Session R08: Surface Tension Effects: Marangoni Phenomena

Marangoni-driven spreading dynamics of ethanol-water mixture droplets on hydrogel surfaces

This study investigates the Marangoni-driven spreading of ethanol-water mixture droplets on hydrogel surfaces, aiming to develop potential technologies of controlling flow for drug delivery on bio surfaces, cleaning flexible displays and hydrogel coating. We conducted experiments to observe the spreading behavior of the binary mixture droplet on various hydrogel surfaces in two main setups: (1) modifying hydrogel properties through varying concentrations, drying, and surfactant addition, and (2) varying the concentrations of ethanol in water. We measured the time evolution of the spreading droplet radius R(t) using a high-speed camera. From the experimental results, we observed that the spreading rate exhibited various power-law trends depending on the initial and boundary conditions. In particular, we found that the ethanol droplet showed R~t^(1/3), which is different from the power-law with previous Marangoni spreading research. Furthermore, the change in spreading-rate due to ethanol concentration in the droplet was more significant (i.e.,R~t^(1/10) to R~t^(1/3)) than the change in spreading-rate due to variations in substrate properties (i.e.,R~t^(1/4) to R~t^(1/3)). At the talk, physical arguments to support the observations will be discussed.   

Unsteady bubble migration by nonlinear surfactant spreading

An analytical study of the unsteady nonlinear motion of an inviscid bubble due to surfactant spreading on its surface is presented. Similar modes of migration due to Marangoni effects are common in biological settings where insects such as microvelia strategically release surfactant at an interface to facilitate propulsion along it. This study adapts this phenomenology to study the following initial value problem: assuming a zero Reynolds and capillary number setting, what is the unsteady speed, and ultimate displacement, of a two-dimensional bubble on which an initial distribution of insoluble surfactant is set up that subsequently spreads around its surface causing it to migrate? Despite its multiphysics nature, it is shown that this nonlinear initial value problem can be solved in analytical form by leveraging new insights from a mathematical connection to a complex equation of Burgers type. Indeed it is shown to be linearizable at any finite surface Peclet number by a variant of the classical Cole-Hopf transformation.   

Time-scales of solutal Marangoni flow

Depositing a microliter isopropanol (IPA) drop on a deep water layer results in a complex mixing process of these fully soluble liquids. Due to the difference in surface tension, the IPA spreads in radial direction after forming a lens in the region of drop deposition. This film spreading reaches a finite radius until it eventually retracts, which is yet not entirely understood. Conducting the drop deposition experiments with IPA drops ranging from 7 to 80 µl, we can provide quantitative results regarding the spreading as well as the retraction time scales. Using particle imaging, we were able to derive the film radius over time and the flow field in the water layer. An analysis of this data enables the derivation of the physical laws involved in the spreading and retraction. Moreover, an estimation of the energy that is converted from the difference in surface tension into the kinetic energy of the bulk may help to estimate the amount of IPA that is actually spreading from the center of deposition compared to the amount of IPA that directly mixes with the water at the center of the IPA deposition.   

The thermocapillary-driven interface deformation and fluid flow in superimposed fluids

The goal of this study is to mimic the thermocapillary-driven flow of continuous fluid streams

in microchannels as a result of micropatterning of the heated wall, using Direct Numerical Simulations. To this end, we consider a

horizontal microchannel that is heated from below by imposing the upper wall to a uniform temperature

and the lower wall to a sinusoidal temperature that is higher (on average) than the temperature of the

upper wall. The equilibrium shape of the interface and the strength of the fluid flow are determined

as a function of the controlling nondimensional parameters of the problem. For small to moderate Marangoin numbers, 

the interface settles to an equilibrium sinusoidal shape; however, depending on the ratio of the thermophysical properties, its sense of the deformation will be concave up

or down. Beyond a critical Marangoni number, the interface deforms continuously and does not settle to an equilibrium shape.    

Manipulation of Multiphase Fluid in Microgravity using Photo-responsive Surfactants

Bubble manipulation is crucial for enhancing electrochemical reactions and heat transfer processes. Previous studies have relied on passive surface modifications or active external stimuli, which require complex fabrication or substantial energy inputs. To date, these methods have not achieved direct bubble control without involving solid surfaces. We report an approach using photo-responsive surfactants to control bubble movement. By programming low-power LEDs, we locally induce reversible changes in the surfactant molecules, altering surface tension and triggering Marangoni flow. To decouple Marangoni and buoyancy effects, we perform microgravity experiments, and successfully demonstrate real-time bubble manipulation.

The tested surfactant exhibits rapid and reversible photo-switching, allowing for long-term control. We achieve bubble propulsion with velocities up to 6 mm/s and accelerations reaching 5 mm/s² under LED illumination of only 38 mW/cm². Additionally, we develop numerical simulations to understand the dependence of bubble velocity on bubble size, switching kinetics, and light duration. These synergistic experimental and numerical findings provide key guidance for managing bubble dynamics in microgravity and designing new photo-surfactants for fluid dynamics.

Using light-actuated photosurfactants for liquid mixing and sculpting

Photosurfactants are soluble surface active agents that can change conformation under light of different frequencies. Under visible light they conform to the trans state, while illumination by shorter wavelength UV light transforms trans surfactants to the cis state by bending of their hydrocarbon tails. The process is reversible. This talk has two objectives. First, to introduce mathematical models that can describe the two surfactant species, their exchange kinetics in the bulk due to light switching, their adsorption/desorption from interfaces (e.g. air-water), and the exchange between them at the interface. Second, to use these models to study theoretically the fundamental problem the utilization of non-uniform light gradients to induce mixing and interfacial non-uniformities in horizontal liquid layers covering a substrate. It is shown that the induced Marangoni flows can produce vortical structures that enhance mixing. In addition, we solve the inverse problem to determine the required light gradients required to produce a pre-determined interfacial amplitudes.   

Light-actuated interfacial flows via photosurfactants: transient effects

Photo-surfactants, also known as light-actuated surfactants, are notable because they provide a means of external control for interfacial flows via light illumination. These surfactants are made up of a hydrophobic tail group and a hydrophilic head group separated by a light-responsive molecule that can reversibly toggle between two orientations (trans or cis) upon light absorption. Because the dominant orientation in a system is primarily a function of the wavelengths of incident light and the two states are characterized by markedly different interfacial properties, photo-surfactant systems can display significantly different values of equilibrium surface tension under different illumination wavelengths. This phenomenon has led to research on so-called chromo-capillarity, i.e. the use of light to drive flows via the formation of surfactant gradients on fluid interface. Experiments have shown systems with photo-surfactants can achieve non-negligible interfacial velocities immediately after illumination of an interface, but nearly all experiments observe a decay of these velocities to near zero at long term steady states. In this talk we discuss the system of PDEs that governs the fluid and surfactant dynamics and investigate this important transient regime via hybrid analytical and numerical methods, discussing among other things the potential of using photo-surfactants in combination with a superhydrophobic surface architecture to pump liquids.   

Retradation of vapor-driven solutal Marangoni effect due to vapor absorption in the droplet

Internal flow can be varied in an evaporating droplet due to changes in surface tension, driven by the Marangoni effect. Among various Marangoni effects, the solutal Marangoni effect is reported to be more significant than those driven by temperature and surfactants. In particular, vapor-driven solutal Marangoni flow, which avoids contamination, has been extensively studied for their potential in applications like mixing, coating, and droplet transport. However, most of previous research has focused on steady-state scenarios, considering only the adsorbed vapor on the droplet interface while overlooking vapor absorption in the droplet. In this talk, we present both experimental and numerical studies on the evolution of time-dependent internal flows and vapor mass flux across the droplet interface, considering vapor absorption. Our findings reveal that high absorption flux near the contact line induces a previously unreported transient inward-outward competing flow before the typical steady outward interfacial flow. This competing flow reduces flow magnitude in the early stages, and the duration of flow retardation is influenced by vapor source properties, such as solubility and vapor pressure, according to Henry's law. We propose that volatile liquids with lower solubility in water are more effective at generating vapor-driven solutal Marangoni flow compared to highly water-soluble liquids like ethanol and acetone, which have been typically used.   

Self-Similarity in Surfactant-Driven Particle Dispersion at Air-Water Interfaces

Many powders rapidly spread radially outward when they come into contact with the air-water interface. Previously, we showed that for non-Brownian (sub-millimetric) particles, this rapid spreading, typically at speeds of centimeters per second, can be significantly suppressed by appropriate cleaning. This suggests that fast and axisymmetric dispersion is primarily driven by surfactant-induced flow caused by common impurities [1].

In this work, we investigate the spreading behavior by varying the amount of surfactant mixed with clean particles. We track the particle spreading radius and the Marangoni-induced waves simultaneously. Our observations reveal that the particle spreading radius exhibits self-similar behavior across a wide range of surfactant concentrations. The Marangoni-induced wave fronts precede the particles, and the spreading dynamics can deviate from power laws once the wave hits the boundary. This indicates a strong coupling between Marangoni flow, capillary waves, and particles dispersion, which is crucial for understanding surfactant and particle transport at liquid interfaces.

[1] To, Kha-I., Rohit Vishwakarma, and Mahesh Bandi. "Effect of Particle Surface Properties on Dispersion at Air-Water Interface." Bulletin of the American Physical Society (2024).