Marangoni Instability Research Articles

Instabilities of Marangoni and elasticity in a molten polymer film

This study conducts a comprehensive exploration of the elasticity and Marangoni instability exhibited by a non-Newtonian polymer film flow down an inclined plane within the context of an upper-convected Maxwell (UCM) model. The asymptotic solutions are derived utilizing the stream function and perturbation method based on the long-wave assumption. The numerical solutions are effectively solved at arbitrary wavelengths through the implementation of the Chebyshev spectral collocation technique. The results show that the presence of elastic stress renders the film more susceptible to destabilization. The underlying mechanisms that instigate the instability are examined from an energy balance perspective. It is determined that the instability of the film is predominantly governed by shear stress (SHE) and elastic stress (DIP) effects. Shear stress increases the perturbation kinetic energy to promote instability, while elastic stress decreases the perturbation kinetic energy to enhance stability. However, for the Weissenberg number Wi=1, the shear stress changes from an unstable to a stabilizing factor, and the elastic stress changes from stable to unstable when the wave number k>1. This intriguing inversion is attributed to the dual nature of elasticity, possessing both stabilizing and destabilizing tendencies. Despite the work of Marangoni stress (MAT) magnitude remaining within the order of 10−3, the Marangoni effect indirectly contributes to instability enhancement.

Nature of instability in flow-driven porous anodic oxide.

Self-organized porous anodic oxide films are formed by the electrochemical oxidation of reactive metal aluminum in acidic solutions in which the oxide is soluble. Recently, viscous flow models have shown using linear stability analysis that the instability results from a trade-off between the destabilizing effect of viscous flow of oxide and the stabilizing effect of oxide formation, which provides the wavelength selection mechanism for pattern formation. Anion adsorption on surface growth sites causes nonuniform compressive stress at the oxide-solution interface, which drives the flow. This anodic instability is analogous to the classical Marangoni instability induced by surface tension gradients. In this work, nature of the instability beyond the stability threshold is determined using a weakly nonlinear analysis. For the growth of well-developed pores beyond the threshold, a subcritical nature of the instability is essential. However, our weakly nonlinear analysis shows that the solutions emerging from neutral stability are supercritical in nature at all wavenumbers for the practical range of anodizing control parameters investigated. We also determine the region where the model is Hadamard stable, a necessary condition for well-posedness.

Возбуждение релаксационных колебаний на искривленной межфазной границе в условиях внутренней задачи

The oscillatory mode of solutal Marangoni convection during the absorption of a surfactant from a homogeneous external solution into a water droplet is studied numerically. This is caused by the effect of gravity, which promotes the sedimentation of surfactant molecules in an aqueous medium. This version of oscillatory convection arising under the conditions of an internal problem was recently discovered experimentally. In the present paper, we consider the case of a chemically inert system, in which there are no reactions. The effects of interfacial deformation are assumed to be insignificant and thus they are neglected. The mathematical model includes the Navier—Stokes equations written in the Hele-Shaw and Boussinesq approximations, and the equations of surfactant transport in the system. We assume that the characteristic time of surfactant adsorption is shorter than the time of its diffusion in both solutions, which makes it possible to ignore the formation of a surface phase. The boundary value problem includes the equilibrium condition of the system, which takes into account different values of the chemical potential in the phases. It is shown that a water droplet is a surfactant accumulator that diffuses from the organic phase. The problem is solved in dimensional form using the COMSOL Multiphysics package and based on a set of physical constants for acetic acid which, like many other members of the carboxylic acid family, has the properties of surfactant in water. It was found that direct numerical simulation of the system is able to reproduce the relaxation oscillations observed in the experiment only under the additional phenomenological assumption of non-Newtonian rheology of the interface, which was previously proposed for the external problem. The physical mechanism which may be responsible for the delayed onset of Marangoni instability is discussed. We demonstrate that periodic oscillations are generated inside the drop due to the competition between the Marangoni effect and the gravity-dependent convective instability of the solution. Using direct numerical simulation, we identified the structures of convective motion at the interface and in its neighborhood, determined the flow intensity as a function of time, and obtained the range of change in the oscillation period.

Interfacial assembly of polyamide nanofilm membranes regulated by surfactants with different structural characteristics

Polyamide (PA) nanofilm membranes are key materials for water treatment and desalination. Although surfactants are widely used to tune the interfacial polymerization (IP) process for PA nanofilm formation, their regulatory mechanisms remain incompletely understood. Herein, we synthesized PA nanofilm membranes at a support-free interface in the presence of anionic surfactants with different tail lengths and counterions and comprehensively characterized them to identify the IP mechanism regulated by the surfactant structure. The use of the surfactant with a longer alkyl tail or a smaller/weaker-bound counterion resulted in greater alterations in the structural and physicochemical properties and separation performance of the PA nanofilm membranes. Collaborated with computational simulations, this phenomenon could be attributed to solutal Marangoni instability triggered by the interfacial migration (via binding to PA) of the surfactant complexed with amine monomers during IP. A longer alkyl chain or smaller/weaker-bound counterion of the surfactant intensified Marangoni instability by promoting the interfacial formation of surfactant–amine complexes and/or facilitating their binding to PA, leading to greater PA deformations. Our work provides new insights into the surfactant-regulated IP mechanism as well as a facile means to rationally tailor the properties and performance of IP-assembled nanofilm membranes for various environmental applications.

Influence of parametric forcing on Marangoni instability

We study a thin, laterally confined heated liquid layer subjected to mechanical parametric forcing without gravity. In the absence of parametric forcing, the liquid layer exhibits the Marangoni instability, provided the temperature difference across the layer exceeds a threshold. This threshold varies with the perturbation wavenumber, according to a curve with two minima, which correspond to long- and short-wave instability modes. The most unstable mode depends on the lateral confinement of the liquid layer. In wide containers, the long-wave mode is typically observed, and this can lead to the formation of dry spots. We focus on this mode, as the short-wave mode is found to be unaffected by parametric forcing. We use linear stability analysis and nonlinear computations based on a reduced-order model to investigate how parametric forcing can prevent the formation of dry spots. At low forcing frequencies, the liquid film can be rendered linearly stable within a finite range of forcing amplitudes, which decreases with increasing frequency and ultimately disappears at a cutoff frequency. Outside this range, the flow becomes unstable to either the Marangoni instability (for small amplitudes) or the Faraday instability (for large amplitudes). At high frequencies, beyond the cutoff frequency, linear stabilization through parametric forcing is not possible. However, a nonlinear saturation mechanism, occurring at forcing amplitudes below the Faraday instability threshold, can greatly reduce the film surface deformation and therefore prevent dry spots. Although dry spots can also be avoided at larger forcing amplitudes, this comes at the expense of generating large-amplitude Faraday waves.

Numerical study of the Marangoni effect induced by soluble surfactants and solute based on rising droplets

In this study, we present a numerical investigation into the phenomenon of rising droplets in immiscible fluids, focusing on the Marangoni effect induced by both solute and a combination of solute and soluble surfactants. We meticulously examine the interfacial behaviors of pure solute droplets and mixed droplets, with a particular interest on the intricate interplay among interfacial concentration, interfacial tension, Marangoni stress, and Marangoni convection. Our investigation provides insight into the influence of key physicochemical parameters, such as viscosity, diffusion coefficient, partition coefficient, and interfacial tension gradient, on the Marangoni instability. Furthermore, we conduct a comprehensive parametric exploration of the impact of dimensionless numbers such as the Langmuir number (La), the Damkohler number (Da), the Peclet number (Pe), and the elasticity number β on the stabilizing efficacy of surfactants. The research findings underscore the effectiveness of our numerical method in capturing the distinctive two-step acceleration characteristics of pure solute droplets and the stabilizing effect of surfactants on mixed droplets. Notably, our study reveals that the Marangoni instability may manifest even when the viscosity and diffusivity ratios of the two-phase fluids are closely matched. Partition coefficients below unity exhibit only a marginal influence on the re-acceleration time of the droplets. Systems characterized by extremely low interfacial tension gradients tend to exhibit no Marangoni instability. Moreover, an increase in La enhances the stability of mixed droplets, while a significant threshold is identified for Da to affect the stability of mixed droplets. The ascent speed of mixed droplets displays pronounced variation across varying Pe magnitudes. Finally, in scenarios involving a wide-ranging variation in β, mixed droplets transition between the states of pure solute droplets and rigid spheres, revealing a distinct-state transition point.

THE ONSET OF LONG-WAVELENGTH MARANGONI CONVECTION IN A BINARY FLUID MIXTURE UNDER HEAT FLUX MODULATION

The Marangoni instability of a horizontal binary mixture layer with a deformable free surface and a solid substrate is investigated under the action of a modulated heat flux. In contrast to a homogeneous liquid, due to thermal diffusion (Soret effect), the modulation of the heat flux creates not only a temperature wave but also a concentration wave, which changes the surface tension. Two cases of the modulation of the heat flux with a zero mean value are considered: (i) on a free surface and (ii) on a rigid substrate. In both cases, the long-wave instability exists within the established frequency intervals. The dependences of the critical Marangoni number and the corresponding modulation frequency on the separation ratio and the Lewis number are obtained for long-wave disturbances. The fundamental features of case (i), as compared to case (ii), are as follows: the instability domains are located in the lower frequency ranges and the minimum Marangoni number is several times smaller.

Dynamics of thin self-rewetting liquid films on an inclined heated substrate

In this paper, we investigate the quadratic Marangoni instability along with inertia in a self-rewetting fluid film that has a nonmonotonic variation of surface tension with temperature. The dynamics of such a thin self-rewetting fluid film flowing along an inclined heated substrate is examined by deriving an evolution equation for the film thickness using long-wave theory and asymptotic expansions. By adopting the derived long-wave model that includes the inertial and thermocapillary effects, we perform a linear stability analysis of the flat film solution. Two cases of the nonlinear flow are explored in depth using Tm (temperature corresponding to the minimum of surface tension) as the cutoff point. One is the case of (Ti,s−Tm)<0, and the other is (Ti,s−Tm)>0, where Ti,s is the interface temperature corresponding to the flat film. The Marangoni effect switches to the anomalous Marangoni effect as (Ti,s−Tm) shifts from a negative value to a positive value. Our calculations reveal that the Marangoni effect augments the flat film instability when (Ti,s−Tm)<0, whereas the stability of the flat film is promoted for (Ti,s−Tm)>0. Our further analysis demonstrates that the destabilizing inertial forces can be entirely compensated by the stabilizing anomalous thermocapillary forces. We verify the linear stability predictions of the long-wave Benney-type model with the solution to the Orr–Sommerfeld problem in the long-wave limit. Our time-dependent computations of the long-wave model establish the modulation of interface deformation in the presence of inertia and temperature gradients in the conventional Marangoni regime, whereas such deformations are suppressed in the anomalous Marangoni regime. A comparison of the numerical computations with the linear theory shows good agreement.

Dynamics of Drop Formation in the Presence of Interfacial Mass Transfer.

The dynamics of drop formation have been investigated in the presence of interfacial mass transfer through controlled flow visualization experiments. The mixtures of n-hexane (solvent) and acetone (solute) were used as a dispersed phase, having different initial compositions varying over a broad range. Drops were formed at the submerged position in the continuous phase (water) at the same operating flow conditions. The unsteady force balance model is developed to analyze the implications of the simultaneously occurring interfacial transfer of the solute on the formation dynamics in real time, and predictions are validated with experimental results. Based on initial compositions, the analysis of the transient drop shape shows a sharp transition in the drop formation regime. At lower initial solute concentrations, i.e., ϕ0 < 0.2, axisymmetric drop formation occurs and the interfacial solute transfer has negligible effects on the formation dynamics. Over an intermediate range of solute concentrations, i.e., 0.2 < ϕ0 < 0.5, Marangoni instability is triggered along the evolving interface, and therefore, the interface deformations and contractions occur during the drop formation. At ϕ0 = 0.5, the drop takes highly nonaxisymmetric shapes and remains away from equilibrium until its detachment from an orifice. For ϕ0 > 0.5, the spontaneous ejection of plumes of the solute results in the rapid generation of multiple droplets of smaller size. This work shows that higher solute concentration gradients not only lead to faster solute transport but also induce strong interfacial instability simultaneously. Thus, the coupled effects of transient change in composition and fluid properties govern the drop size and its formation time in such systems under non-equilibrium.

Marangoni instability of an evaporating binary mixture droplet

Evaporation of a binary mixture droplet (BMD) is a common natural phenomenon and widely applied in many industrial fields. For the case of a sessile BMD being the only contact-line pinning throughout an entire evaporation, a theoretical model describing the evaporating dynamics is established when considering the comprehensive effect of evaporative cooling, the thermal Marangoni effect, the solutal Marangoni effect, the convection effect, and the Stefan flow. The dynamics of a binary ethanol–water droplet on a heated substrate is simulated using a cylindrical coordinate system. The reasons for Marangoni instability-driven flow (MIF) are discussed, and the influence of initial ethanol concentration and substrate heating temperature are examined. An evaporating BMD first forms a MIF at the contact line and quickly affects the whole droplet. Under the influence of the Marangoni instability, the BMD presents a complex internal flow structure with multiple-vortex and nonlinear temperature and ethanol concentration distributions. The positive feedback induced by vortices and the nonlinear distribution of concentration and temperature promotes the development of a MIF. At low initial ethanol concentrations, the MIF loses its driving force and turns into a stable counterclockwise single-vortex flow as ethanol evaporates completely. However, at high initial ethanol concentrations, the MIF exists in the entire evaporation. Increasing ethanol concentration and substrate heating temperature can delay the appearance of the MIF; ethanol concentration affects the MIF duration time, and heating temperature alters the MIF intensity. To enhance flow intensity and mass transfer of BMDs, the temperature difference should first be increased, followed by increased ethanol concentration.

Essence into the kinetic enhanced extraction induced by Marangoni convection on the surface of freely rising oil droplets

The enhanced separation of rare earth ions depending on different kinetic extraction behaviors can be achieved by extraction on the surface of rising droplets, where exists the nonhomogeneous chemical reaction. Marangoni instability might occur dependent on nonhomogeneous chemical reaction, which is conducive to the enhancement of interfacial mass transfer. To explore the influence from a nonhomogeneous chemical reaction on the generation of Marangoni instability, influences from the flow rate of oil droplets and the oil droplet size on interfacial extraction behaviors were performed, the interfacial tension was evaluated, and MD simulations combined DFT calculations were adopted. It was revealed that the higher interface renewal rate of the large oil droplet was favorable for the interfacial chemical reaction. Whether the interfacial extraction rate is greater than the interface renewal rate decided the occurrence of Marangoni convection. The current research highlights a novel viewpoint towards understanding microscopic nature of kinetic enhanced extraction.

Marangoni instability in oblate droplets suspended on a circular frame

We study theoretically internal flows in a small oblate droplet suspended on the circular frame. Marangoni convection arises due to a vertical temperature gradient across the drop and is driven by the surface tension variations at the free drop interface. Using the analytical basis for the solutions of Stokes equation in coordinates of oblate spheroid, we have derived the linearly independent stationary solutions for Marangoni convection in terms of Stokes stream functions. The numerical simulations of the thermocapillary motion in the drops are used to study the onset of the stationary regime. Both analytical and numerical calculations predict the axially symmetric circulatory convection motion in the drop, the dynamics of which is determined by the magnitude of the temperature gradient across the drop. The analytical solutions for the critical temperature distribution and velocity fields are obtained for the large temperature gradients across the oblate drop. These solutions reveal the lateral separation of the critical and stationary motions within the drops. The critical vortices are localized near the central part of a drop, while the intensive stationary flow is located closer to its butt end. A crossover to the limit of the plane film is studied within the formalism of the stream functions by reducing the droplet ellipticity ratio to zero value. The initial stationary regime for the strongly oblate drops becomes unstable relative to the many-vortex perturbations in analogy with the plane fluid films with free boundaries.

Autonomous Interfacial Assembly of Polymer Nanofilms via Surfactant-Regulated Marangoni Instability.

Interfacial polymerization (IP) provides a versatile platform for fabricating defect-free functional nanofilms for various applications, including molecular separation, energy, electronics, and biomedical materials. Unfortunately, coupled with complex natural instability phenomena, the IP mechanism and key parameters underlying the structural evolution of nanofilms, especially in the presence of surfactants as an interface regulator, remain puzzling. Here, we interfacially assembled polymer nanofilm membranes at the free water-oil interface in the presence of differently charged surfactants and comprehensively characterized their structure and properties. Combined with computational simulations, an in situ visualization of interfacial film formation discovered the critical role of Marangoni instability induced by the surfactants via various mechanisms in structurally regulating the nanofilms. Despite their different instability-triggering mechanisms, the delicate control of the surfactants enabled the fabrication of defect-free, ultra-permselective nanofilm membranes. Our study identifies critical IP parameters that allow us to rationally design nanofilms, coatings, and membranes for target applications.

Experimental and simulation studies on damage mechanisms of tungsten and molybdenum under compressed plasma flow irradiation

The failure mechanism of plasma-facing components (PFCs) under extreme plasma conditions relevant for fusion reactors were investigated. Here, edge-localized mode (ELM)-like transient thermal shock irradiation experiments were performed on tungsten and molybdenum using compressed plasma flow, and combined with thermal–mechanical analysis by means of finite element simulations to discuss the grain structure evolution, cracking behavior and variations of hardness. When ELM-like thermal shock irradiation was sufficient to melt tungsten and molybdenum, a submicron-sized cellular sub-grain structure was created on their surface due to the high temperature gradient of the molten layer under the effect of Bénard–Marangoni instability. Rapid directional solidification from the bottom of the molten layer to the surface induced the formation of columnar grains dominated by the <200> orientation. While the formation of cellular sub-grains increased hardness, the thermal effect of irradiation and the formation of columnar grains led to softening. The high thermal stress induced by the ELM-like thermal shock produced macro-cracks and micro-cracks on the surface of tungsten and only micro-cracks on the surface of molybdenum. Macro-cracks were generated due to the intrinsic brittleness of tungsten. As a result of stress evolution, longitudinal macro-cracks extending perpendicular to the surface experienced transverse transformation within the material. Micro-cracks formed due to the embrittlement of the re-solidification zone, and their width increased with the melting depth. These results help us to understand failure mechanisms in PFCs under extreme operating conditions and are valuable for developing future fusion reactors.

Surface-temperature-induced Marangoni effects on developing buoyancy-driven flow

To investigate the initial development of the Rayleigh–Bénard–Marangoni (RBM) instability in a relatively deep domain, direct numerical simulations for a large range of Marangoni and Rayleigh numbers were performed. In the simulations, the surface was assumed to be flat and surface cooling was modelled by a constant heat flux. The small-scale dynamics of the flow and temperature fields near the surface was fully resolved by using a non-uniform vertical grid distribution. A detailed investigation of the differences in physical mechanisms that drive the Rayleigh- and Marangoni-dominated instabilities is presented. To this end, various properties such as the maturation rate of convection cells, the fluctuating kinetic energy and the surface characteristic length scale were studied. It was confirmed that buoyancy forces and surface-temperature-gradient-driven Marangoni forces enhance one another in promoting the development of the RBM instability. When using a relevant measure of the effective thermal boundary layer thickness as length scale, both the critical Marangoni and Rayleigh numbers, obtained for the purely Marangoni- and purely Rayleigh-driven instabilities, were found to be in good agreement with the literature.

Rayleigh-Marangoni-Bénard instability in an Oldroyd-B fluid layer overlying a highly porous layer with a deformable surface

This paper describes the linear stability analysis of Rayleigh–Marangoni–Bénard convection with a deformable surface in a fluid overlying a highly porous layer. Using the Chebyshev tau-QZ method, we investigate the oscillatory mode of both the Rayleigh and Marangoni instabilities for non-Newtonian fluids. The numerical results indicate that a deformable upper surface destabilizes the system. Moreover, the Marangoni instabilities in long-wave branches first decrease and then increase with increasing depth ratio, while the opposite effects are observed in short-wave branches. The Rayleigh instabilities decrease monotonically as the depth ratio increases. For certain reference parameters, the system becomes more stable as the Biot number and Galileo number increase. A greater strain retardation time and a smaller stress relaxation time lead to more stable Marangoni convection in long-wave branches, whereas these viscoelastic times have the opposite effects in short-wave branches. The influence of viscoelasticity on the Rayleigh instability is also investigated. Finally, the coupling mode of the two instabilities is studied in detail. Variations in the Marangoni number influence long- and short-wave branches differently. Interestingly, there is an interval of the Marangoni number in short-wave branches for which no critical Rayleigh number exists.

Marangoni destabilization of bidimensional-confined gas–liquid co-flowing streams in rectangular microfluidic channels

In microchannels, the stability of a fluid jet injected into another immiscible fluid strongly depends on its degree of geometric confinement. When the width of the jet, w, is larger than the channel height, H, the surface tension driven Rayleigh–Plateau instability is suppressed so that the 2D (bidimensional)-confined jet is absolutely stable and never collapses into bubbles (or drops) in contrast to what occurs when w ≤ H [Dollet et al., “Role of the channel geometry on the bubble pinch-off in flow-focusing,” Phys. Rev. Lett. 100(3), 034504 (2008); Guillot et al., “Stability of a jet in confined pressure-driven biphasic flows at low Reynolds number in various geometries,” Phys. Rev. E 78(1), 016307 (2008)]. We here demonstrate both experimentally and theoretically that this picture is, indeed, no longer valid when Marangoni effects are considered. We experimentally show that the addition of small length alcohol molecules into the liquid phase destabilizes a 2D-confined gas–water microfluidic stream ( w &amp;gt; H), leading to the generation of steady non-linear waves and further to the production of bubbles. Using a simple hydrodynamic model, we show through a linear analysis that the destabilization of the gas stream may result from a Marangoni instability due to the fast adsorption of the alcohol molecules, which occurs on a timescale comparable to that of the microfluidic flow.

Investigation into the laser polishing of an austenitic stainless steel

Gas shielding is critical for improving the quality of laser polishing. The processing effects of laser polishing under the chamber and nozzle gas shielding were compared and analyzed. The influence of the volume flow rate on the surface roughness of the polished workpiece was analyzed, determining the optimal volume flow rate (Q = 5 L/min). At the optimum volume flow rate, the effects of laser power and scanning speed on surface roughness were explored in further research on nozzle gas shielding laser polishing with wider application prospects. A shielding gas jet model for nozzle gas shielding laser polishing was established and verified. The influence mechanism of the shielding gas jet on the polished surface topography was explored using the established shielding gas jet model and laser polishing model, revealing the formation mechanism of surface ripples on the polished surface: the shielding gas jet acts as a perturbation of the molten pool, causing the Marangoni instability of the molten pool when the Marangoni number exceeds the critical Marangoni number.

Nonlinear three-dimensional patterns of the Marangoni convection in a thin film on a poorly conducting substrate.

We investigate the dynamics of a thin liquid film that is placed atop a heated substrate of very low thermal conductivity. The direct numerical simulation of the stationary long-wave Marangoni instability is performed with the system of coupled partial differential equations. These equations were previously derived within the lubrication approximation; they describe the evolution of film thickness and fluid temperature. We compare our results with the early reported results of the weakly nonlinear analysis. A good qualitative agreement is observed for values of the Marangoni number near the convective threshold. In the case of supercritical excitation, our results for the amplitudes are described by the square root dependence on the supercriticality. In the case of subcritical excitation, we report the hysteresis. For relatively high supercriticality, the convective regimes evolve into film rupture via the emergence of secondary humps. For the three-dimensional patterns, we observe rolls or squares, depending on the problem parameters. We also confirm the prediction of the asymptotic results concerning the nonlinear feedback control for the pattern selection. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.

Experimental and numerical study of droplet formation with Marangoni instability

The Marangoni effect produces some complex phenomena during droplet formation and has an important influence on the mass transfer state. In this paper, the droplet formation process of toluene/acetone/water droplet extraction system accompanied by Marangoni instability was numerically simulated, and the actual mass transfer states of droplets were photographed using schlieren imaging technology. The results reveal that: suspended droplets may have mass transfer states such as diffusion layer, natural convection, jet and turbulence, and the Marangoni instability causes the droplets to jet solute intermittently. Compared to droplets with constant surface tension, the Marangoni effect increases the mass transfer rate during droplet formation, and the Marangoni stress generates Marangoni convection at the interface, whose mutual annexation with the internal circulation leads to droplet oscillations. The Marangoni effect also causes pulsations in droplet vorticity, increasing the solute concentration exacerbates the vortex disorder, while increasing the injection rate may suppress the pulsations, which are physically dependent on the relative advantage of droplet internal circulation over Marangoni convection.