Marangoni Instability Research Articles

Rayleigh–Bénard–Marangoni convection in a weakly non-Boussinesq fluid layer with a deformable surface

The influence of surface deformations on the Rayleigh–Bénard–Marangoni instability of a uniform layer of a non-Boussinesq fluid heated from below is investigated. In particular, the stability of the conductive state of a horizontal fluid layer with a deformable surface, a flat isothermal rigid lower boundary, and a convective heat transfer condition at the upper free surface is considered. The fluid is assumed to be isothermally incompressible. In contrast to the Boussinesq approximation, density variations are accounted for in the continuity equation and in the buoyancy and inertial terms of the momentum equations. Two different types of temperature dependence of the density are considered: linear and exponential. The longwave instability is studied analytically, and instability to perturbations with finite wavenumber is examined numerically. It is found that there is a decrease in stability of the system with respect to the onset of longwave Marangoni convection. This result could not be obtained within the framework of the conventional Boussinesq approximation. It is also shown that at Ma = 0 the critical Rayleigh number increases with Ga (the ratio of gravity to viscous forces or Galileo number). At some value of Ga, the Rayleigh–Bénard instability vanishes. This stabilization occurs for each of the density equations of state. At small values of Ga and when deformation of the free surface is important, it is shown that there are significant differences in stability behavior as compared to results obtained using the Boussinesq approximation.

Vibration influence on the onset of the longwave Marangoni instability in two-layer system

We study the longwave Marangoni convection in two-layer films under the influence of a low frequency vibration. A linear stability analysis is performed by means of the Floquet theory. A competition of subharmonic, synchronous, and quasiperiodic modes is considered. It has been found that the monotonic instability, which exists at constant gravity, is transformed into a synchronous instability, which is critical in a wide range of vibration amplitude. At parameters where oscillatory instability exists, the longwave quasiperiodic mode remains critical until a subharmonic mode becomes critical with the growth of the vibration amplitude.

Modeling of the Marangoni instability of uniform diffusion through the interphase boundary in weightlessness conditions

Modeling of the Marangoni instability of uniform diffusion through the interphase boundary in weightlessness conditions

Thermo-capillary effect on the linear temporal and spatial instability of viscous liquid jets falling under gravity

Abstract The thermal modulation of Newtonian liquid jets at the orifice causes a variation in surface tension, which propagates downstream inducing Marangoni instability. Therefore, the linear temporal and spatial instability should be investigated to predict the same size of producing small spherical pellets. In this paper, we consider a viscous liquid jet emerging from a nozzle subject to thermo-capillary effects falling under gravity. Moreover, we use the asymptotic approach to reduce the governing equation into one-dimensional (1-D). The steady state solutions have been found using a modified Newton's method, and then the linear instability analysis has been investigated of the resulting set of equations.

Parametric Excitation of Marangoni Instability in a Heated Thin Layer Covered by Insoluble Surfactant

The paper presents the analysis of the impact of vertical periodic vibrations on the long-wavelength Marangoni instability in a liquid layer with poorly conducting boundaries in the presence of insoluble surfactant on the deformable gas-liquid interface. The layer is subject to a uniform transverse temperature gradient. Linear stability analysis is performed in order to find critical values of Marangoni numbers for both monotonic and oscillatory instability modes. Longwave asymptotic expansions are used. At the leading order, the critical values are independent on vibration parameters; at the next order of approximation we obtained the rise of stability thresholds due to vibration.

Novel criteria for the development of monotonic and oscillatory instabilities in a two-layer film

The development of the Marangoni instability in a two-layer film in the presence of a transverse temperature gradient and a heat source/sink at the liquid-liquid interface is investigated. The problem is solved by means of a linear stability theory and nonlinear simulations. Novel criteria for the development of monotonic and oscillatory instabilities have been formulated. It has been found that the nonlinear development of a monotonic instability leads to a rupture of the bottom layer or the top layer. Numerous types of nonlinear film evolution have been observed in the case of an oscillatory instability, among them alternating roll patterns of different scales and orientations, temporally non-periodic motions, and the rupture of either layer.

Parametric excitation of oscillatory Marangoni instability in a heated liquid layer covered by insoluble surfactant

This paper is a continuation of our previous research reported in the two last IMA conferences. While in our previous works the driving modulation was a modulation of the temperature gradient, here the temperature gradient is fixed in the whole liquid layer and the liquid is vertically vibrated with some fixed driving frequency. Two kinds of waves can be generated in this system. The first kind of waves are transverse (capillary-gravity) waves. The second kind of waves are longitudinal (Marangoni) waves caused by the dependence of the surface tension on the temperature and the surfactant concentration. A linear analysis with arbitrary wave numbers is performed. Two different heating regimes were considered. Multiple instability regions depending on the heating conditions are analyzed. Among three possible modes of the system’s response to external forcing, the most “dangerous” one is the subharmonic instability mode.

On nature of mass transfer near liquid-liquid interface in the presence of Marangoni instabilities

We report on mass transfer statistics in low Reynolds number system (Rep∼0.053) with Marangoni instabilities. Data from our previous paper (Khanwale et al., 2015a) has been used concerning velocity and concentration fields around the drop interface measured using combination of Particle Image Velocimetry (PIV) and Planar Laser Induced Fluorescence (PLIF) techniques. To understand the effect of interfacial instabilities on mass transfer process, fluid dynamical variations resulting due to relative motion of two phases and the influence of deformation of interface are made negligible. This has been achieved by selection of fluid system with particle Reynolds numbers (Rep) of 0.053 (creeping flow), Eötvös number, Eo=1.95, and Morton number, M=78.20. The multi-scale nature and similarity of physics with intermittent turbulence of velocity fields, arising due to Marangoni instabilities are reported in detail by Khanwale et al. (2015a). Calculation of mass transfer coefficient due to the aforementioned multi-scale nature of velocity field is non-trivial, and requires detailed investigation of flow structures. We employ advanced wavelet based methods to calculate length scales of flow structures, which are then used for detailed calculations of mass transfer coefficients using the small eddy formalism. Being an inherently dynamic system the temporal variations of mass transfer statistics are also reported.

Modeling hydrodynamic flows in plasma fluxes when depositing metal layer on the surface of catalyst converters

Air pollution with harmful substances resulting from combustion of liquid hydrocarbons and emitted into atmosphere became one of the global environmental problems in the late 20th century. The systems of neutralization capable to reduce toxicity of exhaust gases several times are very important for making environmentally safer combustion products discharged into the atmosphere. As revealed in the literature review, one of the most promising purification procedures is neutralization of burnt gases by catalyst converter systems. The principal working element in the converter is a catalytic layer of metals deposited on ceramics, with thickness 20-60 micron and a well-developed micro-relief. The paper presents a thoroughly substantiated new procedure of deposing a nano-scale surface layer of metal-catalyst particles, furthering the utilization of catalysts on a new level. The paper provides description of mathematical models and computational researches into plasma fluxes under high-frequency impulse input delivered to electrode material, explorations of developing Kelvin-Helmholtz, Marangoni and magnetic hydrodynamic instabilities on the surface of liquid electrode metal droplet in the nano-scale range of wavelengths to obtain a flow of nano-meter particles of cathode material. The authors have outlined a physical and mathematical model of magnetic and hydrodynamic instability for the case of melt flowing on the boundary with the molten metal with the purpose to predict the interphase shape and mutual effect of formed plasma jet and liquid metal droplet on the electrode in the nano-scale range of wavelengths at high-frequency impact on the boundary “electrode-liquid layer”.

Nanolayer formation during hydrodynamic instability under external stimuli

Experimental observations regarding the formation of strengthening surface nanostructures under various external stimuli (electroexplosive alloying, electron-beam treatment, thermomechanical strengthening of rolled strip by fast cooling, and intense mechanical treatment in long-term rail operation) are interpreted on the basis of consistent principles. The formation of nanostructures due to unstable equilibrium states in the surface layers (Kelvin–Helmholtz and Marangoni instabilities) is simulated. The corresponding dispersion equations are analyzed, and analytical formulas are derived for the decrement α as a function of the wavelength λ in the micro and nano ranges. The numerical values of the maxima in the α(λ) curve correspond to the experimental parameters of the nanostructures. A physical interpretation is offered.

Marangoni waves in two-layer films under the action of spatial temperature modulation

The nonlinear dynamics of waves generated by the deformational oscillatory Marangoni instability in a two-layer film under the action of a spatial temperature modulation on the solid substrate is considered. A system of long-wave equations governing the deformations of the upper surface and the interface between the liquids is derived. The nonlinear simulations reveal the existence of numerous dynamical regimes, including two-dimensional stationary flows and standing waves, three-dimensional standing waves with different spatial periods, and three-dimensional travelling waves. The general diagram of the flow regimes is constructed.

Placing Marangoni instabilities under arrest

Soap bubbles occupy the rare position of delighting and fascinating both young children and scientific minds alike. Sir Isaac Newton, Joseph Plateau, Carlo Marangoni, and Pierre-Gilles de Gennes, not to mention countless others, have discovered remarkable results in optics, molecular forces and fluid dynamics from investigating this seemingly simple system. We present here a compilation of curiosity-driven experiments that systematically investigate the surface flows on a rising soap bubble. From childhood experience, we are familiar with the vibrant colors and mesmerizing display of chaotic flows on the surface of a soap bubble. These flows arise due to surface tension gradients, also known as Marangoni flows or instabilities. In Figure 1, we show the surprising effect of layering multiple instabilities on top of each other, highlighting that unexpected new phenomena are still waiting to be discovered, even in the simple soap bubble.

Oscillatory Marangoni instability in a heated layer with insoluble surfactant adsorbed on the free surface

Onset of surface-tension driven convection in a heated liquid layer with insoluble surfactant adsorbed on the free surface is analyzed in the framework of the linear stability theory. The limit of a deep layer is considered. The general dispersion relation is obtained and investigated analytically and numerically.

Hydrodynamic effects on phase separation morphologies in evaporating thin films of polymer solutions

We examine effects of hydrodynamics on phase separation morphologies developed during drying of thin films containing a volatile solvent and two dissolved polymers. Cahn-Hilliard and Flory-Huggins theories are used to describe the free energy of the phase separating systems. The thin films, considered as Newtonian fluids, flow in response to Korteweg stresses arising due to concentration non-uniformities that develop during solvent evaporation. Numerical simulations are employed to investigate the effects of a Peclet number, defined in terms of system physical properties, as well as the effects of parameters characterizing the speed of evaporation and preferential wetting of the solutes at the gas interface. For systems exhibiting preferential wetting, diffusion alone is known to favor lamellar configurations for the separated phases in the dried film. However, a mechanism of hydrodynamic instability of a short length scale is revealed, which beyond a threshold Peclet number may deform and break the lamellae. The critical Peclet number tends to decrease as the evaporation rate increases and to increase with the tendency of the polymers to selectively wet the gas interface. As the Peclet number increases, the instability moves closer to the gas interface and induces the formation of a lateral segregation template that guides the subsequent evolution of the phase separation process. On the other hand, for systems with no preferential wetting or any other property asymmetries between the two polymers, diffusion alone favors the formation of laterally separated configurations. In this case, concentration perturbation modes that lead to enhanced Korteweg stresses may be favored for sufficiently large Peclet numbers. For such modes, a second mechanism is revealed, which is similar to the solutocapillary Marangoni instability observed in evaporating solutions when interfacial tension increases with the concentration of the non-volatile component. This mechanism may lead to multiple length scales in the laterally phase separated configurations.

Nonlinear Development of the Marangoni Instability in Liquid Films

A nonlinear mathematical model of the state of the free surface of a nonisothermal liquid film is presented. The basic wave characteristics and the liquid film free surface state have been calculated for moderate Reynolds numbers in the presence of Marangoni instability. A nonlinear parabolic equation for the amplitude of the envelope of wave train and the results of computational experiment on the nonlinear development of Marangoni instability in liquid films are presented.

Thermal Marangoni instability of a thin film flowing down a thick wall deformed in the backside

The nonlinear instability of a thin liquid film flowing down a heated thick wall with deformations in the backside is investigated. Here it is assumed that the wall deformations are sinusoidal in space. Time dependent perturbations are imposed at the origin of the free surface of the film. It is found that the wall deformations have an important influence on the flow instability. Moreover, it is shown that the free surface has a large amplitude spatial response to the backside deformations of the wall. This response increases its amplitude considerably when decreasing the wall spatial wavelength down to the wavelength of the time dependent perturbations. At that point, numerical analysis reveals that the time dependent perturbations in some cases are almost impossible to observe on the free surface response. However, in other cases, their interaction produces large amplitude nonlinear wave modulations.

A simplified nonlinear model of the Marangoni instability in gas absorption

The process of gas absorption into initially motionless liquid layer is investigated. The convective instability caused by the temperature dependence of the surface tension. The critical time of transition of the process to unstable convective regime, as well as the intensity of mass transfer in a surface convection are estimated numerically. The mathematical model includes the equations of convective diffusion, thermal conduction and fluid motion. The problem was solved numerically in the two-dimensional formulation. In the coordinate along the interface the concentration of the absorbed substance is represented by three terms of the trigonometric Fourier series. A difference approximation of equations with an exponentially changing grid in the direction normal to the interface is used. The simulations results agree with the well-known experimental data on the absorption of carbon dioxide in water.

Solutal Marangoni instability in layered two-phase flows

In this paper, the instability of layered two-phase flows caused by the presence of a soluble surfactant (or a surface-active solute) is studied. The fluids have different viscosities, but are density matched to focus on Marangoni effects. The fluids flow between two flat plates, which are maintained at different solute concentrations. This establishes a constant flux of solute from one fluid to the other in the base state. A linear stability analysis is performed, using a combination of asymptotic and numerical methods. In the creeping flow regime, Marangoni stresses destabilize the flow, provided that a concentration gradient is maintained across the fluids. One long-wave and two short-wave Marangoni instability modes arise, in different regions of parameter space. A well-defined condition for the long-wave instability is determined in terms of the viscosity and thickness ratios of the fluids, and the direction of mass transfer. Energy budget calculations show that the Marangoni stresses that drive long- and short-wave instabilities have distinct origins. The former is caused by interface deformation while the latter is associated with convection by the disturbance flow. Consequently, even when the interface is non-deforming (in the large-interfacial-tension limit), the flow can become unstable to short-wave disturbances. On increasing the Reynolds number, the viscosity-induced interfacial instability comes into play. This mode is shown to either suppress or enhance the Marangoni instability, depending on the viscosity and thickness ratios. This analysis is relevant to applications such as solvent extraction in microchannels, in which a surface-active solute is transferred between fluids in parallel stratified flow. It is also applicable to the thermocapillary problem of layered flow between heated plates.

On the Yih–Marangoni instability of a two-phase plane Poiseuille flow in a hydrophobic channel

The linear stability analysis of a plane Poiseuille flow of two immiscible, incompressible fluids of different viscosities and densities in a hydrophobic channel, in the presence of an insoluble surfactant at the interface is examined, within the framework of Orr–Sommerfeld system. The walls of the channel are modeled as walls with velocity slip/no-slip. The equations governing the flow system are solved numerically by a Chebyshev collocation method for a wide range of dimensionless parameters describing the flow system. The effects of slip on the neutral stability boundaries for the interface modes in the presence/absence of an insoluble surfactant at the interface are examined for different thickness ratios of the two layers, with density and/or viscosity stratification. Slip conditions at the wall show a promise for control of the Yih–Marangoni instability of the corresponding flow system in a rigid channel. The influence of the parameters on the critical Reynolds number for the shear mode is assessed. The study reveals that it is possible to control instabilities in interface dominated rigid channel flows by designing the walls of the channel as hydrophobic/rough/porous or undulated surfaces as these can be modeled as one with slip at the substrates.

NANOLAYERS FORMATION AT HYDRODYNAMIC INSTABILITY DEVELOPMENT UNDER THE EXTERNAL ENERGY EFFECTS

The attempt to interpret the experimentally established regularities of strengthening surface nanostructures formation under different energy effects (electro-explosive alloying, electron-beam treatment, rolling products thermomechanical strengthening due to accelerated cooling, severe mechanical action at long term operation) was made on unified position. The mathematical modeling of nanostructured states formation in consideration of equilibrium states instabilities development in surface layers (Kelvin–Helmholtz and Marangoni instabilities) was carried out, the corresponding dispersion equations were analyzed and the analytical dependences of instability decrement α on perturbation wave length λ in micro and nanoranges were established. The correspondence of numerical values of maximum observed on the α(λ) dependences to experimental nanostructure parameters was noted and its physical interpretation was made.