Marangoni-driven flower-like patterning of an evaporating drop spreading on a liquid substrate

Ring-shaped colloidal patterns on saline water films

HYPOTHESIS

Electrostatically stabilised colloidal particles destabilise when brought into contact with cations causing the particles to aggregate in clusters. When a drop with stabilised colloidal partices is deposited on a liquid film containing cations the delicate balance between the fluid-mechanical and physicochemical properties of the system governs the spreading dynamics and formation of colloidal particle clusters.

EXPERIMENTS

High-speed imaging and digital holographic microscopy were used to characterise the spreading process.

FINDINGS

We reveal that a spreading colloidal drop evolves into a ring-shaped pattern after it is deposited on a thin saline water film. Clustered colloidal particles aggregate into larger trapezoidally-shaped 'supraclusters'. Using a simple model we show that the trapezoidal shape of the supraclusters is determined by the transition from inertial spreading dynamics to Marangoni flow. These results may be of interest to applications such as wet-on-wet inkjet printing, where particle destabilisation and hydrodynamic flow coexist.

Volatile Droplets on Water are Sculpted by Vigorous Marangoni-Driven Subphase Flow

The shapes of highly volatile oil-on-water droplets become strongly asymmetric when they are out of equilibrium. The unsaturated organic vapor atmosphere causes evaporation and leads to a strong Marangoni flow in the bath, unlike that previously seen in the literature. Inspecting these shapes experimentally on millisecond and submillimeter time and length scales and theoretically by scaling arguments, we confirm that Marangoni-driven convection in the subphase mechanically stresses the droplet edges to an extent that increases for organic droplets of smaller contact angle and accordingly smaller thickness. The viscous stress generated by the subphase overcomes the thermodynamic Laplace pressure. The oil droplets develop copious regularly spaced fingers, and these fingers develop spike-shaped and branched treelike structures. Unlike this behavior for single-component (surfactant-free) oil droplets, droplets composed of two miscible (surfactant-free) organic liquids develop a rim of the less volatile component along the droplet perimeter, from which jets of monodisperse smaller droplets eject periodically due to the Rayleigh-Plateau instability. When evaporation shrinks droplets to μm size, their shapes fluctuate chaotically, and ellipsoidal shapes rupture into smaller daughter droplets when subphase convection flow pulls them in opposite directions. The shape of the evaporating oil droplets is kneaded and sculpted by vigorous flow in the water subphase.

Evaporation-induced fractal patterns: A bridge between uniform pattern and coffee ring

HYPOTHESIS

The rich variety of patterns induced by evaporating drops containing particles has significant guidance for coating processes, inkjet printing, and nanosemiconductors. However, most existing works construct a uniform pattern by suppressing the coffee ring effect, and establishing the connection between them is still an academic challenge.

EXPERIMENTS

We report uniform, polygonal, and coffee ring patterns obtained by adjusting the solute concentration that sets in when an ethanol drop with dissolved ibuprofen is deposited on a silicon wafer.

FINDINGS

Pattern formation involves rich hydrodynamic events: spreading, evaporative instability, dewetting, film formation, and particle deposition. Based on the distinct multiscale properties, this series of patterns is directly connected from the perspective of fractal geometry, which allows us to name them "fractal deposition patterns". A theoretical model considering film stability is established to explain the mechanism behind pattern formation, which is well verified by experiments. This work has presented a unique strategy that can directly connect uniform, polygonal, and coffee ring patterns under the same physics, hoping to provide instructive guidance for practical applications.

Generation of Fermat's spiral patterns by solutal Marangoni-driven coiling in an aqueous two-phase system

The solutal Marangoni effect is attracting increasing interest because of its fundamental role in many isothermal directional transport processes in fluids, including the Marangoni-driven spreading on liquid surfaces or Marangoni convection within a liquid. Here we report a type of continuous Marangoni transport process resulting from Marangoni-driven spreading and Marangoni convection in an aqueous two-phase system. The interaction between a salt (CaCl₂) and an anionic surfactant (sodium dodecylbenzenesulfonate) generates surface tension gradients, which drive the transport process. This Marangoni transport consists of the upward transfer of a filament from a droplet located at the bottom of a bulk solution, coiling of the filament near the surface, and formation of Fermat's spiral patterns on the surface. The bottom-up coiling of the filament, driven by Marangoni convection, may inspire automatic fiber fabrication.

Complexity and bifurcations in the motion of a self-propelled rectangle confined in a circular water chamber

We consider the motion of a self-propelled object of rectangular shape inside a circular water chamber. The mathematical model of self-motion includes equations for the orientation and location of the rectangle and reaction-diffusion equation with an effective diffusion coefficient for the time evolution of the surface concentration of active molecules. Numerical simulations of motion were performed for different values of the ratio between the supply rate S and the evaporation rate a of active molecules. Treating S₀ = S/a as a control parameter, we found the critical behavior in variables characterizing the trajectory and identified different types of motion. If the value of S₀ is small, the rectangle rests at the chamber center. For larger S₀, a reciprocal motion during which the rectangle passes through the center is observed. At yet higher supply rates, the star-polygonal motion appears, and the trajectory remains at a distance from the chamber center. In the experiments with a rectangle made of camphor-camphene-polypropylene plastic moving in a Petri dish, we observed the transition from the star-polygonal motion to the reciprocal motion in time. This transition can be understood on the basis of the developed model if we assume that the supply rate decreases in time.

Visual Sensing System to Investigate Self-Propelled Motion and Internal Color of Multiple Aqueous Droplets

This study proposes a visual sensing system to investigate the self-propelled motions of droplets. In the visual sensing of self-propelled droplets, large field-of-view and high-resolution images are both required to investigate the behaviors of multiple droplets as well as chemical reactions in the droplets. Therefore, we developed a view-expansive microscope system using a color camera head to investigate these chemical reactions; in the system, we implemented an image processing algorithm to detect the behaviors of droplets over a large field of view. We conducted motion tracking and color identification experiments on the self-propelled droplets to verify the effectiveness of the proposed system. The experimental results demonstrate that the proposed system is able to detect the location and color of each self-propelled droplet in a large-area image.

Periodic Motion in the Chaotic Phase of an Unstirred Ferroin-Catalyzed Belousov Zhabotinsky Reaction

The Belousov Zhabotinsky reaction, a self-organized oscillatory color-changing reaction, can show complex behavior when left unstirred in a cuvette environment. The most intriguing behavior is the transition from periodicity to chaos and back to periodicity as the system evolves in time. It was shown that this happens thanks due to the decoupling of reaction, diffusion and convection. We have recently discovered that, as the so-called chaotic transient takes place, periodic bulk motions in form of convective cells are created in the reaction solution. In this work we investigated this phenomenon experimentally by changing cuvette size and reaction volume, in order to allow different types of convection patterns to appear. So far, we have observed single and double convection cells in the system. There are indications that the convection patterns are connected to the duration of the chaotic phase. A simplified mathematical model confirms the form and dynamics of the observed convection cells and explains the connection between chemical chaos and hydrodynamical order.

Wall-Confined Spreading Dynamics on the Surface of Surfactant Solution

A liquid spreading over another is a universal physical process in the nature, which was investigated by the scaling law to reveal the underlying mechanical mechanism over the decades. However, scaling laws are restricted to piecewise physical stages, respectively. It is a challenge to present a full physical picture for a dynamic spreading process covering a wide-spectrum speed. We propose a general wall-confined spreading dynamics (WCSD) model originating from molecular kinetic theory (MKT). It creatively illustrates the order and domination between driving energy and energy dissipation (or transfer) using a phase diagram according to theory and experiments. This work reveals the deep mechanical mechanism of WCSD which provides an indirect guidance on the solution processing methods of two-dimensional molecular crystals (2DMCs) growth.

Size-Dependent Dried Colloidal Deposit and Particle Sorting via Saturated Alcohol Vapor-Mediated Sessile Droplet Spreading

We experimentally and theoretically investigate a distinct problem of spreading, evaporation, and the associated dried deposits of a colloidal particle-laden aqueous sessile droplet on a surface in a saturated alcohol vapor environment. In particular, the effect of particle size on monodispersed suspensions and efficient self-sorting of bidispersed particles have been investigated. The alcohol vapor diffuses toward the droplet's curved liquid-vapor interface from the far field. The incoming vapor mass flux profile assumes a nonuniform pattern across the interface. The alcohol vapor molecules are adsorbed at the liquid-vapor interface, which eventually leads to absorption into the droplet's liquid phase due to the miscibility. This phenomenon triggers a liquid-vapor interfacial tension gradient and causes a reduction in the global surface tension of the droplet. This results in a solutal Marangoni flow recirculation and spontaneous droplet spreading. The interplay between these phenomena gives rise to a complex internal fluid flow within the droplet, resulting in a significantly modified and strongly particle-size-dependent dried colloidal deposit. While the smaller particles form a multiple ring pattern, larger particles form a single ring, and additional "patchwise" deposits emerge. High-speed visualization of the internal liquid-flow revealed that initially, a ring forms at the first location of the contact line. Concurrently, the Marangoni flow recirculation drives a collection of particles at the liquid-vapor interface to form clusters. Thereafter, as the droplet spreads, the smaller particles in the cluster exhibit a "jetlike" outward flow, forming multiple ring patterns. In contrast, the larger particles tend to coalesce together in the cluster, forming the "patchwise" deposits. The widely different response of the different-sized particles to the internal fluid flow enables an efficient sorting of the smaller particles at the contact line from bidispersed suspensions. We corroborate the measurements with theoretical and numerical models wherever possible.

Marangoni spreading and contracting three-component droplets on completely wetting surfaces

SignificanceThe shape and dynamics of small sessile droplets are dictated by capillary forces. For liquid mixtures, evaporation adds spatio-temporal modulation to these forces that can either enhance or inhibit droplet spreading, depending on the direction of the resulting Marangoni flow. This work experimentally and numerically demonstrates the coexistence of two antagonistic Marangoni flows in a ternary mixture. Played against each other, they can choreograph a boomerang-like wetting motion: Droplets initially rapidly spread, then contract into a compact cap shape. While such a behavior has been impossible in wetting scenarios of simple liquids, it enables spread-retract-remove surface processing with the addition of a single small liquid volume, demonstrated here in a surface-cleaning experiment.

An alternate approach to simulate the dynamics of perturbed liquid drops

Liquid drops when subjected to external periodic perturbations can execute polygonal oscillations. In this work, a simple model is presented that demonstrates these oscillations and their characteristic properties. The model consists of a spring-mass network such that masses are analogous to liquid molecules and the springs correspond to intermolecular links. Neo-Hookean springs are considered to represent these intermolecular links. The restoring force of a neo-Hookean spring depends nonlinearly on its length such that the force of a compressed spring is much higher than the force of the spring elongated by the same amount. This is analogous to the incompressibility of liquids, making these springs suitable to simulate the polygonal oscillations. It is shown that this spring-mass network can imitate most of the characteristic features of experimentally reported polygonal oscillations. Additionally, it is shown that the network can execute certain dynamics, which so far have not been observed in a perturbed liquid drop. The characteristics of dynamics that are observed in the perturbed network are polygonal oscillations, rotation of network, numerical relations (rational and irrational) between the frequencies of polygonal oscillations and the forcing signal, and that the shape of the polygons depends on the parameters of perturbation.

Self-Organized Liquid Crystal Droplets as Phototunable Softmasks

A single-step self-organized pathway is harnessed to generate large-area and high-density liquid-crystal (LC) microdroplets via rapid spreading of an LC-laden volatile liquid film on an aqueous surfactant bath. The surfactant loading on the water bath and LC loading in the solvent fluid help in tuning the size, periodicity, and ordering of LC microdroplets. Remarkably, the experiments reveal a transition from a spinodal to heterogeneous nucleation pathway of dewetting when the surfactant loading is modulated from below to beyond the critical micellar concentration in the aqueous phase. In the process, a host of unprecedented drop formation modes, such as dewetting and contact-line instability, random ejection, and "fire cracker" toroid splitting, have been uncovered. Subsequently, the LC microdroplets on the air-water interface are employed as photomasks suitable for soft-photolithography applications. Such masks help in the decoration of a host of mesoscale three-dimensional features on the films of photoresists when photons are guided through the LC droplets. In such a scenario, phase transition of LC droplets under solvent vapor annealing is employed to control the movement of photons through drops and subsequently modulate the light exposure on the photoresist surface. Such a simple soft-photolithography setup leads to an array of flattened droplets on a positive resist, while donut features are observed on the negative tone. Remarkably, the orientation of nematogens within 4-cyano-4'-pentylbiphenyl droplets and at the three-phase contact-line provides additional handles in controlling the transmission of photons, which facilitates such a unique pattern formation. A number of low-cost and simple strategies are also discussed to order such soft-photolithography patterns. Importantly, with a minor modification to the same experimental setup, we could also measure the variation in the order parameter of the LC droplet during its phase transitions from the nematic to isotropic state.

Compound jetting from bubble bursting at an air-oil-water interface

Bursting of bubbles at a liquid surface is ubiquitous in a wide range of physical, biological, and geological phenomena, as a key source of aerosol droplets for mass transport across the interface. However, how a structurally complex interface, widely present in nature, mediates the bursting process remains largely unknown. Here, we document the bubble-bursting jet dynamics at an oil-covered aqueous surface, which typifies the sea surface microlayer as well as an oil spill on the ocean. The jet tip radius and velocity are altered with even a thin oil layer, and oily aerosol droplets are produced. We provide evidence that the coupling of oil spreading and cavity collapse dynamics results in a multi-phase jet and the follow-up droplet size change. The oil spreading influences the effective viscous damping, and scaling laws are proposed to quantify the jetting dynamics. Our study not only advances the fundamental understanding of bubble bursting dynamics, but also may shed light on the airborne transmission of organic matters in nature related to aerosol production.

Propelling microdroplets generated and sustained by liquid-liquid phase separation in confined spaces

Flow transport in confined spaces is ubiquitous in technological processes, ranging from separation and purification of pharmaceutical ingredients by microporous membranes and drug delivery in biomedical treatment to chemical and biomass conversion in catalyst-packed reactors and carbon dioxide sequestration. In this work, we suggest a distinct pathway for enhanced liquid transport in a confined space via propelling microdroplets. These microdroplets can form spontaneously from localized liquid-liquid phase separation as a ternary mixture is diluted by a diffusing poor solvent. High speed images reveal how the microdroplets grow, break up and propel rapidly along the solid surface, with a maximal velocity up to ∼160 μm s-1, in response to a sharp concentration gradient resulting from phase separation. The microdroplet propulsion induces a replenishing flow between the walls of the confined space towards the location of phase separation, which in turn drives the mixture out of equilibrium and leads to a repeating cascade of events. Our findings on the complex and rich phenomena of propelling droplets suggest an effective approach to enhanced flow motion of multicomponent liquid mixtures within confined spaces for time effective separation and smart transport processes.

Spontaneous Motion and Rotation of Acid Droplets on the Surface of a Liquid Metal

Self-propulsion of droplets is of great significance in many fields. The spontaneous horizontal motion and self-jumping of droplets have been well realized in various ways. However, there is still a lack of an effective method to enable a droplet to rotate spontaneously and steadily. In this paper, by employing an acid droplet and a liquid metal, the spontaneous and steady rotation of droplets is achieved. For an acid droplet, it may spontaneously move when it is deposited on the surface of the liquid metal. By adjusting experimental parameters to the proper range, the self-rotation of droplet happens. This phenomenon originates from the fluctuation of the droplet boundary and the collective movement of bubbles that are generated by the chemical reactions between the acid droplet and liquid metal. This rotation has a simpler implementation method and more steady rotation state. Its angular velocity is much higher than that driven by other mechanisms. Moreover, the movements of acid droplets on the liquid metal are classified according to experimental conditions. The internal flow fields, the movements and distribution of bubbles, and the fluctuation of the droplet boundary are also explored and discussed. The theoretical model describing the rotational droplet is given. Our work may deepen the understanding of the physical system transition affected by chemical reactions and provide a new way for the design of potential applications, e.g., micro- and nanodevices.

Hydrodynamic Process in the Langmuir-Blodgett Film Method

Preparing organic coatings in a very controlled manner through the spreading of organic molecules on the water surface is one of the emphases for research in Langmuir-Blodgett (LB) technology. For preparing a homogeneous film and improving the quality of the film, it is our concern to have a deeper understanding of the dynamic process involved in spreading. Here, we present an overview of the hydrodynamic process under the influence of assisting the spreading solvent, which mainly focuses on the mechanical mechanisms of related phenomena. A typical spreading experiment of two-component mixed droplets on water substrate for the purpose of preparing LB films was carried out in this research. We perform the spreading of a liquid of silicone oil and oleic acid mixture on the horizontal surface of another immiscible deep water substrate, where the volatile silicone oil is the assisting spreading solvent with low viscosity. We find that it needs to exceed a certain critical value (60% in our experiment) to achieve a uniform and centrosymmetric spreading process, which is a key factor for getting a homogeneous film. We observe that the evolution of a large droplet into liquid film and then into small droplets under the action of surface tension gradient in experiments. Gravity-viscous and surface tension-viscous dominate successively in the whole spreading process, with its spreading radius r(t) ∝ t^1/4 and r(t) ∝ t^3/4, respectively. However, we also obtain singular values of scaling exponents -0.033 and -0.180, which is attributed to nonuniform distribution of the Laplace pressure caused by different curvatures near the capillary wave.

Stability of a directional Marangoni flow

Marangoni flows result from surface-tension gradients, and these flows occur over finite distances on the surface, but the subsequent secondary flows can be observed on much larger lengthscales. These flows play major roles in various phenomena, from foam dynamics to microswimmer propulsion. We show here that if a Marangoni flow of soluble surfactants is confined laterally, the flow forms an inertial surface jet. A full picture of the flows on the surface is exhibited, and the velocity profile of the jet is predicted analytically, and is successfully compared with the experimental measurements. Moreover, this straight jet eventually destabilizes into meanders. A quantitative comparison between the theory and our experimental observations yields a very good agreement in terms of critical wavelengths. The characterization and understanding of the 2D flows generated by confined Marangoni spreading is a first step to understand the role of inertial effects in the Marangoni flows with and without confinement.

Spreading of soap bubbles on dry and wet surfaces

The spreading of soap bubbles after forming contact with a substrate is experimentally studied. We find for dry glass substrate that the rim of the spreading soap bubble follows the well known scaling law for inertia dominated spreading \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r \sim t^{1/2}$$\end{document}r∼t1/2 [Eggers, J., Lister, J., and Stone, H., J. Fluid Mech. 401, 293–310 (1999)]. Varying the viscosity of the soap solutions and the coating of the glass does not affect this spreading behavior qualitatively. Yet, on a wetted surface, the rim obtains a constant radial velocity. Here, the rim splits into two and this new rim trails the main rim. Interestingly, the central film enclosed by the two rims develops radially oriented wrinkles.

Effect of a product on spontaneous droplet motion driven by a chemical reaction of surfactant

We focus on the self-propelled motion of an oil droplet within an aqueous phase or an aqueous droplet within an oil phase, which originates from an interfacial chemical reaction of surfactant. The droplet motion has been explained by mathematical models, which require the assumption that the chemical reaction increases the interfacial tension. However, several experimental reports have demonstrated self-propelled motion with the chemical reaction decreasing the interfacial tension. Our motivation is to construct an improved mathematical model, which explains these experimental observations. In this process, we consider the concentrations of the reactant and product on the interface and of the reactant in the bulk. Our numerical calculations indicate that the droplet potentially moves in the cases of both an increase and a decrease in the interfacial tension. In addition, the reaction rate and size dependencies of the droplet speed observed in experiments were well reproduced using our model. These results indicate the potential of our model as a universal one for droplet motion.

Robust Method to Determine Critical Micelle Concentration via Spreading Oil Drops on Surfactant Solutions

The spreading of a liquid on another is often encountered in oil spills and coatings and is also of industrial relevance in pharmaceuticals and petrochemicals. In this study, the spreading of oil drops on aqueous solutions containing cationic, anionic, and nonionic surfactants over a wide range of surfactant concentrations is investigated. The spreading behavior quantified by measuring the time evolution of the projected area of the oil lens reveals the occurrence of a maximum, which is strongly dependent on the concentration of the surfactant in the aqueous solution. Our experiments show that this dependence is different at concentrations above and below the critical micelle concentration (CMC) of the surfactant and can be captured by two straight lines of different slopes. Interestingly, these two straight lines intersect at a concentration that coincides with the CMC of the surfactants in solution. We find that this behavior is universal as shown by performing experiments with different types of surfactants, their purity, and other system variables. Thus, we propose a method to unambiguously determine the CMC of surfactant solutions compared to the conventional techniques. The proposed method is simple, versatile, and applicable for the determination of CMC of both ionic and nonionic surfactants.

Flower-like droplets obtained by self-emulsification of a phase-separating (SEPS) aqueous film

Self-emulsification, referring to the spontaneous formation of droplets of one phase in another immiscible phase, is attracting growing interest because of its simplicity in creating droplets. Existing self-emulsification methods usually rely on phase inversion, temperature cycling, and solvent evaporation. However, achieving spatiotemporal control over the morphology of self-emulsified droplets remains challenging. In this work, a conceptually new approach of creating both simple and complex droplets by self-emulsification of a phase-separating (SEPS) aqueous film, is reported. The aqueous film is formed by depositing a surfactant-laden aqueous droplet onto an aqueous surface, and the fragmentation of the film into droplets is triggered by a wetting transition. Smaller and more uniform droplets can be achieved by introducing liquid-liquid phase separation (LLPS). Moreover, properly modulating quadruple LLPS and film fragmentation enables the creation of highly multicellular droplets such as flower-like droplets stabilized by the interfacial self-assembly of nanoparticles. This work provides a novel strategy to design aqueous droplets by LLPS, and it will inspire a wide range of applications such as membraneless organelle synthesis, cell mimics and delivery.

Tuning Contact Line Dynamics and Deposition Patterns in Volatile Liquid Mixtures

The spreading of a pure, volatile liquid on a wettable substrate has been studied in extensive detail. Here we show that the addition of a miscible, nonvolatile liquid can strongly alter the contact line dynamics and the final liquid deposition pattern. We observe two distinct regimes of behavior depending on the relative strength of solutal Marangoni forces and surface wetting. Fingerlike instabilities precede the deposition of a submicron thick film for large Marangoni forces and small solute contact angles, whereas isolated pearl-like drops emerge and are deposited in quasicrystalline patterns for small Marangoni forces and large solute contact angles. This behavior can be tuned by directly varying the contact angle of the solute liquid on the solid substrate.

Interfacial Dynamics in the Spontaneous Motion of an Aqueous Droplet

Self-propelled droplets can spontaneously move using chemical energy. In several reports of self-propelled droplets, interfacial chemical reactions occur at the oil/aqueous interface to induce the Marangoni flow. While the dynamics of interfacial tension is essential to the droplet motion, there are few reports that quantitatively discuss the moving mechanism based on interfacial tension measurements. In this study, we focused on the self-propelled motion of an aqueous droplet in the oil phase, where the surfactant monoolein reacts with bromine at the interface, and estimated the physicochemical parameters related to the droplet motion based on the time series of interfacial tension. These results may reveal the general mechanism for the self-propelled motion of aqueous/oil droplets driven by the interfacial chemical reaction.

Information transmission by Marangoni-driven relaxation oscillations at droplets

Marangoni-driven relaxation oscillations can be observed in many systems where concentration gradients of surface-active substances exist. In the present paper, we describe the experimentally observed coupling between relaxation oscillations at neighboring droplets in a concentration gradient. By a numerical parameter study, we evaluate the oscillation characteristics depending on relevant material parameters and the pairwise droplet distance. Based on these findings, we demonstrate that hydrodynamic interaction in multidroplet configurations can lead to a synchronization of the oscillations over the whole ensemble. This effect has the potential to be used as a novel approach for information transmission in microfluidic applications.