Fingering instability in thin wetting films.

Marangoni flow is the motion induced by a surface tension gradient along a fluid–fluid interface. In this study, we report a Marangoni flow generated when a bath of surfactant contacts a pre-wetted film of deionized water on a vertical substrate. The thickness profile of the pre-wetted film is set by gravitational drainage and so varies with the drainage time. The surface tension is lower in the bath due to the surfactant, and thus a liquid film climbs upwards along the vertical substrate due to the surface tension difference. Particle tracking velocimetry is performed to measure the dynamics in the film, where the mean fluid velocity reverses direction as the draining film encounters the front of the climbing film. The effect of the surfactant concentration and the pre-wetted film thickness on the film climbing is then studied. High-speed interferometry is used to measure the front position of the climbing film and the film thickness profile. As a result, higher surfactant concentration induces a faster and thicker climbing film. Also, for high surfactant concentrations, where Marangoni driving dominates, increasing the film thickness increases the rise speed of the climbing front, since viscous resistance is less important. In contrast, for low surfactant concentrations, where Marangoni driving balances gravitational drainage, increasing the film thickness decreases the rise speed of the climbing front while enhancing gravitational drainage. We rationalize these observations by utilizing a dimensionless parameter that compares the magnitudes of the Marangoni stress and gravitational drainage. A model is established to analyse the climbing front, either in the Marangoni-driving-dominated region or in the Marangoni-balanced drainage region. Our work highlights the effects of the gravitational drainage on the Marangoni flow, both by setting the thickness of a pre-wetted film and by resisting the film climbing.

Effect of nonionic surfactant on wetting behavior of an evaporating drop under a reduced pressure environment

Italian physicist Carlo Marangoni published a treatise in 1865 which first described the spontaneous flow of a liquid film caused by gradients in surface t ension at a gas/liquid interface. Such gradients are established by variations in surface concentration of molecular species which lower the surface tension in proportion to the interface concentration. While the dynamics and power law behavior of the initial circular advancing front in surfactant coated films has been studied for about two decades, there has been relatively little work conducted on characterizing the fractal spreading patterns which develop behind this front. In this thesis, we examine the dynamics of front propagation and subsequent fractal evolution in ultrathin liquid films of glycerol driven to spread by concentration gradients in Aerosol OT, an insoluble anionic surfactant. We vary only the initial deposition volume and concentration while maintaining the initial liquid film thickness at 2.5 microns. Contrary to theoretical analyses in the literature, our results reveal that the coefficient and exponent characterizing the advance of both the first front as well as the following unstable front is not a constant depending only on geometry (i.e. rectilinear vs axisymmetric spreading) but varies with the initial surfactant concentration of the deposition volume. Furthermore, the overall speed of the fronts is observed to increase with ambient relative humidity, an effect we ascribe to a reduction in the viscosity of the glycerol film clue to absorption of water from the ambient atmosphere. Only in cases of relatively high humidity (higher than approximately 40% relative humidity) do we observe the formation of fractal patterns in the unstable front. Measurements of the fractal dimension yield values in the range 1.45-1.65. The largest values approximate those fractal dimensions observed in systems undergoing diffusion driven aggregation or viscous fingering, neither of which mechanism is pertinent to Marangoni flow.

Foaming, foam films, antifoaming and defoaming

Thermocapillary convection in a two-layer fluid system with flat interface

The dynamical behaviour of a Newtonian reacting interface separating two homogeneous incompressible and semi-infinite Newtonian fluids is considered. The temperature is constant and uniform, electrical effects are not taken into account and the system is maintained in non-equilibrium conditions. Indeed, surfactants cross the interface where they are free to react and to diffuse. The surface tension depends on the interfacial concentrations of surfactants through an interfacial equation of state. The interfacial chemi-diffusion, adsorption–desorption and convective processes determine the surface tension and its variations. This provides a link between chemical and mechanical effects. Indeed, according to the Marangoni equation, a surface tension gradient is compensated for by the mechanical forces acting on the interface, especially the viscous tractions of the bulk phases. The Scriven theory of interfacial hydrodynamics is the starting point for a linear analysis of interfacial mechano-chemical stability. Our purpose is to obtain the conditions for the occurrence of surface motions and deformations in a system initially at rest and characterized by a flat interface. In the present treatment, the surface chemi-diffusion steps, the adsorption–desorption and the surface convection processes are the only relaxation processes responsible for the instability. We consider a mono-enzymatic Michaelian surface reaction catalysing the deprotonation of a substrate. In addition to a monoprotonated active form, the enzyme exists in unprotonated and biprotonated inactive forms. The reaction rate is then a function of the pH of the reacting medium. Consequently, the reaction is auto-exalted for a range of values of pH > pH(where the peculiar value pH corresponds to the optimum enzyme activity), while for pH < pH, it is auto-inhibited. We show that aperiodic (time) hydrodynamic and chemical instabilities are possible in the non-autocatalytic conditions pH < pH when the chemical and convective processes are coupled. Quantitative and qualitative stability criteria are reported. The stability behaviour differs depending on whether the enzyme forms are soluble in the bulk phases or not. Indeed, when they are soluble, the instability occurs for a finite range of non-vanishing values of the wavenumber characterizing one normal mode of perturbation. Furthermore, the viscous effects then play an expected stabilizing role since increasing but finite values of the viscosity coefficients completely remove the instability. Finally, the smallest value of the chemical constraint compatible with a state of neutral stability (transitory régimes between aperiodically stable and unstable situations), i.e. the critical constraint, corresponds to a non-vanishing and finite value of the wavenumber. On the other hand, when the enzymes are insoluble in the bulk phases, the instability occurs for an infinite range of wavelengths. Furthermore, the instability is only removed for infinite values of the viscosity coefficients. Finally, the critical constraint now corresponds to an infinite wavelength. The results obtained are discussed and interpreted by invoking the Marangoni effect caused by the mechano-chemical processes considered.

A biharmonic stream function equation is solved analytically in axisymmetric toroidal coordinates for Stokes flow in a sessile droplet with a surface tension gradient and diffusive evaporation on the surface. Four different types of streamlines are defined and utilized to predict particle deposition either at the center or at the contact line of the droplet. The impact of UV light radius, droplet's contact angle, and humidity level on the flow pattern is investigated. When the relative humidity is high, the formation of Moffatt eddies is observed. However, the eddy size and the number of eddies decrease with an increase in UV light radius or droplet contact angle. As humidity decreases, the Moffatt eddies are restricted to a specific region, decrease in number and size, and ultimately disappear. Under lower humidity, the Marangoni flow near the contact line is dominated by capillary action. The toroidal streamlines are broken from outside and turned into transporting streamline to deposit more particles on the contact line. The region near the droplet center, where the surface tension gradient is significant, is always dominated by toroidal streamlines.

The linear stability of a thin film of volatile liquid flowing over a surface with embedded, regularly spaced heaters is investigated. The temperature gradients at the upstream edges of the heaters induce gradients in surface tension that create a pronounced non-uniformity in the film profile due to the formation of capillary ridges. The Governing equations for the evolution of the film thickness are derived within the lubrication approximation, and three important parameters that affect the dynamics and stability of the film are identified. The computed two-dimensional, steady solutions for the local film thickness reveal that due to evaporation there is a slight change in the height of capillary ridge at subsequent heaters downstream. Using a linear stability analysis, it is shown that, as for a single heater, the film is susceptible to two types of instabilities. A rivulet instability leads to spanwise-periodic rivulets, and an oscillating thermocapillary instability leads to streamwise, time-periodic oscillations in the film thickness. The critical Marangoni number is calculated for both types of instability for a range of parameter values. The effect of the number of heaters, heater width, and gap between the heaters on the critical Marangoni number is computed and analyzed. For small evaporation rates and less volatile films, the presence of multiple heaters has almost no noticeable effect on the film stability. For larger evaporation rates and more volatile films, additional heaters decrease the Marangoni number at instability onset. The destabilizing effect of multiple heaters is sensitive to the heater geometry and spacing. Furthermore, the limitations of streamwise periodic boundary conditions for analyzing the stability of such flows are discussed. Computations on the transient and nonlinear growth of perturbations are also presented and indicate that the results of eigenanalysis are physically determinant.

The Marangoni effect describes fluid flow near an interface in response to a surface tension gradient. Here, we demonstrate that the Marangoni effect is the underlying mechanism for flow driven feature formation in an azobenzene-containing polymer film; features formed in azobenzene-containing polymers are often referred to as surface relief gratings or SRGs. An amorphous poly(4-(acryloyloxyhexyloxy)-4′-pentylazobenzene) was synthesized and studied as a model polymer. To isolate the surface tension driven flow from the surface tension pattern inscription step, the surface tension gradient was preprogrammed via photoisomerization of azobenzene in a glassy polymer film without forming topographical features. Subsequently, the latent image was developed in the absence of light by annealing above the glass transition temperature where the polymer is a liquid. The polymer flow direction was controlled with precision by inducing different surface tension changes in the exposed regions, in accordance with expect...

Double-diffusive boundary layers along vertical free surfaces

Characterisation of hydraulic jumps/falls with surface tension variations in thin film flows

We consider a small droplet of water sitting on top of a heated superhydrophobic surface. A toroidal convection pattern develops in which fluid is observed to rise along the surface of the spherical droplet and to accelerate downwards in the interior towards the liquid/solid contact point. The internal dynamics arise due to the presence of a vertical temperature gradient; this leads to a gradient in surface tension which in turn drives fluid away from the contact point along the interface. We develop a solution to this thermocapillary-driven Marangoni flow analytically in terms of streamfunctions. Quantitative comparisons between analytical and experimental results, as well as effective heat transfer coefficients, are presented.

Surface tension gradient driven spreading of trisiloxane surfactant solution on hydrophobic solid

Fuelled chemical systems have considerable functional potential that remains largely unexplored. Here we report an approach to transient amide bond formation and use it to harness chemical energy and convert it to mechanical motion by integrating dissipative self-assembly and the Marangoni effect in a source-sink system. Droplets are formed through dissipative self-assembly following the reaction of octylamine with 2,3-dimethylmaleic anhydride. The resulting amides are hydrolytically labile, making the droplets transient, which enables them to act as a source of octylamine. A sink for octylamine was created by placing a drop of oleic acid at the air-water interface. This source-sink system sets up a gradient in surface tension, which gives rise to a macroscopic Marangoni flow that can transport the droplets in solution with tunable speed. Carbodiimides can fuel this motion by converting diacid waste back to anhydride. This study shows how fuelling at the molecular level can, via assembly at the supramolecular level, lead to liquid flow at the macroscopic level.

In this work, we used a previously described computational fluid dynamics (CFD) model of a roll‐to‐roll coating process for the fabrication of thin‐film composite membranes to predict the final coating thickness for PolyActive™, a commercially available multiblock copolymer utilized for CO2 removal membranes. We found a strong thickening effect that could not be explained by our previous model. We investigated the process experimentally. In addition, we conducted a variety of simulations with extensions of the initial CFD model. Based on our findings, we conclude that the Marangoni effect, that is, gradients of surface tension that induce secondary flow patterns in the meniscus region, is the most likely source of the observed thickening. We explain the simulation results in order to understand the physical mechanisms at play and to show how especially surface tension gradients that arise from the particular flow structure in the meniscus may explain the additional transfer of polymer solution to the membrane. Finally, we draw some conclusions on future research and give ideas on future improvements of the process. To our knowledge, Marangoni effects for the coating of PolyActive™ were not described so far in the literature, even though it is a well‐known polymer for gas separation membranes targeted at CO2 removal. Roll‐to‐roll coating is a well‐established coating method and often believed to be suitable for the scale‐up of membrane production, therefore we think that this work will help membrane researchers who are using similar coating devices to be cautious about possible complications in the process.