Collective interactions in the nucleation and growth of surface droplets

Microfluidic formation of surface nanodroplets using green deep eutectic solvents for liquid-liquid nanoextraction and controlled precipitation

HYPOTHESIS

Surface nanodroplets have recently been employed for in situ chemical analysis leveraging their low volume, e.g. O(10^-15 L), that enables rapid analyte extraction and pre-concentration. So far, most surface nanodroplets have been formed using single organic solvents such as 1-octanol, toluene, among others. Designing multicomponent surface nanodroplet with controllable composition is highly desirable for extending their application as extractant.

EXPERIMENT

Here, we formed surface nanodroplets using green deep eutectic solvent (gDES) composed of thymol and decanoic acid, both of which are naturally occurring chemicals. The influence of parameters such as flowrate and the composition of deep eutectic solvent on the surface nanodroplet formation were studied. As proof-of-concept, the gDES surface nanodroplets were further used to extract and detect trace amounts of fluorescent rhodamine 6G dye and copper ions from water.

FINDINGS

The formation of gDES surface nanodroplets follows the theoretical model which states that the final droplet volume (V_f) scales with the Peclét number (Pe) of the flow during formation by the solvent exchange process, that is V_f ∼ Pe^3/4, and the nanodroplets demonstrate excellent ability as extractant for rhodamine 6G and copper ions from water. Surprisingly, the confined volume of gDES surface nanodroplets enables fast and controlled formation of Cu (II)-decanoate crystal.

Surface nanodroplet-based nanoextraction from sub-milliliter volumes of dense suspensions

A greener analytical technique for quantifying compounds in dense suspensions is needed for wastewater and environmental analysis, chemical or bio-conversion process monitoring, biomedical diagnostics, and 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 is 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 a proof of principle, we demonstrate the nanoextraction for the quantification of model compounds in wastewater slurry containing 30 wt% solids and oily components (i.e. heavy oils). The nanoextraction and detection technology developed in this work may be used in fast analytical technologies for complex slurry samples in the environment, industrial waste, or in biomedical diagnostics.

Transient Solubility Gradients Mediate Oversaturation during Solvent Exchange

Solvent exchange facilitates high-density nucleation of sessile nanodroplets or nanobubbles by successively wetting a surface with two solvents of contrasting solubility with respect to a target species. Yet the key physical mechanisms underlying its efficacy have yet to be theoretically explained. We develop a minimal model for solvent exchange, for the prototypical example of water and ethanol as the solvents and nitrogen as the target species. Our calculations show that solvent exchange is mediated by transient solubility gradients that dominate over the intrinsic concentration gradient of nitrogen in the incipient moments after exchange. Solubility gradients advect nitrogen toward the substrate during ethanol-water exchange but away from it in water-ethanol exchange, consistent with the directionality observed in experiments.

Temperature-induced liquid crystal microdroplet formation in a partially miscible liquid mixture

Liquid-in-liquid droplets are typically generated by the partitioning of immiscible fluids, e.g. by mechanical shearing with macroscopic homogenisers or microfluidic flow focussing. In contrast, partially miscible liquids with a critical solution temperature display a temperature-dependent mixing behaviour. In this work, we demonstrate how, for a blend of methanol (MeOH) and the thermotropic liquid crystal (LC) 4-Cyano-4'-pentylbiphenyl (5CB), cooling from a miscible to an immiscible state allows the controlled formation of microdroplets. A near-room-temperature-induced phase separation leads to nucleation, growth and coalescence of mesogen-rich droplets. The size and number of the droplets is tunable on the microscopic scale by variation of temperature quench depth and cooling rate. Further cooling induces a phase transition to nematic droplets with radial configuration, well-defined sizes and stability over the course of an hour. This temperature-induced approach offers a scalable and reversible alternative to droplet formation with relevance in diagnostics, optoelectronics, materials templating and extraction processes.

Modified Voronoi Analysis of Spontaneous Formation of Interfacial Droplets on Immersed Oil-Solid Substrates

The nucleation and growth of liquid droplets on solid substrates have received much attention because of the significant relevance of these multiphase processes to both nature and practical applications. There have been extensive studies on the condensation of water from the air phase on solid substrates. Here, we focus on water diffusion through the oil phase and subsequent settlement on solid substrates because such interfacial droplets are formed. Voronoi diagram analysis is proposed to statistically characterize the size distribution of the growing droplets. It is found that modification of the standard Voronoi diagram is required for systems of interfacial droplets which have a noncircular shape and/or whose centers change with time. The modified Voronoi analysis of the growing droplets provides an automatic quantification of the droplet distribution and reveals that (i) during the nucleation stage, the interfacial droplets do not nucleate at the same time because the nucleation of newly formed droplets competes with the growth of the existing ones; (ii) the growth of interfacial droplets comes from water diffusion from the bulk water layer, and/or from adjacent interfacial droplets, and/or from coalescence of interfacial droplets; and (iii) the sizes of interfacial droplets become more polydispersed on P-glass but more monodispersed on OTS-glass as time goes. This work opens a new perspective on the formation of interfacial droplets at the interface between oil and the solid substrate and demonstrates the capability of an automatic analysis method, which can be potentially applied to similar interfacial multiphase systems.

Steiner triangular drop dynamics

Steiner's circumellipse is the unique geometric regularization of any triangle to a circumscribed ellipse with the same centroid, a regularization that motivates our introduction of the Steiner triangle as a minimal model for liquid droplet dynamics. The Steiner drop is a deforming triangle with one side making sliding contact against a planar basal support. The center of mass of the triangle is governed by Newton's law. The resulting dynamical system lives in a four dimensional phase space and exhibits a rich one-parameter family of dynamics. Two invariant manifolds are identified with "bouncing" and "rocking" periodic motions; these intersect at the stable equilibrium and are surrounded by nested quasiperiodic motions. We study the inherently interesting dynamics and also find that this model, however minimal, can capture space-time symmetries of more realistic continuum drop models.

Spatially arranging interfacial droplets at the oil-solid interface

The controlling and patterning of small droplets on a solid surface is of significant interest to understand interfacial phenomena and for practical applications. Among interfacial phenomena, the formation of interfacial droplets attracts scientists' attention, as the mechanism of this phenomenon where water molecules can spontaneously accumulate at the hydrophobic oil/solid interface is still not fully understood. Further investigation is needed to find out specifically where the driving force comes from and how to spatially arrange the interfacial droplets. Herein, self-assembled monolayers are formed on a gold substrate, and it turns out that the hydrophobic surface with a monolayer formed from HS(CH₂)₁₁CH₃ could inhibit the formation of interfacial droplets; by contrast, the hydrophilic surfaces with monolayers formed from HS(CH₂)₁₁COOH, HS(CH₂)₁₁NH₃·Cl and HS(CH₂)₁₁OH, all promote water accumulation. It suggests that the hydrogen bonding between the surface and water proves to be critical in inducing interfacial droplet formation but this has been neglected in past studies. Taking advantage of microcontact printing, the surface chemistry can be controlled at the micron scale and allows spatial arrangement of interfacial droplets at specific regions. This work moves a further step in understanding the mechanism of interfacial droplet formation, and can be potentially exploited for the collection of water and fabrication of microtemplates.

Surface Nanodroplets: Formation, Dissolution, and Applications

Droplets at solid-liquid interfaces play essential roles in a broad range of fields, such as compartmentalized chemical reactions and conversions, high-throughput analysis and sensing, and super-resolution near-field imaging. Our recent work has focused on understanding and controlling the nanodroplet formation on solid surfaces in ternary liquid mixtures. These surface nanodroplets resemble tiny liquid lenses with a typical height of <1 μm and a volume of subfemtoliters. The solvent exchange is based on the process of displacing a droplet liquid solution by a poor solvent to create a transient oversaturation for droplet formation. A quantitative understanding of growth dynamics of surface nanodroplets in ternary liquid mixtures not only provides insight into the liquid-liquid phase separation induced by solvent addition in general but also has made it possible to control the droplet size well. This review article will summarize our findings in the last ∼5 years from the research with our collaborators. The first part will explain the fundamental aspects that are key to the formation and stability of surface nanodroplets. In the second part, we will highlight the applications of nanodroplets in chemical analysis and functional surface fabrication and finally point out future directions in droplet-based applications.

Growth dynamics of surface nanodroplets during solvent exchange at varying flow rates

Solvent exchange is a simple solution-based process to produce surface nanodroplets over a large area. The final size of the droplets is determined by both the flow and solution conditions for a given substrate. In this work, we investigate the growth dynamics of surface nanodroplets during solvent exchange by using total internal reflection fluorescence microscopy (TIRF). The results show that during the solvent exchange, the formation of surface nanodroplets advanced on the surface in the direction of the flow. The time for the number density and surface coverage of the droplets to reach their respective plateau values is determined by the flow rate. From the observed evolution of the droplet volume and of the size of individual growing droplets, we are able to determine that the growth time of the droplets scales with the Peclet number Pe with a power law ∝Pe-1/2. This is consistent with Taylor-Aris dispersion, shedding light on the diffusive growth dynamics during the solvent exchange. Further, the spatial rearrangement of the droplets during coalescence demonstrates a preference in position shift based on size inequality, namely, the coalesced droplet resides closer to the larger of the two parent droplets. These findings provide a valuable insight toward controlling droplet size and spatial distribution.

Kinetics of first-order phase transitions with correlated nuclei

We demonstrate that the time evolution of a first-order phase transition may be described quite generally in terms of the statistics of point processes, thereby providing an intuitive framework for visualizing transition kinetics. A number of attractive and repulsive nucleation scenarios is examined followed by isotropic domain growth at a constant rate This description holds for both uncorrelated and correlated nuclei, and may be employed to calculate the nonequilibrium, n-point spatiotemporal correlations that characterize the transition. Furthermore, it is shown that the interpretation of the one-point function in terms of a stretched-exponential, Kolmogorov-Johnson-Mehl-Avrami result is problematic in the case of correlated nuclei, but that the calculation of higher-order correlation functions permits one to distinguish among various nucleation scenarios.

Formation of surface nanodroplets of viscous liquids by solvent exchange

Surface nanodroplets are essential units for many compartmentalised processes from catalysis, liquid-liquid reactions, crystallization, wetting and more. Current techniques for producing submicron droplets are mainly based on top-down approaches, which are increasingly limited as scale reduces. Herein, solvent exchange is demonstrated as a simple solution-based approach for the formation of surface nanodroplets with intermediate and extremely high viscosity (1 000 000 cSt). By solvent exchange, the viscous droplet liquid dissolves in a good solvent that is then displaced by a poor solvent to yield surface droplets for the oversaturaion pulse at the mixing front. Within controlled flow conditions, the geometry of droplets of low and intermediate viscosity liquids can be tailored on the nano and microscale by controlling the flow rate. Meanwhile for extremely viscous liquids, the droplet size is shown to be dependent on the liquid temperature. This work demonstrates that solvent exchange offers a versatile tool for the formation of droplets with a wide range of viscosity.