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The ability to transfer microdroplets between fluid phases offers numerous advantages in various fields, enabling better control, manipulation, and utilization of small volumes of fluids in pharmaceutical formulations, microfluidics, and lab-on-a-chip devices, single-cell analysis or droplet-based techniques for nanomaterial synthesis. This study focuses on the stability and morphology of a sessile oil microdroplet at the four-phase contact line of solid-water-oil-air during the droplet transfer from underwater to air. We observed a distinct transition in microdroplet dynamics, characterized by a shift from a scenario dominated by Marangoni forces to one dominated by capillary forces. In the regime dominated by Marangoni forces, the oil microdroplets spread in response to the contact between the water-air interface and the water-oil interface and the emergence of an oil concentration gradient along the water-air interface. The spreading distance along the four-phase contact line follows a power law relationship of $t^{3/4}$, reflecting the balance between Marangoni forces and viscous forces. On the other hand, in the capillarity-dominated regime, the oil microdroplets remain stable at the contact line and after being transferred into the air. We identify the crossover between these two regimes in the parameter space defined by three factors: the approaching velocity of the solid-water-air contact line ($v_{cl}$), the radius of the oil microdroplet ($r_o$), and the radius of the water drop ($r_w$). Furthermore, we demonstrate how to use the four-phase contact line for shaping oil microdroplets using a full liquid process by the contact line lithography. The findings in this study may be also applied to materials synthesis where nanoparticles, microspheres, or nanocapsules are produced by microdroplet-based techniques., Comment: 6 figures

Evaporation of multi-component liquid mixtures in confined geometries, such as capillaries, is crucial in applications such as microfluidics, two-phase cooling devices, and inkjet printing. Predicting the behaviour of such systems becomes challenging because evaporation triggers complex spatio-temporal changes in the composition of the mixture. These changes in composition, in turn, affect evaporation. In the present work, we study the evaporation of aqueous glycerol solutions contained as a liquid column in a capillary tube. Experiments and direct numerical simulations show three evaporation regimes characterised by different temporal evolutions of the normalised mass transfer rate (or Sherwood number, $Sh$), namely $Sh (\tilde{t}) = 1$, $Sh \sim 1/\sqrt{\tilde{t}}$, and $Sh \sim \exp\left(-\tilde{t}\right)$. Here $\tilde{t}$ is a normalised time. We present a simplistic analytical model which shows that the evaporation dynamics can be expressed by the classical relation $Sh = \exp \left( \tilde{t} \right) \mathrm{erfc} \left( \sqrt{\tilde{t}}\right)$. For small and medium $\tilde{t}$, this expression results in the first and second of the three observed scaling regimes, respectively. This analytical model is formulated in the limit of pure diffusion and when the penetration depth $\delta(t)$ of the diffusion front is much smaller than the length $L(t)$ of the liquid column. When $\delta \approx L$, finite length effects lead to $Sh \sim \exp\left(-\tilde{t}\right)$, i.e. the third regime. Finally, we extend our analytical model to incorporate the effect of advection and determine the conditions under which this effect is important. Our results provide fundamental insight into the physics of selective evaporation from a multi-component liquid column.

Switchable hydrophilicity solvents (SHSs) are solvents defined by their ability to switch from their hydrophobic form to a hydrophilic form when put in contact with an acidic trigger such as $CO_2$. As a consequence, SHSs qualify as promising alternatives to volatile organic compounds during the industrial solvent extraction processes, as greener and inexpensive methods can be applied to separate and recover SHSs. Furthermore, because of their less volatile nature, SHSs are less flammable and so increase the safety of a larger-scale extraction process. In this work, we study the dynamics and in-drop phase separation during the dissolution process of a drop composed of SHS and polymer, triggered by an acid in the surrounding aqueous environment. From 70 different experimental conditions, we found a scaling relationship between the drop dissolution time and initial volume with an overall scaling coefficient $\sim$ 0.53. We quantitatively assessed and found a shorter dissolution time related with a decrease in pH of the aqueous phase or an increase in initial polymer concentration in the drop. Examining the internal state of the drop during the dissolution revealed an in-drop phase separation behavior, resulting in a porous morphology of the final polymer particle. Our experimental results provide a microscopic view of the SHS dissolution process from droplets, and findings may help design SHS extraction processes for particle formation from emulsions., Comment: 15 pages, 8 figures

Asphaltene precipitation is a crucial phase separation phenomenon in the oil industry, especially in paraffinic froth treatment to extract bitumen from oil sands ores. This work reveals the formation of particles at 0.2 to 0.4 um in radius, defined as a primary sub-micron particle (PSMP), which is ubiquitous from diffusive mixing between asphaltene solution and any of 23 types of precipitants examined in our experiments. The yield and quantity of asphaltene particles are affected not only by the Hildebrand solubility parameter of the precipitants but also by the diffusion coefficients of the asphaltene solution and the precipitant. The Population Balance Model (PBM) with the Hildebrand solubility parameter has been used to model particle size distribution. Good agreement has been achieved between numerical predictions and the experimental data. It indicates that the colloid theory can describe the size distribution of PSMP and larger aggregates. Therefore, this study provides new insight into the mechanism for the dependence of yield and size distribution of the precipitated asphaltene particles on the composition of precipitants and adding inhibitors. Controlling of asphaltene yield and size distribution may be applied to the process of hydrocarbon separation or asphaltene precipitation prevention., Comment: Preprint submitted to Fuel

In this work, we unravel the role of surface properties of colloidal particles on the formation of supraparticles (clusters of colloidal particles) in a colloidal Ouzo droplet. Self-lubricating colloidal Ouzo droplets are an efficient and simple approach to form supraparticles, overcoming the challenge of the coffee stain effect in situ. Supraparticles are an efficient route to high-performance materials in various fields, from catalysis to carriers for therapeutics. Yet, the role of the surface of colloidal particles in the formation of supraparticles using Ouzo droplets remains unknown. Therefore, we used silica particles as a model system and compared sterically stabilized versus electrostatically stabilized silica particles - positively and negatively charged. Additionally, we studied the effect of hydration. Hydrated negatively charged silica particles and sterically stabilized silica particles form supraparticles. Conversely, dehydrated negatively charged silica particles and positively charged amine-coated particles form flat film-like deposits. Notably, the assembly process is different for all the four types of particles. The surface modifications alter (a) the contact line motion of the Ouzo droplet and (b) the particle-oil and particle-substrate interactions. These alterations modify the particle accumulation at the various interfaces, which ultimately determines the shape of the final deposit. Thus, by modulating the surface properties of the colloidal particles, we can tune the shape of the final deposit, from a spheroidal supraparticle to a flat deposit. In the future, this approach can be used to tailor the supraparticles for applications such as optics and catalysis, where the shape affects the functionality., Comment: 38 pages, 9 figures

The sensitive and reliable in-droplet chemical analysis benefits from the enhanced partition of an analyte into the droplets. This work, we will show that chemical reactions in surface nanodroplets can shift the partition of analytes from a highly diluted solution to the droplets. Seven types of organic acids with partition coefficients (LgP) ranging from -0.7 to 1.87 are used as model analytes dissolved in an oil solution that are extracted from the flow into aqueous nanodroplets immobilized on a substrate. The timescale of integrated extraction and reaction in droplets was represented by the decoloration time of the droplets. Our results show that the effective distribution coefficient of the analyte can be decreased by 3 to 11 times of the distribution coefficient of the analyte in the bulk liquids. The principle behind the significantly shifted partition is proposed to be enhanced the transfer of the analyte across the droplet surface. The chemical reaction in the droplets enhances the partition of the analyte from a highly diluted solution. Our results show that the interfacial behavior of the analyte may be advantageous as it may improve extraction and partition. Such enhanced extraction may be leveraged for sensitive chemical detection using reactive droplets.

Compartmentalizing reagents within small droplets is promising for highly efficient conversion and simplified procedures in many biphasic chemical reactions. In this work, surface nanodroplets (i.e., less than 100 nm in their maximal height) were employed to quantitatively understand the size effect on the chemical reaction rate of droplets. In our systems, a surface-active reactant in pure or binary nanodroplets reacted with the reactant in the bulk flow. Meanwhile, the product was removed from the droplet surface. The shrinkage rate of the nanodroplets was characterized by analyzing the lateral size as a function of time, where the droplet size was solely determined by chemical reaction rate at a given flow condition for the transport of the reactant and the product. We found that the overall kinetics increases rapidly with the decrease of droplets lateral radius R, as dR/dt ~ R^(-2). The faster increase in the concentration of the product in smaller droplets contributes to accelerating reaction kinetics. The enhancement of reaction rates from small droplet sizes was further confirmed when a non-reactive compound presented inside the droplets without reducing the concentrations of the reactant and the product on the droplet surface. The results of our study improve the understanding of chemical kinetics with droplets. Our findings highlight the effectiveness of small droplets for the design and control of enhanced chemical reactions in a broad range of applications.

How liquid transport occurs in confined spaces is relevant to many industrial and lab-scale processes, ranging from enhanced oil recovery to drug delivery systems. In this work, we investigate propelling microdroplets that form from liquid-liquid phase separation in a quasi-2D chamber, focusing on the direction and speed of microdroplets in response to local composition gradients. The confined ternary solution in our experiments comprises a model oil, a good solvent (ethanol) and a poor solvent (water). Depending on the initial solution composition, water-rich or oil-rich microdroplets, form and move spontaneously as the ternary solution mixes with and is displaced by water diffusing from a deep side channel. Microdroplet movement is followed in situ using high-speed bright-field imaging or fluorescence imaging when the solution is doped with a dye. Local ethanol composition gradients are estimated from the variation of fluorescence intensity in the local continuous liquid surrounding the mobile microdroplets. From phase separation of the ternary solution with high oil concentration, mobile oil-rich microdroplets form in a water-rich zone, accompanying the formation of water-rich microdroplets in an oil-rich zone. The fast movement of oil-rich microdroplets induces directional flow transport that mobilizes water-rich microdroplets close to the water-rich zone. The average microdroplet speed increases with the initial oil concentration in the ternary solution. The fastest speed of oil-rich microdroplets observed in our experiments is ~150 ${\mu}$m/s along the surface of a hydrophobic wall. The presence of a sharp ethanol composition gradient is the primary driving force for the fast movement of oil-rich microdroplets in confinement. Our results demonstrate the potential of enhancing liquid transport in confinement through composition gradients arising from phase separation., Comment: This is the authors' submitted version of the manuscript to Energy & Fuels

Cleaner analytic technique for quantifying compounds in dense suspension is needed for wastewater and environment analysis, chemical or bio-conversion process monitoring, biomedical diagnostics, food quality control among others. In this work, we introduce a green, fast, one-step method called nanoextraction for extraction and detection of target analytes from sub-milliliter dense suspensions using surface nanodroplets without toxic solvents and pre-removal of the solid contents. With nanoextraction, we achieve a limit of detection (LOD) of 10^(-9) M for a fluorescent model analyte obtained from a particle suspension sample. The LOD lower than that in water without particles 10^(-8) M, potentially due to the interaction of particles and the analyte. The high particle concentration in the suspension sample thus does not reduce the extraction efficiency, although the extraction process was slowed down up to 5 min. As proof of principle, we demonstrate the nanoextraction for quantification of model compounds in wastewater slurry containing 30 wt% sands and oily components (i.e. heavy oils). The nanoextraction and detection technology developed in this work may be used as fast analytic technologies for complex slurry samples in environment industrial waste, or in biomedical diagnostics., Comment: This is an unedited, original author's version of the manuscript

In this work, we investigate crystallization from droplets formed on micro-patterned surfaces. By solvent exchange in a micro-chamber, a ternary solution consisting of a model compound beta-alanine, water, and isopropanol, was displaced by a flow of isopropanol. In the process, oiling-out droplets formed and crystallized. Our results showed that the shape and size of the crystals on micro-patterned surfaces could be simply mediated by the flow conditions of solvent exchange. Varying flow rate, concentration, or channel height led to the formation of a thin film with micro-holes, connected network of crystals, or small diamond-shaped crystals. Rough micro-structures on the surface allowed the easy detachment of crystals from the surface. Beyond oiling-out crystallization, we demonstrated that the crystal formation from another solute dissolved in the droplets could be triggered by solvent exchange. The length of crystal fibers after the solvent exchange process was shorter at a faster flow rate. This study may provide further understanding to effectively obtain crystallization from surface droplets through the solvent exchange approach., Comment: 23 pages, 11 figures

Displacing liquid in a confined space is important for technological processes, ranging from porous membrane separation to CO$_{2}$ sequestration. The liquid to be displaced usually consists of multiple components with different solubilities in the displacing liquid. Phase separation and chemical composition gradients in the liquids can influence the displacement rate. In this work, we investigate the effects of liquid composition on the displacement process of ternary liquid mixtures in a quasi-2D microchannel where liquid-liquid phase separation occurs concurrently. We focused on model ternary mixtures containing 1-octanol, ethanol, and water. These mixtures are displaced with water or with ethanol aqueous solution. The spatial distribution of subphases arising from phase separation and the displacement rates of the solution are impacted by the initial ternary solution composition. The boundary between the solution and displacing liquid changes from a defined interface to a diffusive interface as the initial 1-octanol composition in the solution is reduced. The displacement rate also varies non-linearly with the initial 1-octanol composition. The slowest displacement rate arises in the intermediate 1-octanol concentration, where a stable three-zone configuration forms at the boundary. At very low 1-octanol concentration, the displacement rate is fast, associated with droplet formation and motion driven by the chemical concentration gradients formed during phase separation. The excessive energy provided from phase separation may contribute to the enhanced displacement at intermediate to high 1-octanol concentrations, but not at the low 1-octanol concentration with enhancement from induced flow in confinement. The knowledge gained from this study highlights the importance of manipulating phase separation to enhance mass transport in confinement for a wide range of separation processes., Comment: This is the authors' submitted version of the manuscript to Energy & Fuels

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 self-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 um/s, in response to a sharp concentration gradient resulting from phase separation. The microdroplet self-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 self-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., Comment: This is the authors' submitted version of the manuscript

In situ observation of precipitation or phase separation induced by solvent addition is important in studying its dynamics. Combined with optical and fluorescence microscopy, microfluidic devices have been leveraged in studying the phase separation in various materials including biominerals, nanoparticles, and inorganic crystals. However, strong scattering from the subphases in the mixture is problematic for in situ study of phase separation with high temporal and spatial resolution. In this work, we present a quasi-2D microfluidic device combined with total internal reflection microscopy as an approach for in situ observation of phase separation. The quasi-2D microfluidic device comprises of a shallow main channel and a deep side channel. Mixing between a solution in the main channel (solution A) and another solution (solution B) in the side channel is predominantly driven by diffusion due to high fluid resistance from the shallow height of the main channel, which is confirmed using fluorescence microscopy. Moreover, relying on diffusive mixing, we can control the composition of the mixture in the main channel by tuning the composition of solution B. We demonstrate the application of our method for in situ observation of asphaltene precipitation and beta-alanine crystallization., Comment: Preprint submitted to The European Physical Journal E

Droplet formation in oiling-out crystallization has important implication for separation and purification of pharmaceutical active ingredients by using an antisolvent. In this work, we report the crystallization processes of oiling-out droplets on surfaces during solvent exchange. Our model ternary solution is beta-alanine dissolved in isopropanol and water mixture. As the antisolvent isopropanol displaced the alanine solution pre-filled in a microchamber, liquid-liquid phase separation occurred at the mixing front. The alanine-rich subphase formed surface microdroplets that subsequently crystallized with progression of solvent exchange. We find that the flow rates have significant influence on the droplet size, crystallization process, and growth rate, and final morphology of the crystals. At fast flow rates the droplets solidified rapidly and formed spherical-cap structures resembling the shape of droplets, in contrast to crystal microdomains or thin films formed at slow flow rates. On a highly hydrophilic surface, the crystals formed thin film without droplets formed on the surface. We further demonstrated that by the solvent exchange crystals can be formed by using a stock solution with a very low concentration of the precursor, and the as-prepared crystals can be used as seeds to trigger crystallization in bulk solution. Our results suggest that the solvent exchange has the potential to be an effective approach for controlling oiling-out crystallization, which can be applied in wide areas, such as separation and purification of many food, medical, and therapeutic ingredients., Comment: Advanced Materials Interfaces (2020)

A combinative approach for chemical analysis makes it possible to distinguish a mixture of a large number of compounds from other mixtures in a single step. This work demonstrates a combinative analysis approach by using surface nanodroplets for integrating nanoextraction and colorimetric reactions for the identification of multi-component mixtures. The model analytes are acidic compounds dissolved in oil that are extracted into aqueous droplets on a solid substrate. The proton from acid dissociation reacts with the halochromic chemical compounds inside the droplets, leading to the color change of the droplets. The rate of the colorimetric reaction exhibits certain specificity for the acid type, distinguishing acid mixtures with the same pH value. The underlying principle is that the acid transport rate is associated with the partition coefficient and the dissociation constant of the acid, in addition to the concentration in oil. As a demonstration, we showed that droplet-based combinative analysis can be applied for anti-counterfeiting of various alcoholic spirits by comparing decolor time of organic acid mixtures in the spirits. The readout can be done by using a common hand-hold mobile phone.

The compartmentalization of chemical reactions within droplets has advantages in low costs, reduced consumption of reagents and increased throughput. Reactions in small droplets have also been shown to greatly accelerate the rate of many chemical reactions. The accelerated growth rate of nanobubbles from nanodroplet reactions is demonstrated in this work. The gaseous products from the reaction at the nanodroplet surface promoted nucleation of hydrogen nanobubbles within multiple organic liquid nanodroplets. The nanobubbles were confined within the droplets and selectively grew and collapsed at the droplet perimeter, as visualized by microscopy with high spatial and temporal resolutions. The growth rate of the bubbles was significantly accelerated within small droplets and scaled inversely with droplet radius. The acceleration was attributed to confinement from the droplet volume and effect from the surface area on the interfacial chemical reaction for gas production. The results of this study provide further understanding for applications in droplet enhanced production of nanobubbles and the on-demand liberation of hydrogen.

Biphasic chemical reactions compartmentalized in small droplets offer advantages, such as streamlined procedures for chemical analysis, enhanced chemical reaction efficiency and high specificity of conversion. In this work, we experimentally and theoretically investigate the rate for biphasic chemical reactions between acidic nanodroplets on a substrate surface and basic reactants in a surrounding bulk flow. The reaction rate is measured by droplet shrinkage as the product is removed from the droplets by the flow. In our experiments, we determine the dependence of the reaction rate on the flow rate and the solution concentration. The theoretical analysis predicts that the life time $\tau$ of the droplets scales with Peclet number $Pe$ and the reactant concentration in the bulk flow $c_{re,bulk}$ as $\tau\propto Pe^{-3/2}c_{re,bulk}^{-1}$, in good agreement with our experimental results. Furthermore, we found that the product from the reaction on an upstream surface can postpone the droplet reaction on a downstream surface, possibly due to the adsorption of interface-active products on the droplets in the downstream. The time of the delay decreases with increasing $Pe$ of the flow and also with increasing reactant concentration in the flow, following the scaling same as that of the reaction rate with these two parameters. Our findings provide insight for the ultimate aim to enhance droplet reactions under flow conditions.

Solvent exchange is a simple method to produce surface nanodroplets on a substrate for a wide range of applications by displacing a solution of good solvent, poor solvent and oil (Solution A) by a poor solvent (Solution B). In this work, we show that the growth and coalescence of nanodroplets on a homogeneous surface is mediated by the viscosity of the solvent. We show that at high flow rates of viscous Solution B, the final droplet volume deviates from the scaling law that correlates final droplet volume to the flow rate of non-viscous Solution B, reported in previous work. We attribute this deviation to a two-regime growth in viscous Solution B, where transition from an initial, fast regime to a final slow regime influenced by the flow rate. Moreover, viscous solution B hinders the coalescence of growing droplets, leading to a distinct bimodal distribution of droplet size with stable nanodroplets, in contrast to a continuous size distribution of droplets in non-viscous case. We demonstrate that the group of small droplets produced in high viscosity environment may be applied for enhanced fluorescence detection with higher sensitivity and shorter response time. The finding of this work can potentially be applied for mediating the size distribution of surface nanodroplets on homogeneous surface without templates., Comment: This is an unedited author's version of the submitted work that has been peer-reviewed and accepted in the Journal of Physical Chemistry C

Droplets abound in nature and technology. In general, they are multicomponent, and, when out of equilibrium, with gradients in concentration, implying flow and mass transport. Moreover, phase transitions can occur, with either evaporation, solidification, dissolution, or nucleation of a new phase. The droplets and their surrounding liquid can be binary, ternary, or contain even more components, and with several even in different phases. In the last two decades the rapid advances in experimental and numerical fluid dynamical techniques has enabled major progress in our understanding of the physicochemical hydrodynamics of such droplets, further narrowing the gap from fluid dynamics to chemical engineering and colloid & interfacial science and arriving at a quantitative understanding of multicomponent and multiphase droplet systems far from equilibrium, and aiming towards a one-to-one comparison between experiments and theory or numerics. This review will discuss various examples of the physicochemical hydrodynamics of droplet systems far from equilibrium and our present understanding of them. These include immiscible droplets in a concentration gradient, coalescence of droplets of different liquids, droplets in concentration gradients emerging from chemical reactions (including droplets as microswimmers) and phase transitions such as evaporation, solidification, dissolution, or nucleation, and droplets in ternary liquids, including solvent exchange, nano-precipitation, and the so-called ouzo effect. We will also discuss the relevance of the physicochemical hydrodynamics of such droplet systems for many important applications, including in chemical analysis and diagnostics, microanalysis, pharmaceutics, synthetic chemistry and biology, chemical and environmental engineering, the oil and remediation industries, inkjet-printing, for micro- and nano-materials, and in nanotechnolgoy., Comment: 38 pages, 7 figures with various panels

The evaporation of droplets occurs in a large variety of natural and technological processes such as medical diagnostics, agriculture, food industry, printing, and catalytic reactions. We study the different droplet morphologies adopted by an evaporating droplet on a surface with an elliptical patch with a different contact angle. We perform experiments to observe these morphologies and use numerical calculations to predict the effects of the patched surfaces. We observe that tuning the geometry of the patches offers control over the shape of the droplet. In the experiments, the drops of various volumes are placed on elliptical chemical patches of different aspect ratios and imaged in 3D using laser scanning confocal microscopy, extracting the droplets shape. In the corresponding numerical simulations, we minimize the interfacial free energy of the droplet, by employing Surface Evolver. The numerical results are in good qualitative agreement with our experimental data and can be used for the design of micropatterned structures, potentially suggesting or excluding certain morphologies for particular applications. However, the experimental results show the effects of pinning and contact angle hysteresis, which are obviously absent in the numerical energy minimization. The work culminates with a morphology diagram in the aspect ratio vs relative volume parameter space, comparing the predictions with the measurements.

Solvent exchange (also called solvent shifting or Ouzo effect) is a generally used bottom-up process to mass-produce nanoscale droplets. In this process, a good solvent for some oil is displaced by a poor one, leading to oil nanodroplet nucleation and subsequent growth. Here we perform this process on a hydrophobic substrate so that sessile droplets so-called surface nanodroplets-develop, following the work of Zhang et al. [Zhang, X.; Lu, Z.; Tan, H.; Bao, L.; He, Y.; Sun, C.; Lohse, D. Proc. Natl. Acad. Sci. U.S.A. 2015, 122, 9253-9257]. In contrast to what was done in that paper, we chose a very well-controlled Hele-Shaw geometry with negligible gravitational effects, injecting the poor solvent in the center of the Hele-Shaw cell, and characterize the emerging nanodroplets as a function of radial distance and flow rates. We find that the mean droplet volume per area _area strongly depends on the local Peclet number Pe and follows a universal scaling law _area~Pe^(3/4). Moreover, the probability distribution function of the droplet volume strongly depends on the local Pe as well, regardless of the flow rates and radial distance, giving strong support to the theoretical model of the solvent exchange process developed in Zhang et al.'s work., Comment: 6 pages, 5 figures

Surface nanobubbles are nanoscopic spherical-cap shaped gaseous domains on immersed substrates which are stable, even for days. After the stability of a {\it single} surface nanobubble has been theoretically explained, i.e. contact line pinning and gas oversaturation are required to stabilize them against diffusive dissolution [Lohse and Zhang, Phys.\ Rev.\ E 91, 031003 (R) (2015)], here we focus on the {\it collective} diffusive interaction of {\it multiple} nanobubbles. For that purpose we develop a finite difference scheme for the diffusion equation with the appropriate boundary conditions and with the immersed boundary method used to represent the growing or shrinking bubbles. After validation of the scheme against the exact results of Epstein and Plesset for a bulk bubble [J. Chem. Phys. 18, 1505 (1950)] and of Lohse and Zhang for a surface bubble, the framework of these simulations is used to describe the coarsening process of competitively growing nanobubbles. The coarsening process for such diffusively interacting nanobubbles slows down with advancing time and thus increasing bubble distance. The present results for surface nanobubbles are also applicable for immersed surface nanodroplets, for which better controlled experimental results of the coarsening process exist.

Moving contact lines of more than two phases dictate a large number of interfacial phenomena. Despite its significance to fundamental and applied processes, the contact lines at a junction of four-phases (two immiscible liquids, solid and gas) have been addressed only in a few investigations. Here, we report an intriguing phenomenon that follows after the four phases of oil, water, solid and gas make contact through the coalescence of two different three-phase contact lines. We combine experimental study and theoretical analysis to reveal and rationalize the dynamics exhibited upon the coalescence between the contact line of a micron-sized oil droplet and the receding contact line of a millimetre-sized water drop that covers the oil droplet on the substrate. We find that after the coalescence a four-phase contact line is formed for a brief period. However, this quadruple contact line is not stable, leading to a `droplet splitting' effect and eventual expulsion of the oil droplet from the water drop. We then show that the interfacial tension between the different phases and the viscosity of oil droplet dictate the splitting dynamics. More viscous oils display higher resistance to the extreme deformations of the droplet induced by the instability of the quadruple contact line and no droplet expulsion is observed for such cases.

The formation and evolution of immersed surface micro- and nanobubbles are essential in various practical applications, such as the usage of superhydrophobic rematerials, drug delivery, and mineral flotation. In this work, we investigate the entrapment of microbubbles on a hydrophobic surface, structured with microwells, when water flow passes along, and the subsequent microbubble dissolution. At entrapment, the microbubble is initially pinned at the edge of the microwell. At some point, the three-phase contact line detaches from one side of the edge and separates from the wall, after which it further recedes. We systematically investigate the evolution of the footprint diameter and the contact angle of the entrapped microbubbles, which reveals that the dissolution process is in the constant contact angle mode. By varying the gas undersaturation level, we quantify how a high gas undersaturation enhances the dissolution process, and compare with simplified theoretical predictions for dissolving bubbles on a plane surface. We find that geometric partial blockage effects of the diffusive flux out of the microbubble trapped in the microwell lead to reduced dissolution rates., Comment: 9 pages, 7 figures

Droplets can self-propel when immersed in another liquid in which a concentration gradient is present. Here we report the experimental and numerical study of a self-propelling oil droplet in a vertically stratified ethanol/water mixture: At first, the droplet sinks slowly due to gravity, but then, before having reached its density matched position, jumps up suddenly. More remarkably, the droplet bounces repeatedly with an ever increasing jumping distance, until all of a sudden it stops after about 30 min. We identify the Marangoni stress at the droplet/liquid interface as responsible for the jumping: its strength grows exponentially because it pulls down ethanol-rich liquid, which in turn increases its strength even more. The jumping process can repeat because gravity restores the system. Finally, the sudden death of the jumping droplet is also explained. Our findings have demonstrated a type of prominent droplet bouncing inside a continuous medium with no wall or sharp interface., Comment: 6 pages, 4 figures

The dissolution of liquid nanodroplets is a crucial step in many applied processes, such as separation and dispersion in food industry, crystal formation of pharmaceutical products, concentrating and analysis in medical diagnosis, and drug delivery in aerosols. In this work, using both experiments and numerical simulations, we \textit{quantitatively} study the dissolution dynamics of femtoliter surface droplets in a highly ordered array under a uniform flow. Our results show that the dissolution of femoliter droplets strongly depends on their spatial positions relative to the flow direction, drop-to-drop spacing in the array, and the imposed flow rate. In some particular case, the droplet at the edge of the array can dissolve about 30% faster than the ones located near the centre. The dissolution rate of the droplet increases by 60% as the inter-droplet spacing is increased from 2.5 $\mu$m to 20 $\mu$m. Moreover, the droplets close to the front of flow commence to shrink earlier than those droplets in the center of the array. The average dissolution rate is faster for faster flow. As a result, the dissolution time $T_{i}$ decreases with the Reynolds number Re of the flow as $T_{i}\propto Re^{-3/4}$. The experimental results are in good agreement with numerical simulations where the advection-diffusion equation for the concentration field is solved and the concentration gradient on the surface of the drop is computed. The findings suggest potential approaches to manipulate nanodroplet sizes in droplet arrays simply by dissolution controlled by an external flow. The obtained droplets with varying curvatures may serve as templates for generating multifocal microlens in one array.

The coalescence between growing droplets is important for the surface coverage and spatial arrangements of droplets on surfaces. In this work, total internal reflection fluorescence (TIRF) microscopy is utilized to in-situ investigate the formation of nanodroplets around the rim of a polymer microcap, with sub-micron spatial and millisecond temporal resolution. We observe that the coalescence among droplets occurs frequently during their growth by solvent exchange. Our experimental results show that the position of the droplet from two merged droplets is related to the size of the parent droplets. The position of the coalesced droplet and the ratio of parent droplet sizes obey a scaling law, reflecting a coalescence preference based on the size inequality. As a result of droplet coalescence, the angles between the centroids of two neighbouring droplets increase with time, obeying a nearly symmetrical arrangement of droplets at various time intervals. The evolution of the position and number from coalescence of growing droplets is modelled. The mechanism for coalescence driven self-organization of growing droplets is general, applicable to microcaps of different sizes and droplets of different liquids. The understanding from this work may be valuable for positioning nanodroplets by nucleation and growth without using templates., Comment: 10 pages, 9 figures

In the study of nanobubbles, nanodroplets or nanolenses immobilised on a substrate, a cross-section of a spherical-cap is widely applied to extract geometrical information from atomic force microscopy (AFM) topographic images. In this paper, we have developed a comprehensive 3D spherical cap fitting procedure (3D-SCFP) to extract morphologic characteristics of complete or truncated spherical caps from AFM images. Our procedure integrates several advanced digital image analysis techniques to construct a 3D spherical cap model, from which the geometrical parameters of the nanostructures are extracted automatically by a simple algorithm. The procedure takes into account all valid data points in the construction of the 3D spherical cap model to achieve high fidelity in morphology analysis. We compare our 3D fitting procedure with the commonly used 2D cross-sectional profile fitting method to determine the contact angle of a complete spherical cap and a truncated spherical cap. The results from 3D-SCFP are consistent and accurate, while 2D fitting is unavoidably arbitrary in selection of the cross-section and has a much lower number of data points on which the fitting can be based, which in addition is biased to the top of the spherical cap. We expect that the developed 3D spherical-cap fitting procedure will find many applications in imaging analysis., Comment: 23 pages, 7 figures

The analogy between evaporating surface droplets in air to dissolving long-chain alcohol droplets in water is worked out. We show that next to the three known modi for surface droplet evaporation or dissolution (constant contact angle mode, constant contact radius mode, and stick-slide mode), a fourth mode exists for small droplets on supposedly smooth substrates, namely the stick-jump mode: intermittent contact line pinning causes the droplet to switch between sticking and jumping during the dissolution. We present experimental data and compare them to theory to predict the dissolution time in this stick-jump mode. We also explain why these jumps were easily observed for microscale droplets but not for larger droplets.

The states of gas accumulated at the liquid-solid interface are analyzed based on the continuum theory where the Hamaker constant is used to describe the long-range interaction at the microscopic scale. The Hamaker constant is always negative, whereas the gas spreading coefficient can be either sign. Despite the complexity of gas, including that the density profile may not be uniform due to absorption on both solid and liquid surfaces, we predict three possible gas states at the liquid-solid interface, i.e. complete wetting, partial wetting and pseudopartial wetting. These possible gas states correspond respectively to a gas pancake (or film) surrounded by a wet solid, a gas bubble with a finite contact angle, and a gas bubble(s) coexisting with a gas pancake. Typical thickness of the gas pancakes is at the nanoscale within the force range of the long-range interaction, whereas the radius of the gas bubbles can be large. The state of gas bubble(s) coexisting with a gas film is predicted theoretically for the first time. Our theoretical results can contribute to the development of a unified picture of gas nucleation at the liquid-solid interface.