the dried deposit is ascertained, by comparing the 2D and 1D diffusion models for the gas phase. Finally, for the very low substrate velocities, we discuss the relative importance of diffusive and advective components of the polymer flux, and consequences on the choice of the boundary conditions.

Internal flow patterns of an evaporating multicomponent droplet on a flat surface

Evaporation processes of droplets with different ethanol/water compositions on a hydrophobic heated surface were investigated utilizing particle image velocimetry (PIV). It is found that the process of an evaporating two-component droplet can be divided into downward vortex stage, transition stage and upward vortex stage sequentially, while a pure water droplet only has upward vortices stage. The three stages were analyzed utilizing experimental results and dimensionless parameters, such as thermal Marangoni number (MaT) and Solutal Marangoni number (MaS). For downward vortex and transition stages, solutal and thermal Marangoni effects were dominating. The occurrence of transition stage indicated buoyancy effect becomes comparable to Marangoni effect as ethanol continuously evaporated, and the occurrence of upward vortex stage indicated most of ethanol gasified and buoyancy effect dominated. The influence of initial composition and heating power on the downward vortices and transition stages has also been investigated. With low input power, droplets with high ethanol concentration have shorter evaporation time in above two stages. On the contrary, however, droplets with high ethanol concentration have longer evaporation time in above two stages with high input power.

Formation and lateral migration of nanodroplets via solvent shifting in a microfluidic device

Solvent shifting is a process in which a non-solvent is added to a solvent/solute mixture and extracts the solvent. The solvent and the non-solvent are miscible. Because of solution supersaturation, a portion of the solute transforms to droplets. In this paper, based on this process, we present an investigation on droplet formation and their radial motion in a microfluidic device in which a jet is injected in a co-flowing liquid stream. Thanks to the laminar flow, the microfluidic setup enables studying diffusion mass transfer in radial direction and obtaining well-defined concentration distributions. Such profiles together with the ternary phase diagram give detailed information about the conditions for droplet formation as well as their radial migration in the channel. The ternary system is composed of ethanol (solvent), de-ionized water (non-solvent), and divinylbenzene (solute). We employ analytical/numerical solutions of the diffusion equation to obtain concentration profiles of the components. We show that in the system under study droplets are formed in a region of the phase diagram between the binodal and the spinodal, i.e., via a thermally activated process. The droplets are driven to the channel centerline by the solutal Marangoni effect but are not able to significantly penetrate into the single-phase region, where they get rapidly dissolved. Therefore, the radial motion of the binodal surface carries the droplets to the centerline where they get collected.

Incipient mixing by Marangoni effects in slow viscous flow of two immiscible fluid layers

Ignoring inertia, a deformable interface separating two fluid films is considered, subject to non-uniform tension driven by the solutal Marangoni effect in the presence of a scalar concentration field. Detailed description of adsorption kinetics is abrogated by a simple ansatz directly relating interfacial tension and bulk solute concentration. Consequently, the formal mathematical treatment and some of the results share features in common with the Rayleigh–Benard–Marangoni thermocapillary problem. Normal mode perturbation analysis in the limit of small interface deformations establishes the existence of an unstable response for low wavenumber excitation. In the classification of Cross & Hohenberg (1993, Pattern formation outside of equilibrium. Rev. Mod. Phys., 65, 851–1112), both type I and type II behaviour are observed. By considering the zero wavenumber situation exactly, it is proved that all eigenvalues are purely imaginary with non-positive imaginary part; hence, a type III instability is not possible. For characteristic timescales of mass diffusion much shorter than the relaxation time of interfacial fluctuations (infinite crispation number): the response growth rate is obtained explicitly; only a single excitation mode is available, and a complete stability diagram is constructed in terms of the relevant control parameters. Otherwise, from a quiescent base state, an infinite discrete spectrum of modes is observed that exhibit avoided crossing and switching phenomena, as well as exceptional points where stationary state pairs coalesce into a single oscillatory standing wave pattern. A base state plane Poiseuille flow, driven by an external pressure gradient, generally exaggerates the response: growth rates of instabilities are enhanced, and stable decay is further suppressed with increasing base flow speed, but the inherent symmetry breaking destroys stationary and standing wave response. Results are obtained in this most general situation by implementing a numerical Chebyshev collocation scheme. The model was motivated by hydrodynamic processes supposed to be involved in gastric digestion of humans.

Quasi-elastic laser scattering for measuring inhomogeneous interfacial tension in non-equilibrium phenomena with convective flows.

An inhomogeneous distribution of interfacial tension can induce different types of non-equilibrium spontaneous motion at the interface by convective flow, or by the solutal Marangoni effect. Several applications of the quasi-elastic laser scattering (QELS) method used to study these effects are presented here. The relationship between the interfacial tension and the non-equilibrium phenomena has been verified experimentally for each application. In a water/nitrobenzene oscillatory system with continuous surfactant addition to the interface, the local adsorption of surfactants at the interface has been demonstrated and shown to be strongly related to the presence of electrolytes. In a donor/membrane/acceptor system, the dual-beam QELS method shows that surfactant adsorption at the membrane/acceptor interface is responsible for oscillations in the electric potential. The differences in the adsorption/desorption behavior of metal complex catalysts between air/liquid and liquid/liquid interfaces were considered in the propagating chemical waves of the Belousov-Zhabotinsky reaction. We successfully measured the distribution of interfacial tension around a self-propelled camphor boat and an alcohol droplet floating on an aqueous phase, and compared the mechanisms of their motion.

Tear film dynamics with evaporation, osmolarity and surfactant transport

In this article we develop a model for the evaporation and rupture of the tear film. The tear film is generally considered a multi-layer structure which we simplify to a single layer in our modeling. We examine how well the floating lipid layer can be approximated by a mobile insoluble surfactant monolayer in the context of lubrication theory with film rupture “breakup” in the tear film literature. This model includes the effects of surface tension, insoluble surfactant monolayer transport, solutal Marangoni effects, evaporation, osmolarity transport, osmosis and wettability of corneal surface. Evaporation is hypothesized to be dependent on pressure, temperature and surface concentration at the surface of the film. A focus of this paper is to study the competition between the effect of increasing surfactant concentration to (1) slowing down evaporation and (2) lowering surface tension. The solutal Marangoni effect, for local increases in surfactant concentration, can induce local thinning and this effect always seems to dominate the reduction in thinning rate due to evaporation in our model. It also seems to eliminate any localized area of increased evaporation due to reduced surfactant concentration. Osmolarity in the tear film increases because water lost to the average evaporation rate and to a lesser extent by flow inside the film. The presence of van der Waals conjoining pressure is only significant when osmosis is very small or absent. The model predicts that the Marangoni effect coupled with evaporation can determine the location of first breakup; it also agrees with another model of breakup that predicts elevated osmolarity when breakup occurs.

Self-patterning induced by a solutal Marangoni effect in a receding drying meniscus

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.

Two-phase modeling of evaporation characteristics of blended methanol–ethanol droplets

The paper presents a two-phase numerical model to simulate transient vaporization of a spherical two-component liquid fuel droplet. The model considers variation of thermo-physical properties in both liquid- and vapor-phases, as functions of temperature and species concentrations. Multi-component diffusion and surface tension effects are also considered. The model has been validated using the experimental data available in literature. The validated model is used to study the vaporization characteristics of both suspended and moving methanol–ethanol blended droplets in an atmospheric pressure environment. Relative strengths of forced convection and Marangoni convection are studied and compared for both suspended and moving droplets. Results in terms of streamlines, isotherms and isopleths at different time instants are reported and discussed. For low relative velocities, solutal Marangoni effects are seen to be important.

Stability of a condensing liquid film in a binary vapor mixture system

We study stability of a condensing liquid film of a binary vapor mixture. When a binary vapor mixture of some kind is cooled on a substrate, a condensing liquid film emerges to take an inhomogeneous form such as a droplet one due to the solutal Marangoni effect. In order to analyze this phenomenon, we apply the long-wave approximation to the condensing liquid film and derive a nonlinear partial differential equation describing the spatio-temporal evolution of the film thickness. An interfacial boundary condition taking account of an effect of mass gain of the liquid film is adopted. Based on this model, we perform a linear stability analysis around a flat-film solution. We obtain an evolution equation of the amplitude of a disturbance, from which the cutoff and fastest growth wavenumbers are deduced. The maximum value of the cutoff wavenumber relative to the film thickness and its film thickness are estimated for water–ethanol mixture at atmospheric pressure. We numerically verify the long-wave nature of the instability of the condensate liquid film in this system. A significant difference in their values is found for low-ethanol fractions of the ambient vapor whether or not the temperature dependence of the mass transfer coefficient is considered. The wavenumber of a pattern of the liquid film observed in the experiment has the same parameter dependence as that of the fastest growth wavenumber.

Numerical study of Marangoni convection during transient evaporation of two-component droplet under forced convective environment

Numerical simulations of the evaporation of stationary, spherical, two-component liquid droplets in a laminar, atmospheric pressure, forced convective hot-air environment are presented. The transient two-phase numerical model includes multi-component diffusion, a comprehensive method to deal with the interface including the surface tension effects and variation of thermo-physical properties as a function of temperature and species concentration in both liquid- and vapor-phases. The model has been validated using the experimental data available in literature for suspended heptane–decane blended droplets evaporating under a forced convective air environment. The validated model is used to study the vaporization characteristics of heptane–decane droplets under different convective conditions. For an initial composition having 75% by volume of more volatile fuel component, the evaporation transients are presented in terms of variations in interface quantities. Flow, species and temperature fields are presented at several time instants to show the relative strengths of forced convection and Marangoni convection. Results show that at low initial Reynolds numbers, the solutal Marangoni effects induce a flow-field within the liquid droplet, which opposes the flow of the external convective field. The strength of this liquid-phase flow field increases with the consumption of the more volatile fuel component.

Experimental reaction-driven liquid film fingering instability

Reaction-driven pattern formation at the interface between two thin liquid films is studied experimentally on a vertical substrate when two organic liquids, an acrylate and a secondary amine, respectively, are put in contact. On a clean glass plate, the pure liquids spread without any instability and no film deformation is observed. On the contrary, if the substrate is pre-wetted with the amine followed by deposition of acrylate on the amine, the two liquids react at the edge of the spreading acrylate film. Fractal patterns are observed to develop at the nominal contact line. No instability is obtained in the reverse reactive case of amine deposited on acrylate. A qualitative explanation of the observed reaction-driven patterns is given in terms of solutal Marangoni effects induced by differences in local values of surface tension.

Marangoni Flows in Polymer Solution Droplets Drying on Heating Surfaces

The effect on substrate temperature on the fluid dynamics in a polymer solution droplet evaporating on a substrate is investigated experimentally and numerically. It is found from the experiments that fluid velocities in the droplets increase with increasing initial substrate temperature and with decreasing initial solute concentration. A mathematical model, which takes thermal and solutal Marangoni effects into account, are numerically solved using a finite element method. The calculated fluid velocities agree with the experiment. Both experiments and calculations show that, though thermal Marangoni forces dominate the fluid dynamics, solute Marangoni forces should never be neglected. The calculations predict that solute Marangoni effects are more emphasized with decreasing contact angle.

Double-diffusive Marangoni convection in a rectangular cavity: Transition to chaos

Transition to chaos in double-diffusive Marangoni convection in a rectangular cavity with horizontal temperature and concentration gradients is considered. Attention is restricted to the special case when the resultant thermal and solutal Marangoni effects are equal and opposing. Direct numerical simulation is used and some techniques from nonlinear dynamics are adopted to identify the different dynamic regimes. It is found that the supercritical solution branch takes a quasi-periodicity and phase locking route to chaos while the subcritical branch follows the Ruelle–Takens–Newhouse scenario. Transient intermittency in the supercritical branch is observed and physical instability mechanisms of the subcritical branch are identified.

Bénard instabilities in a binary-liquid layer evaporating into an inert gas

A linear stability analysis is performed for a horizontal layer of a binary liquid of which solely the solute evaporates into an inert gas, the latter being assumed to be insoluble in the liquid. In particular, a water-ethanol system in contact with air is considered, with the evaporation of water being neglected (which can be justified for a certain humidity of the air). External constraints on the system are introduced by imposing fixed “ambient” mass fraction and temperature values at a certain effective distance above the free liquid–gas interface. The temperature is the same as at the bottom of the liquid layer, where, besides, a fixed mass fraction of the solute is presumed to be maintained. Proceeding from a (quasi-)stationary reference solution, neutral (monotonic) stability curves are calculated in terms of solutal/thermal Marangoni/Rayleigh numbers as functions of the wavenumber for different values of the ratio of the gas and liquid layer thicknesses. The results are also presented in terms of the critical values of the liquid layer thickness as a function of the thickness of the gas layer. The solutal and thermal Rayleigh and Marangoni effects are compared to one another. For a water–ethanol mixture of 10 wt.% ethanol, it appears that the solutal Marangoni effect is by far the most important instability mechanism. Furthermore, its global action can be described within a Pearson-like model, with an appropriately defined Biot number depending on the wavenumber. On the other hand, it is also shown that, if taken into account, water evaporation has only minor quantitative consequences upon the results for this predominant, solutal Marangoni mechanism.

Double-diffusive Marangoni convection in a rectangular cavity: Onset of convection

Double-diffusive Marangoni convection in a rectangular cavity with horizontal temperature and concentration gradients is considered. Attention is restricted to the case where the opposing thermal and solutal Marangoni effects are of equal magnitude (solutal to thermal Marangoni number ratio Rσ=−1). In this case a no-flow equilibrium solution exists and can remain stable up to a critical thermal Marangoni number. Linear stability analysis and direct numerical simulation show that this critical value corresponds to a supercritical Hopf bifurcation point, which leads the quiescent fluid directly into the oscillatory flow regime. Influences of the Lewis number Le, Prandtl number Pr, and the cavity aspect ratio A (height/length) on the onset of instability are systematically investigated and different modes of oscillation are obtained. The first mode is first destabilized and then stabilized. Sometimes it never gets onset. A physical illustration is provided to demonstrate the instability mechanism and to explain why the oscillatory flow after the onset of instability corresponds to countersense rotating vortices traveling from right to left in the present configuration, as obtained by direct numerical simulation. Finally the simultaneous existence of both steady and oscillatory flow regimes is shown. While the oscillatory flow arises from small disturbances, the steady flow, which has been described in the literature, is induced by finite amplitude disturbances.

Specific Behaviors of Polymer Solution Droplets on Surfaces due to Solutal Marangoni Effect

Specific behaviors of polymer solution droplets evaporating on a lyophilic surface are reported. Polystyrene (solute) is dissolved in acetophenone, anisole and mesitylene (solvent). The single solvents and acetophenone/mesitylene solvents are stationary during drying and form ring-like polymer films. On the other hand, mesitylene/anisole droplets move around on the surface at low solute concentrations. This movement results from solutal Marangoni flow, whose direction is the opposite to the direction of the acetophenone/mesitylene solvents. The movement is almost inhibited at low temperatures. At low temperatures, the droplets comprise a core film surrounded by a ring structure. The morphology of the core film depends on the mixing ratio of the components of the solvent.

Decomposition driven interface evolution for layers of binary mixtures. II. Influence of convective transport on linear stability

We study the linear stability with respect to lateral perturbations of free surface films of polymer mixtures on solid substrates. The study focuses on the stability properties of the stratified and homogeneous steady film states studied in Part I [U. Thiele, S. Madruga, and L. Frastia, Phys. Fluids 19, 122106 (2007)]. To this aim, the linearized bulk equations and boundary equations are solved using continuation techniques for several different cases of energetic bias at the surfaces corresponding to linear and quadratic solutal Marangoni effects. For purely diffusive transport, an increase in the film thickness either exponentially decreases the lateral instability or entirely stabilizes the film. Including convective transport leads to a further destabilization as compared to the purely diffusive case. In some cases the inclusion of convective transport and the related widening of the range of available film configurations (it is then able to change its surface profile) change the stability behavior qualitatively. We furthermore present results regarding the dependence of the instability on several other parameters, namely, the Reynolds number, the surface tension number, and the ratio of the typical velocities of convective and diffusive transport.