Session R39: Marangoni Effect

Marangoni meets Burgers: analytical solutions describing the formation of stagnant caps of surfactant

This talk will demonstrate the theoretical importance of a complex Burgers equation in describing unsteady surfactant evolution on interfaces at low Reynolds and capillary numbers. Methods familiar to fluid dynamicists from compressible gas dynamics, where the real Burgers equation is well known, are shown to be relevant also to Marangoni flows driven by surfactants. It will be shown that a nonlinear dynamical system governing insoluble surfactant evolution at an interface can be linearized, at arbitrary surface Peclet number, by a generalization of the Cole-Hopf transformation. And, at infinite surface Peclet number, exact solutions describing the time dependent formation of stagnant caps can be derived using a generalization of the method of characteristics.   

Direct Numerical Simulations of surfactant transport and Marangoni forces at the interface between two fluids

The dissolved molecules of surfactants present in liquid are adsorbed at the interface between two fluids and can modify the dynamics of drops, bubbles or waves. For example, the non-uniform distribution of surfactant while a bubble is rising results in gradients of surface tension at the interface and retards the rise velocity of the bubble (Levich, 1962) and modifies the dynamics (Tagawa et. al., 2013). These effects have been studied experimentally and theoretically. To study the effect of surfactants through Direct Numerical Simulations (DNS), we provide a numerical method for two-phase Navier-Stokes solver coupled with the surface transport equation for insoluble surfactants (Stone, 1990) using the Basilisk solver (Popinet 2023). The Marangoni force due to the surface tension gradient is modeled as a body force using a continuum surface model (Seric et. al 2018, Tripathi and Sahu 2018). We validate the method for mass conservation and surface convective transport of surfactants using analytical solutions. We perform DNS of rising bubble in quiescent liquid and show that the surfactants adsorbed at the bubble interface get transported due to the motion of fluids and get concentrated at the bottom of bubble. The rise velocity of bubble gets reduced compared to the case of clean bubble as well as the terminal shape. Other configurations such as surfactant effect on breaking waves or thin films could be investigated within this numerical framework.   

Interaction between a particle and a liquid surface covered by a surfactant

The interaction of particles with liquid surfaces takes place in many engineering processes. When the liquid surface is covered by a surfactant, the liquid motion creates its nonuniform distribution, which generates a Marangoni stress acting on the flow. We consider the motion of a spherical particle rising in a viscous fluid towards a surface covered by a surfactant, in the framework of the Stokes equation. The presence of the surfactant changes the flow significantly. It is shown that with the decrease of the distance between the particle and the surface, a "hole" free of the surfactant is created. Analytical and numerical solutions of the problem are obtained.   

Marangoni flows triggered by interactions of cationic-anionic surfactant mixtures

Marangoni flow, which is an interfacial flow triggered by surface tension gradients, is a topic of broad interest in complex fluids and interface communities. In this study, we investigate the interplay between cationic and anionic surfactant interactions in Marangoni flow patterns. By introducing a minute droplet of cationic surfactant into a bath of anionic surfactant, and vice versa, we observe diverse flow patterns resulting from the reactive transport of cationic-anionic surfactant mixtures due to surfactant-surfactant complexation. Our approach combines reaction kinetics, interfacial tension measurements, high-speed flow visualization, thermal imaging, and computational simulations to unravel the underlying mechanisms governing the observed flow phenomena. These insights shed light on the potential applications of our research, such as developing effective oil remediation techniques or understanding the spreading of waterborne pathogens in contaminated water bodies.   

Modeling Marangoni flows induced by photo-responsive surfactants

Photo-responsive surfactants can reversibly change their molecular conformation when illuminated, thereby tuning interfacial tensions in a multi-phase flow. These "photosurfactants" can therefore induce targeted and complex Marangoni flows, including droplet and bubble motion in the fluid interior or along interfaces, and may enable new avenues for enhancing the performance of microfluidic, thermal, and water harvesting devices. However, to the best of our knowledge, there are currently no general models for predicting the resulting flows from a given combination of photosurfactant type, geometry, illumination and fluid properties. As a consequence, the potential capabilities and benefits that could be derived from photosurfactants remain largely unknown. We examine several photosurfactants, and leverage experimental data from nuclear magnetic resonance, time-dependent tensiometry, as well as photosurfactant-driven flows of increasing complexity, both on Earth and in microgravity. We deduce models for the photo-switch mechanism and the attendant tension change, which we use to implement numerical simulations, as well as to derive scaling relations for several key flows of fundamental and technological importance.   

Thermo-Marangoni flows induced at a moving contact line

This work focuses on the flow near a contact line, which is induced when a plate is moved vertically on the water surface in its own plane. The aim is to investigate the influence of the difference between the water and plate temperatures and the plate speed on the induced flow. The temperature difference causes a thermocapillary flow near the contact line, and its direction depends on the direction of the temperature gradient. The plate speed, which is varied between 0.1 and 2 mm/s, also influences the flow speed. The flow field near the contact line is measured using the particle image velocimetry (PIV) technique. The velocity is obtained on a plane perpendicular to the water surface, and the temperature distribution is measured on the water surface using an infrared camera. The latter is used to estimate the strength of the thermo-Marangoni contribution.   

Bulk flow investigation of solutal Marangoni flow

Depositing isopropanol (IPA) drops in the microliter range on the surface of a deep water layer induces a Marangoni flow as a result of the surface tension difference between IPA and water. The IPA sits on the water surface forming a quasi-static lens. From the contact line of the lens, an IPA film spreads in a radial direction on the surface until it eventually retracts. During this spreading and retracting process, the IPA lens dissolves into the water completely. All this happens in a duration on the order of a second. While the spreading process is studied quite extensively, including models of the spreading speed and spreading extent, the flow that is induced in the water has so far only been studied qualitatively, which also applies for the retraction process. Using Particle Image Velocimetry (PIV), we investigated the bulk flow of such a solutal Marangoni flow including the formation and the development of the tip vortex that appears due to the IPA film spreading on the surface. In addition to the qualitative description of the flow pattern, we can provide quantitative results of the flow field as a function of the drop volumes. Up to now it remains not entirely clear why the retraction process of the IPA film appears and it is also unclear what the time-scale of its appearance is. With the bulk flow analysis we can provide some further insights on the mechanisms leading to the retraction of the IPA film, including the quantification of the amount of fresh water that is transported towards the IPA lens at the surface. The fresh water transported to the surface may explain why the Marangoni flow is reversed, since the fresh water leads to a reversal of the surface tension gradient as compared to the beginning of the process.   

Drainage-induced Marangoni flows in circular tubes and the double role of surface tension

In this study, the drainage-induced Marangoni effect of Sodium dodecyl sulfate (SDS) (concentration 1.44 g/L) added aqueous Methylene blue solution (concentration 0.1 – 10 g/L) was studied in circular tubes of variable diameter (within the order of 1mm). During the drainage process, we hypothesize that the sudden conversion of hydrostatic to inertial drainage imparts a gradient of SDS concentration on the surface causing a Marangoni-induced film climbing due to the surface tension gradient. The upward climbing velocity diminished with decreasing tube diameter indicating that capillarity due to the meniscus dampens the inertial impulse upon drainage, reducing the SDS concentration gradient and thus the Marangoni force.