Times of metastable droplet relaxation to equilibrium states

Times of metastable droplet relaxation to their equilibrium state are calculated at saturated vapor pressures, depending on the droplet size. It is shown that for small droplets with radius R = 6 molecular diameters (or ~2 nm) the relaxation times are ~1 ns (which is comparable to the characteristic flight times of rarefied gas molecules). For large droplets with radius R ~ 800 molecular diameters, the relaxation times are as long as 10 μs. At a fixed droplet radius (6 ≤ R ≤ 800), the range of variation in relaxation time from the melting point to the critical temperature does not exceed one order of magnitude: the lower the temperature, the slower the relaxation process.     

Monte Carlo simulation study of droplet nucleation

A new rigorous Monte Carlo simulation approach is employed to study nucleation barriers for droplets in Lennard-Jones fluid. Using the gauge cell method we generate the excess isotherm of critical clusters in the size range from two to six molecular diameters. The ghost field method is employed to compute the cluster free energy and the nucleation barrier with desired precision of (1-2)kT. Based on quantitative results obtained by Monte Carlo simulations, we access the limits of applicability of the capillarity approximation of the classical nucleation theory and the Tolman equation. We show that the capillarity approximation corrected for vapor nonideality and liquid compressibility provides a reasonable assessment for the size of critical clusters in Lennard-Jones fluid; however, its accuracy is not sufficient to predict the nucleation barriers for making practical estimates of the rate of nucleation. The established dependence of the droplet surface tension on the droplet size cannot be approximated by the Tolman equation for small droplets of radius less than four molecular diameters. We confirm the conclusion of ten Wolde and Frenkel [J. Chem. Phys. 109, 9901 (1998)] that integration of the normal component of the Irving-Kirkwood pressure tensor severely underestimates the nucleation barriers for small clusters.     

Liquid marbles prepared from pH-responsive sterically stabilized latex particles

Submicrometer-sized pH-responsive sterically stabilized polystyrene (PS) latex particles were synthesized by dispersion polymerization in isopropyl alcohol with a poly[2-(diethylamino)ethyl methacrylate]- (PDEA-) based macroinitiator. These PDEA-PS latexes were extensively characterized with respect to their particle size distribution, morphology, chemical composition, and pH-responsive behavior. Millimeter- and centimeter-sized "liquid marbles" with aqueous volumes varying between 15 μL and 2.0 mL were readily prepared by rolling water droplets on the dried PDEA-PS latex powder. The larger liquid marbles adopted nonspherical shapes due to gravitational forces; analysis of this deformation enabled the surface tension to be estimated. Scanning electron microscopy and fluorescence microscopy studies indicated that flocs of the PDEA-PS particles were adsorbed at the surface of these water droplets, leading to stable liquid marbles. The relative mechanical integrity of the liquid marbles prepared from alkaline aqueous solution (pH 10) was higher than those prepared from acidic aqueous solution (pH 2) as judged by droplet roller experiments. These liquid marbles exhibited long-term stability (over 1 h) when transferred onto the surface of liquid water, provided that the solution pH of the subphase was above pH 8. In contrast, the use of acidic solutions led to immediate disintegration of these liquid marbles within 10 min, with dispersal of the PDEA-PS latex particles in the aqueous solution. Thus the critical minimum solution pH required for long-term liquid marble stability correlates closely with the known pK(a) value of 7.3 for the PDEA stabilizer chains. Stable liquid marbles were also successfully prepared from aqueous Gellan gum solution and glycerol.     

Effects of formulation variables on liquid‐crystal droplet size distributions in ultraviolet‐cured polymer‐dispersed liquid‐crystal cells

The size distributions of liquid‐crystal droplets in ultraviolet‐cured polymer‐dispersed liquid‐crystal cells have been studied with optical microscopy. It has been observed that (1) the relative masses of the liquid crystal and crosslinking agent determine the droplet size distribution for submicrometer droplet diameters and (2) only the liquid‐crystal mass fraction affects the droplet size distribution for diameters ranging from 1 to 4 μm. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1842–1848, 2005     

Simultaneous preconcentration and determination of 2,4‐D,alachlor and atrazine in aqueous samples using dispersive liquid–liquid microextraction followed by high‐performance liquid chromatography ultraviolet detection

Dispersive liquid–liquid microextraction coupled with high‐performance liquid chromatography‐ultraviolet detection as a fast and inexpensive technique was applied to the simultaneous extraction and determination of traces of three common herbicides, 2,4‐D, alachlor and atrazine, in aqueous samples. The critical experimental parameters, including type of the extraction and disperser solvents as well as their volumes, sample pH, salt addition, extraction time and centrifuging time, and speed were investigated and optimized. Under the optimum conditions, the calibration graphs found to be linear in the range of 0.3–200 μg/L with limits of detection in the range of 0.05–0.1 μg/L. The relative standard deviations were in the range of 4.5–6.2% (n = 7). The relative recoveries of well, tap, and river water samples which have been spiked with different levels of herbicides were 92.0–107.0, 82.0–104.0, and 82.0–86.0%, respectively.     

Stochastic diffusion interactions and coarsening in a system of droplets growing from a supersaturated gas mixture

In this work we study diffusion interactions among liquid droplets growing in stochastic population by condensation from supersaturated binary gas mixture. During the postnucleation transient regime collective growth of liquid droplets competing for the available water vapor decreases local supersaturation leading to the increase of critical radius and the onset of coarsening process. In coarsening regime the growth of larger droplets is prevailing noticeably broadening the droplet size-distribution function when the condensation process becomes more intensive than the supersaturation yield. Modifications in the kinetic equation are discussed and formulated for a stochastic population of liquid droplets when diffusional interactions among droplets become noteworthy. The kinetic equation for the droplet size-distribution function is solved together with field equations for the mass fraction of disperse liquid phase, mass fraction of water vapor component of moist air, and temperature during diffusion-dominated regime of droplet coarsening. The droplet size and mass distributions are found as functions of the liquid volume fraction, showing considerable broadening of droplet spectra. It is demonstrated that the effect of latent heat of condensation considerably changes coarsening process. The coarsening rate constant, the droplet density (number of droplets per unit volume), the screening length, the mean droplet size, and mass are determined as functions of the temperature, pressure, and liquid volume fraction.     

Double transfer printing of small volumes of liquids

We report here a technique to print small volumes of liquid on a hydrophobic substrate. This process is based on the control of the critical parameters that govern a quasi-equilibrium liquid transfer process from one surface to another. We present a qualitative model that describes the physics of a transfer printing process between hydrophobic surfaces, and we use the parameters outlined in this model to manipulate the amount of liquid transferred between surfaces. We demonstrate the printing of discrete, small volumes (approximately 70 fL) of different liquid inks on a polymer substrate starting with volumes that are 8 orders of magnitude larger (a droplet of approximately 10 microL) in a simple two-step procedure.     

Picoliter droplet formation on thin optical fiber tips

In this paper, we present experimental results on how minute droplets are formed on fiber optic end faces. Results show that reproducible picoliter volumes can be generated when fibers are retracted from an aqueous phase contained under an inert fluorinated immiscible liquid, with a coefficient of variation (CV) of 0.7-2.3%. The droplet formation was analyzed as a function of the fiber diameter, retraction speed, and wettability. Experiments reveal a volume-determining critical equilibrium contact angle between 60 degrees and 75 degrees , defining the onset of fiber end-face dewetting. The dynamics of the droplet snap-off progression was characterized using high-speed imaging in order to explain the observed wettability-volume dependency.     

Design and evaluation of a sandwich phase separator for on-line liquid/liquid extraction

Sandwich phase separators with various groove dimensions were constructed and as part of a post-column extraction detector for liquid chromatography and for a flow-injection system. The construction materials are stainless steel and PTFE; no membranes are used. The groove volumes vary between 8 and 43 μl; the dimensions of the groove are not critical. Several aqueous (acetonitrile/water and methanol/water mixtures) and organic (1,2-dichloroethane and n-heptane) phases were successfully separated by gravity as well as by wetting. Measurement of statistical second moments showed the total disperson of the extraction system to be 2.5–4 s at the optimum separation efficiency (organic flow through detector/total organic flow) of 0.3–0.4.     

Uniform-sized silicone oil microemulsions: preparation, investigation of stability and deposition on hair surface

Emulsions are commonly used in foods, pharmaceuticals and home-personal-care products. For emulsion based products, it is highly desirable to control the droplet size distribution to improve storage stability, appearance and in-use property. We report preparation of uniform-sized silicone oil microemulsions with different droplets diameters (1.4-40.0 μm) using SPG membrane emulsification technique. These microemulsions were then added into model shampoos and conditioners to investigate the effects of size, uniformity, and storage stability on silicone oil deposition on hair surface. We observed much improved storage stability of uniform-sized microemulsions when the droplets diameter was ≤22.7 μm. The uniform-sized microemulsion of 40.0 μm was less stable but still more stable than non-uniform sized microemulsions prepared by conventional homogenizer. The results clearly indicated that uniform-sized droplets enhanced the deposition of silicone oil on hair and deposition increased with decreasing droplet size. Hair switches washed with small uniform-sized droplets had lower values of coefficient of friction compared with those washed with larger uniform and non-uniform droplets. Moreover the addition of alginate thickener in the shampoos and conditioners further enhanced the deposition of silicone oil on hair. The good correlation between silicone oil droplets stability, deposition on hair and resultant friction of hair support that droplet size and uniformity are important factors for controlling the stability and deposition property of emulsion based products such as shampoo and conditioner.     

Electrowetting of nonwetting liquids and liquid marbles

Transport of a water droplet on a solid surface can be achieved by differentially modifying the contact angles at either side of the droplet using capacitive charging of the solid-liquid interface (i.e., electrowetting-on-dielectric) to create a driving force. Improved droplet mobility can be achieved by modifying the surface topography to enhance the effects of a hydrophobic surface chemistry and so achieve an almost complete roll-up into a superhydrophobic droplet where the contact angle is greater than 150 degrees . When electrowetting is attempted on such a surface, an electrocapillary pressure arises which causes water penetration into the surface features and an irreversible conversion to a state in which the droplet loses its mobility. Irreversibility occurs because the surface tension of the liquid does not allow the liquid to retract from these fixed surface features on removal of the actuating voltage. In this work, we show that this irreversibility can be overcome by attaching the solid surface features to the liquid surface to create a liquid marble. The solid topographic surface features then become a conformable "skin" on the water droplet both enabling it to become highly mobile and providing a reversible liquid marble-on-solid system for electrowetting. In our system, hydrophobic silica particles and hydrophobic grains of lycopodium are used as the skin. In the region corresponding to the solid-marble contact area, the liquid marble can be viewed as a liquid droplet resting on the attached solid grains (or particles) in a manner similar to a superhydrophobic droplet resting upon posts fixed on a solid substrate. When a marble is placed on a flat solid surface and electrowetting performed it spreads but with the water remaining effectively suspended on the grains as it would if the system were a droplet of water on a surface consisting of solid posts. When the electrowetting voltage is removed, the surface tension of the water droplet causes it to ball up from the surface but carrying with it the conformable skin. A theoretical basis for this electrowetting of a liquid marble is developed using a surface free energy approach.     

Dynamics of Synthetic Membraneless Organelles in Microfluidic Droplets

Cells can form membraneless organelles by liquid–liquid phase separation. As these organelles are highly dynamic, it is crucial to understand the kinetics of these phase transitions. Here, we use droplet‐based microfluidics to mix reagents by chaotic advection and observe nucleation, growth, and coarsening in volumes comparable to cells (pL) and on timescales of seconds. We apply this platform to analyze the dynamics of synthetic organelles formed by the DEAD‐box ATPase Dhh1 and RNA, which are associated with the formation of processing bodies in yeast. We show that the timescale of phase separation decreases linearly as the volume of the compartment increases. Moreover, the synthetic organelles coarsen into one single droplet via gravity‐induced coalescence, which can be arrested by introducing a hydrogel matrix that mimics the cytoskeleton. This approach is an attractive platform to investigate the dynamics of compartmentalization in artificial cells.     

Size-dependent surface tension and Tolman's length of droplets

A model for the size-dependent surface tension gammalv(D) of liquid droplets, free of any adjustable parameter, is presented in terms of the size-dependent surface energy gammasv(D). It is found that gammalv(D) drops monotonically with the size of the droplet in the nanometer region. Modeling predictions agree with computer simulations for sodium, aluminum, and water droplets. Meanwhile, the Tolman's equation is found to be valid for small particles, and the Tolman's length is always positive and becomes longer when the droplet size is decreased.     

Application of dispersive liquid–liquid microextraction based on solidification of floating organic drop for simultaneous determination of alachlor and atrazine in aqueous samples

Dispersive liquid–liquid microextraction based on solidification of floating organic drop coupled with HPLC‐UV detection as a fast and inexpensive technique was applied to the simultaneous extraction and determination of traces of two common herbicides, alachlor and atrazine, in aqueous samples. The critical experimental parameters, including type of the extraction and disperser solvents as well as their volumes, sample pH, salt addition, and extraction time were investigated and optimized. Under the optimum conditions, the calibration graphs found to be linear in the range of 0.1–200 μg/L with LOD in the range of 0.02–0.05 μg/L. The RSDs were in the range of 4.2–5.3% (n = 5). The relative recoveries of well, tap, and river water samples which have been spiked with different levels of herbicides were 94.0–106.0, 99.0–105.0, and 88.5–97.0%, respectively.     

Fast Quantitation of Target Analytes in Small Volumes of Complex Samples by Matrix‐Compatible Solid‐Phase Microextraction Devices

Herein we report the development of solid‐phase microextraction (SPME) devices designed to perform fast extraction/enrichment of target analytes present in small volumes of complex matrices (i.e. V≤10 μL). Micro‐sampling was performed with the use of etched metal tips coated with a thin layer of biocompatible nano‐structured polypyrrole (PPy), or by using coated blade spray (CBS) devices. These devices can be coupled either to liquid chromatography (LC), or directly to mass spectrometry (MS) via dedicated interfaces. The reported results demonstrated that the whole analytical procedure can be carried out within a few minutes with high sensitivity and quantitation precision, and can be used to sample from various biological matrices such as blood, urine, or Allium cepa L single‐cells.     

Plasmonic Colloidosomes as Three‐Dimensional SERS Platforms with Enhanced Surface Area for Multiphase Sub‐Microliter Toxin Sensing

Colloidosomes are robust microcapsules attractive for molecular sensing because of their characteristic micron size, large specific surface area, and dual‐phase stability. However, current colloidosome sensors are limited to qualitative fluorogenic receptor‐based detection, which restrict their applicability to a narrow range of molecules. Here, we introduce plasmonic colloidosome constructed from Ag nanocubes as an emulsion‐based 3D SERS platform. The colloidosomes exhibit excellent mechanical robustness, flexible size tunability, versatility to merge, and ultrasensitivity in SERS quantitation of food/industrial toxins down to sub‐femtomole levels. Using just 0.5 μL of sample volumes, our plasmonic colloidosomes exhibit >3000‐fold higher SERS sensitivity over conventional suspension platform. Notably, we demonstrate the first high‐throughput multiplex molecular sensing across multiple liquid phases.     

Equilibrium shapes of liquid bridges under gravity: Symmetry breaking and imperfect bifurcations of two-dimensional bridges

The equilibrium shapes of a two-dimensional liquid bridge are constructed via a shooting and continuation numerical solution of the Laplace—Young equation which focuses on the bifurcation points of the solution branches. For the neutrally buoyant case, two new asymmetric shapes bifurcate from the point of maximum excess pressure where circular profiles with reflective symmetry have been shown to be unstable with respect to constant pressure disturbances. This occurs when the profile is exactly at right angles to the support. With the introduction of gravitational effects, this codimension 5 singularity is retained although the critical contact angle decreases slightly below 90° as one increases the difference between the interior and the exterior densities. However, when a slight tilt angle is introduced to the bridge, the maximum pressure singularity degenerates into two turning points (folds) and the solution branches are isolated from each other. This indicates that hysteretic jumps in the surface curvature and excess pressure exist with respect to changes in diameter/length ratio or liquid volume. Our numerical solution also reveals the existence of a maximum bridge volume that can be sustained by a nonneutrally buoyant bridge. No equilibrium shapes, symmetric or asymmetric, exist for bridge volumes beyond this critical value.     

Dynamic wetting and spreading characteristics of a liquid droplet impinging on hydrophobic textured surfaces

We report on the wetting dynamics of a 4.3 μL deionized (DI) water droplet impinging on microtextured aluminum (Al 6061) surfaces, including microhole arrays (hole diameter 125 μm and hole depth 125 μm) fabricated using a conventional microcomputer numerically controlled (μ-CNC) milling machine. This study examines the influence of the texture area fraction ?(s) and drop impact velocity on the spreading characteristics from the measurement of the apparent equilibrium contact angle, dynamic contact angle, and maximum spreading diameter. We found that for textured surfaces the measured apparent contact angle (CA) takes on values of up to 125.83°, compared to a CA of approximately 80.59° for a nontextured bare surface, and that the spreading factor decreases with the increased texture area fraction because of increased hydrophobicity, partial penetration of the liquid, and viscous dissipation. In particular, on the basis of the model of Ukiwe and Kwok (Ukiwe, C.; Kwok, D. Y. Langmuir 2005, 21, 666), we suggest a modified equation for predicting the maximum spreading factor by considering various texturing effects and wetting states. Compared with predictions by using earlier published models, the present model shows better agreement with experimental measurements of the maximum spreading factor.     

Analysis of the equilibrium droplet shape based on an ellipsoidal droplet model

The extent of a droplet's spreading over a flat, smooth solid substrate and its equilibrium height in the presence of gravity are determined approximately, without a numerical solution of the governing nonlinear differential equation, by assuming that the droplet takes on the shape of an oblate spheroidal cap and by minimizing the corresponding free energy. The comparison with the full numerical evaluations confirms that the introduced approximation and the obtained results are accurate for contact angles below about 120° and for droplet sizes on the order of the capillary length of the liquid. The flattening effect of gravity is to increase the contact radius and decrease the height of the droplet, with these being more pronounced for higher values of the Bond number.     

Nucleation and cavitation of spherical, cylindrical, and slablike droplets and bubbles in small systems

Computer simulations are employed to obtain subcritical isotherms of small finite sized systems inside the coexistence region. For all temperatures considered, ranging from the triple point up to the critical point, the isotherms gradually developed a sequence of sharp discontinuities as the system size increased from approximately 8 to approximately 21 molecular diameters. For the smallest system sizes, and more so close to the critical point, the isotherms appeared smooth, resembling the continuous van der Waals loop obtained from extrapolation of an analytic equation of state outside the coexistence region. As the system size was increased, isotherms in the chemical potential-density plane developed first two, then four, and finally six discontinuities. Visual inspection of selected snapshots revealed that the observed discontinuities are related to structural transitions between droplets (on the vapor side) and bubbles (on the liquid side) of spherical, cylindrical, and tetragonal shapes. A capillary drop model was developed to qualitatively rationalize these observations. Analytic results were obtained and found to be in full agreement with the computer simulation results. The analysis shows that the shape of the subcritical isotherms is dictated by a single characteristic volume (or length scale), which depends on the surface tension, compressibility, and coexistence densities. For small reduced system volumes, the model predicts that a homogeneous fluid is stable across the whole coexistence region, thus explaining the continuous van der Waals isotherms observed in the simulations. When the liquid and vapor free energies are described by means of an accurate mean-field equation of state and surface tensions from simulation are employed, the capillary model is found to describe the simulated isotherms accurately, especially for large systems (i.e., larger than about 15 molecular diameters) at low temperature (lower than about 0.85 times the critical temperature). This implies that the Laplace pressure differences can be predicted for drops as small as five molecular diameters, and as few as about 500 molecules. The theoretical study also shows that the extrema or apparent spinodal points of the finite size loops are more closely related to (finite system size) bubble and dew points than to classical spinodals. Our results are of relevance to phase transitions in nanopores and show that first order corrections to nucleation energies in finite closed systems are power laws of the inverse volume.