Dissolution dynamics of a suspension droplet in a binary solution for controlled nanoparticle assembly

Ziyang Lu a, Amgad Rezk b, Fernando Jativa ca, Leslie Yeo b and Xuehua Zhang *a
aSoft Matter & Interfaces Group, School of Engineering, RMIT University, Melbourne, VIC 3001, Australia. E-mail: xuehua.zhang@rmit.edu.au
bMicro/Nanophysics Research Laboratory, School of Engineering, RMIT University, Melbourne, VIC 3001, Australia
cDepartment of Mechanical Engineering, University of Melbourne, Parkville, VIC 3010, Australia

Received 16th April 2017 , Accepted 19th June 2017

First published on 20th June 2017

Toroidal microstructures of nanocolloidal assemblies promise important applications ranging from sensing, catalysis, drug delivery, and separation. In this work, we will first investigate the rich dissolution dynamics of a droplet comprising a nanoparticle suspension in a binary solution, and then show that the dissolution dynamics can be a potential approach to assembling a wide range of colloids with microtoroids. As the sessile droplet dissolves in the binary solution of miscible and immiscible solvents, two simultaneous effects are observed: if the dissolution rate is sufficiently high under large concentrations of the cosolvent in the surrounding solution, a strong plume emanates from the droplet pole as a consequence of a body force (i.e. the Korteweg force) driven by the chemical potential gradient between the water in the droplet and in the surrounding phase. Concurrently, the convection drives internal recirculation flow dynamics, leading to the inversion of the droplet curvature such that its initially spherical shape gradually contracts to evolve into a toroidal structure. We further demonstrate that the dissolution of a suspension droplet is an approach to assemble nanoparticles into toroidal microstructures. The resultant toroidal shapes are extrinsically governed by the composition and the geometrical confinement of the surrounding solution phase.

1. Introduction

The assembly of nanocolloids within microtoroidal structures offers vast opportunities for their exploitation in applications associated with sensing, catalysis and drug delivery, among other uses.1–6 Anisotropic geometries in these microtoroids can be advantageous. For example, toroidal shapes provide excellent mechanical and mass transfer properties that can, at times, be desirable for microencapsulation, separation and catalysis.7–9 While it has long been known that toroidal microstructures of amorphous nanoparticulate aggregates can form under fast evaporation processes such as spray drying,10–15 it was not until the work of Velev et al.16 that crystalline nanoparticle assemblies within these structures were demonstrated. The toroid formation from a suspension of nanoparticles using the drying technique is governed primarily by physical parameters intrinsic to the droplet, such as the initial particle concentration as well as the presence of surfactants.17,18 The mechanical instability of the shell around the droplet is essential for the buckling and doughnut shape arising from the drying process.13–15 In particular, the formation of a toroid microstructure is predicted for intermediate particle concentrations.

Although nanoparticle assembly from droplet evaporation has been extensively studied, the formation of toroidal microstructures and simultaneous nanoparticle assembly with the droplet due to the dissolution process has however yet to be reported. Generally a water droplet dissolves when immersed in a binary solution consisting of ethanol (the cosolvent) and an oil-like liquid (immiscible to water but miscible with ethanol).19,20 Varying the ratio between the two solvents in the binary solution leads to different dissolution rates of the water droplet. The chemical potential gradient across the droplet surface also drives rich mass transport and phase separation processes.21–24 For example, dynamical phenomena that have been observed in such ternary systems include self-propulsion and splitting of droplets, kicking interfaces and droplet morphology transformation.22,25,26 In the present work, we will show the interesting dissolution dynamics of a droplet in a binary solution consisting of a cosolvent and an immiscible solvent. Furthermore we will demonstrate that colloidal crystal assemblies within toroidal microstructures can be achieved through controlled droplet dissolution. The formation of the toroidal shape is mainly governed by the composition and the depth of the surrounding phase, while the inner and outer diameters of these toroidal structures are simply tuned by controlling the droplet dissolution rate. The findings in this work show that controlled droplet dissolution may be a general and valuable approach for toroid formation.

2. Results and discussion

2.1 Dependence of droplet dissolution rate on external solution composition and hydrostatic pressure

In our experiments, a droplet of 0.5 μl SiO2 nanoparticle suspension is deposited on a hydrophobic substrate that is immersed in a binary ethanol–toluene solution (see the schematic in Fig. 1). The initial compositional ratios of the solution are indicated in the ternary phase diagram in the same figure. The surrounding phase comprises only toluene and ethanol. The initial compositions of the surrounding phase are labelled by the colourful points in the three-phase diagram in Fig. 1. As dissolution of the droplet occurs, the concentration of water in the surrounding phase increases, and, at the droplet surface, the solution becomes saturated with water. The dissolution of the droplet does not lead to the saturation of water in the bulk surrounding phase, due to the very small volume of the droplet (less than 0.1% of the total volume). The water solubility increases with the increase in ethanol concentration, represented by the distance from the colourful point to the phase boundary in Fig. 1(b).
image file: c7nr02704d-f1.tif
Fig. 1 Left: Schematic depiction of the experimental setup in which a water droplet containing the nanoparticle suspension is placed on an OTS–Si substrate immersed within a binary mixture of miscible (ethanol) and immiscible (toluene) solvents. Right: Phase diagram of the ternary water–ethanol–toluene system; the arrow indicates the composition of the surrounding ethanol–toluene mixture wherein the ethanol concentration is varied from 2% to 10%. The points shown with the different colors represent different initial compositional ratios. The composition near the droplet changes along the path indicated by dotted lines.

The side-view of the droplet was recorded over time. The droplets on the substrate were nearly spherical with a contact angle of 154° ± 5° in 10% ethanol and 167° ± 5° in 2% ethanol. After a brief period of initial transient, the shrinkage in the droplet dimension can be seen in Fig. 2 showing the time course snapshots of the droplet in the binary solution of three ethanol concentrations. While the shrinking droplet maintains its initial shape in the early stages of the dissolution, it will become evident subsequently that this is no longer true over longer times.

image file: c7nr02704d-f2.tif
Fig. 2 (a) Snapshots showing the shape evolution of the water droplets comprising the nanoparticle suspension as it dissolves into the surrounding ethanol–toluene solution at different initial concentrations; the scale bar denotes a length of approximately 200 μm. (b) Droplet diameter D as a function of time in the early stages of the dissolution, measured when it still existed in the form of a regular spherical cap. (c) Dissolution rate and water solubility as a function of the initial ethanol concentration in the binary mixture. The derivation of the dissolution rate at low ethanol concentration is too small to be visible in the plot. (d) Diameter of the droplet, measured when it still existed in the form of a regular spherical cap, as a function of time for varying height levels of the surrounding liquid phase. The ethanol concentration is 5% and the initial nanoparticle concentration is fixed at 5%.

We found that the dissolution rate of the droplet is clearly dependent on the initial composition of the binary mixture as shown in Fig. 2. The lifetime of the droplet is substantially longer in 2% ethanol solution than in 10% solution. In Fig. 2, the plot of the droplet diameter as a function of time shows that after the initial short transition, the diameter of the droplet decreases almost linearly with time regardless of ethanol concentration. The dissolution rate that represents the slope of the linear line fitting the curve increases with the increase in ethanol concentration, suggesting that a higher ethanol concentration in the initial surrounding phase leads to a faster dissolution rate. Such dissolution behaviour appears to be similar to what is observed in the dissolution of graphene oxide suspension droplets.27

Remarkably, it can be seen that the dissolution rate is also dependent on the height of the surrounding liquid above the droplet (Fig. 2(d)). While all other parameters (i.e., ethanol concentration, initial droplet size and nanoparticle concentration) are kept constant, the lifetime of a droplet is more than 450 min under the liquid with a depth of 10 mm, and is less than 100 min with a depth of 150 mm. Obviously faster dissolution rates were observed from a droplet under a deeper body of the surrounding phase. This result suggests that external hydrostatic pressure somehow plays an important role in droplet dissolution. To understand the dissolution rate, however, it is essential to examine the hydrodynamics arising during this initial dissolution period.

2.2 External flow induced by the droplet dissolution

High speed videos of the droplet show three dominant effects as a consequence of the dissolution. Firstly, the droplet is observed to oscillate periodically (ESI). The oscillation is particularly strong for the higher (i.e., 5% and 10%) ethanol concentrations, possibly attributed to the fast dissolution dynamics. This droplet motion may be not dissimilar to the self-propulsion of droplets in a system far from equilibrium.25 The droplet oscillation nevertheless ceases at the later stages of the dissolution process.

Secondly, we observe strong meridional hydrodynamic convection in the surrounding phase, based on the movement of the tracer microparticles. Initially in the first several minutes, the flow occurs downwards to the droplet, as shown in the velocity profiles of the tracers in Fig. 3. This downward flow possibly arises due to differences in densities. Here the water ejected from the droplet is denser than the binary solution. The direction of the downward plume is consistent with the direction predicted in the work by Dietrich et al.,28 where the dissolving droplet liquid was lighter and the flow was upward.

image file: c7nr02704d-f3.tif
Fig. 3 Flow velocity profiles in the phase surrounding the dissolving droplet (a) at 2 min and (b) at 19 min for ethanol concentrations of 2%, 5% and 10%. Details on how the velocity field was measured are provided in the Experimental section. The scale bar represents a length of approximately 500 μm.

The flow nevertheless reverses subsequently after a period of droplet dissolution as seen in Fig. 4, wherein an upward flow trajectory from the droplet is observed. We noticed that due to the oscillation of the droplet, the plume appears to be off-center and can be seen to alternate laterally depending on the specific time frame at which the images were acquired. This effect is suppressed at higher ethanol concentrations (e.g., 10%) in which the stronger plumes are dominant.

image file: c7nr02704d-f4.tif
Fig. 4 Flow velocity profiles in the phase surrounding the droplet, driven by its dissolution at longer times when the reduction of the droplet volume is 50%, 66%, 83% and 97% for an ethanol concentration of (a) 5%, and, (b) 10%. The scale bar represents a length of approximately 400 μm.

We speculate that the reversal of the flow occurs because the density difference becomes progressively smaller as more and more water is mixed with the surrounding phase. In other words, the density of the ternary mixture of ethanol–water–toluene gradually increases with time, in particular, for the solution near the droplet. As the density difference is damped from the droplet dissolution, the difference in the chemical potential of water in the droplet surface and in the surrounding phase may become a primary factor contributing to the upward direction of the flow from the droplet. These composition-dependent interfacial properties can give rise to a Korteweg body force,21 a force present between two miscible liquids, such as ethanol and water. In the literature, the Korteweg force has been attributed to the kicking phenomenon of a droplet surface and the self-propulsion of a droplet.21,23,25,29 Here for our dissolving droplets the Korteweg force drives a potential flow in the form of an upward plume to the pole of the droplet, due to symmetry breaking from the presence of the substrate.

Considering that force is proportional to the chemical potential gradient,21,29 we can estimate that the velocity of the plume emanating from the droplet scales as ΔC. Here, ΔC = CeC is the difference in the solubility concentration Ce of water in the droplet. It can then be seen from Fig. 3 together with Fig. 2(c) that both the velocity of the plume as well as the droplet dissolution rate increases with higher ethanol concentrations in the surrounding phase, given the increase in the water chemical potential gradient ΔC. The plume is then observed to subsequently fade away as the water concentration C increases in the surrounding phase as the droplet dissolves. The plume velocity in the surrounding liquid above the droplet top may be influenced by the hydrostatic pressure, possibly related to the density difference between the surrounding phase and water from the droplet. Meanwhile, the droplet retains its spherical shape when immersed in a liquid of different depth, and hence the droplet does not deform significantly to substantially increase the surface area and, in turn, the dissolution rate. Faster dissolution rates observed for a droplet immersed under a deeper body of the surrounding phase is consistent with the relationship between the dissolution rate and the plume dynamics.

Finally, we note that the chemical potential gradient concurrently drives simultaneous internal convection within the droplet. We were able to qualitatively observe that the velocity of tracer particles increased with increasing ethanol concentration. In addition, the internal flow consisted of meridional recirculation from the pole to the contact line along the droplet interface, consistent with the upward plume emanating from the droplet. However we were not able to precisely visualise the internal velocity profile through the usual particle tracking technique, due to the high concentration of nanoparticles within the droplet.

2.3 Late stage dissolving droplet morphology

Towards the late stages of droplet dissolution, the shape of the droplet remains a spherical cap in the solution with a low concentration of ethanol. However, the droplet shape departs from a spherical cap beyond a critical ethanol concentration—typically 5%—as seen in Fig. 5. The lateral diameter of the droplet in both 5% and 10% ethanol solution appears almost constant with time as the height of its center decreases, suggesting that the droplet boundaries are pinned. We observed an inversion of the droplet curvature, akin to the formation of the toroidal shape droplet due to the buckling instability that arises in the case of the evaporating droplet in Velev et al.16 The inversion of the droplet curvature is closely related to the internal flow dynamics that leads to the dispersion of the nanoparticles away from the droplet center. The consequence of the fast flow from the droplet pole is a thinner and more permeable interfacial shell at the polar region that, together with the reduction in the droplet volume, results in a negative pressure in the center of the droplet and the inversion of the droplet.
image file: c7nr02704d-f5.tif
Fig. 5 (a, b) Time course snapshots from which (c, d) the base diameter and central height of the shrinking droplet at late stages of the dissolution process are recorded. The base diameter was measured from the side-view of the droplet's contact line on the substrate. The concentration of ethanol in the binary solution is 5% in (a) and (c), and, 10% in (b) and (d). The scale bar represents a length of approximately 20 μm.

2.4 Spherical and toroidal structures of nanoparticle assemblies

Now we examine the final structures of assembled nanoparticles at the end of the droplet dissolution. Fig. 6 shows the resultant structures in the surrounding phase of different ethanol concentration. At the concentration of 2% ethanol, the nanoparticles assembled into a spherical microstructure. Both the outer surface and the exposed surface of a cut sphere were examined in SEM images in Fig. 6 and 7(a–d), showing that the nanoparticles are regularly arranged in a hexagonal and square lattice. These spherical assemblies of colloidal particles appear to be similar to the colloidal assemblies from droplet evaporation on a superhydrophobic substrate.30 Interestingly, at intermediate ethanol concentrations (4%–9%) we obtained ordered assemblies in toroidal microstructures. A bright red ring around the microtoroid in the reflection-mode optical image (Fig. 6) suggests the ordered arrangement of the nanoparticles. Long-range and regular arrangements are observed at different locations on the outer and on the inner surfaces along the cross section of the microtoroid as shown in the SEM images in Fig. 6 and 7(e)–(h). The nature of the particle packing varies between the hexagonal and square lattice at different locations within the toroid. At high ethanol concentrations beyond 10%, we observe the ordering of the nanoparticles becoming shorter in range. In addition, cracks across the rim and voids among the ordered domains can also be seen in the SEM images in Fig. 6. There is no colourful hue from light reflection due to the lack of ordering in the particles consisting of the toroid.
image file: c7nr02704d-f6.tif
Fig. 6 Optical and SEM images showing the resultant droplet morphology and internal structure of the nanoparticle assembly after its dissolution into the ethanol–toluene binary mixture for various initial ethanol concentrations. The toroidal microstructures are only observed to form at 5% and 10% ethanol concentrations; at 2% concentration, the droplet is observed to maintain its spherical shape. Additionally, the SEM images also reveal long-range ordered packing only for low (2% and 5%) ethanol concentrations.

image file: c7nr02704d-f7.tif
Fig. 7 SEM images showing the nanoparticle assembly in (a–d) the spherical microstructures formed in 2% ethanol, and, (e–h) the toroidal microstructure formed in 5% ethanol. The magnification of the structures in the insets shows the lattice to vary between hexagonal and square packing at different locations.

The external dimensions of the toroidal microstructure were found to be sensitive to the ethanol concentration. At 5%, the ring had outer and inner diameters of 490 μm and 174 μm, respectively. With increasing ethanol concentration, we observe both the inner and outer diameter to increase, at the expense of the rim thickness (Fig. 8). With the same concentration of ethanol in the surrounding phase, the inner and outer diameters of the toroidal microstructures can also be tuned by varying the initial nanoparticle concentration in the droplet. As shown in Fig. 8, the initial volumetric concentration of nanoparticles increases from 5% to 20%, leading to an increase in the outer diameter of the toroids by 1.3–1.5 times. When the ethanol concentration is below 4%, spheres instead of toroids are produced with a larger diameter from a more concentrated suspension. The ordered arrangement of the nanoparticles from suspensions of different concentrations is reflected by the regular circular hue from light reflection in the optical images of the microspheres and microtoroids.

image file: c7nr02704d-f8.tif
Fig. 8 Representative optical images showing the nanoparticle assemblies from the suspension droplet with particle concentrations of (a) 5 vol%, and, (b) 20 vol%. The scale bar denotes a length of approximately 200 μm. The percentage labelled in the images is the concentration of ethanol in the surrounding phase. (c) Plot of the inner and outer diameter of the toroidal microstructure as a function of the ethanol concentration.

The above results show that there is clear correlation between the structure of the assemblies and the droplet dissolution dynamics. As described in the Results, section 2.1–2.3, the outflux from a dissolving droplet with a surrounding phase with less than 2% ethanol is too slow to lead to inversion of its curvature at the late stage of the dissolution. The droplet retains its spherical cap shape, resulting in the spherical shape of the assemblies. At higher ethanol concentrations, the inversion of the droplet curvature occurs in the later stage of droplet dissolution, due to the meridional flow within the droplet and the pinned boundary of the droplet. Inversion of the droplet curvature leads to the toroidal-shaped self-assembly. The thicker rings at higher ethanol concentration may be attributed to the faster dissolution, which drives greater surface enrichment of the nanoparticles and results in a bigger void within the toroid after the inversion of the curvature. Strong internal convection at even higher ethanol concentration leads to appreciable disruption in the nanoparticle packing and eventual disordering in the particles.

The mechanism of the toroid formation driven by droplet inversion is different from its droplet evaporation counterpart where the doughnut shape formation is attributed to the inversion of a viscoelastic shell of nanoparticles.16,31,32 The mechanical properties of the interfacial layer, and hence the particle properties, are essential for the curvature inversion and the formation of toroidal assemblies.16 Evaporation of water from a suspension droplet can lead to self-assembly of the nanoparticles only if the mechanical properties of the shell that forms over the droplet are appropriate for the inversion of the curvature. Therefore interfacial active materials (such as surfactants) are required to tune the shell formation, in addition to the ratio of the colloidal particles in the droplet of the suspension. However, in our approach the inner and outer diameters of the toroidal microstructures are simply adjusted by controlling the droplet dissolution rate. We believe that the plume dynamics plays an essential role in the formation of the toroidal structures. This ability is particularly useful, and constitutes an obvious advantage of the droplet dissolution method. What is important in our system for toroid formation is that the supporting substrate breaks the symmetry around the droplet, essentially giving rise to an upward plume at the droplet center. A droplet suspended freely is exposed to a symmetrical surrounding, which may not necessarily lead to a plume with a certain direction. It will be interesting to study this configuration in the future, if a method can be found to suspend a drop with a size comparable to that in our experiment.

Given that the curvature inversion is driven by droplet dissolution dynamics, the toroidal structure formation is expected to be generic, potentially achievable for many types of nanoparticles as long as the droplet dissolution is not altered by the nature of the particles. As a demonstration, we have tried the suspension of nanoparticles with diameters of 100 nm, 200 nm and 300 nm and the mixture of nanoparticles with diameters of 200 nm and 300 nm. We obtained toroidal assemblies from the dissolution of all these suspension droplets (see Fig. S1 and S2). Moreover, we also observed the formation of a toroidal shape with mixed particles and particles of varying sizes and shapes (such as Fe3O4@SiO2 nanoparticles and silica nanorods), although the arrangement of the nanorods within them is not regular, as shown in the ESI. The results suggest that the formation of the toroidal structure is indeed possible for a wide range of types and initial concentrations of the nanoparticles.

3. Conclusion

In summary, we have reported the dissolution dynamics of a sessile droplet comprising a nanoparticle aqueous suspension in a binary solution. The two solvents in the surrounding phase are ethanol and toluene. An upward flow emanates from the droplet as the concentration of the miscible solvent (i.e. ethanol) in the outer phase is above a certain level. Meanwhile a meridional flow within the droplet along with the pinned contact line of the droplet contributes to the inversion of droplet curvature at the late stage of the dissolution. We further demonstrated that the droplet dissolution dynamics may be explored for the formation of toroidal nanocolloidal assemblies, applicable to many types of suspensions of a wide range of initial particle concentration and of particles with different materials and shapes. These toroidal assemblies with highly ordered particle arrangement may find potential applications in separation, catalysis, biosensing, or optoelectronics for display technologies.

4. Experimental section

4.1. Substrate and solutions

Toluene (anhydrous, 95%) and ethanol (99.5%) were acquired from Sigma-Aldrich Pty. Ltd (Castle-Hill, NSW, Australia). All chemicals were used without further purification. Prior to use, the hydrophilic silicon substrate was cleaned in piranha solution [H2SO4 (70%)[thin space (1/6-em)]:[thin space (1/6-em)]H2O2 (30%)] at 75 °C for 20 min, followed by thorough rinsing in ethanol and water. The substrate was then completely dried at 400 °C for 2 hours. A hydrophobicized substrate (octadecyltrichlorosilane coated silicon, OTS-Si) was then prepared and cleaned by following the protocol reported in a previous work.33 The advancing and receding contact angles of water on the substrate in air were 112° and 97°, respectively.

4.2. Droplet dissolution

A 0.5 μl water droplet comprising a suspension of 300 nm diameter SiO2 nanoparticles at a concentration of 5 vol% was deposited on the hydrophobic substrate that is completely submerged in a binary mixture of ethanol and toluene at an initial ethanol concentration that ranged between 2% and 10% (see the ESI). The droplet had an initial radius of approximately 0.5 mm. The initial physical properties of the droplet are as follows: density ρ = 1000 kg m−3, surface tension γ = 39 mN m−1 and viscosity μ = 0.89 cP, such that the capillary length Lc = (γ/ρg)1/2 = 1.97 mm, wherein g denotes the gravitational acceleration. On completion of the droplet dissolution process, the resultant microstructures were carefully removed from the solution and imaged in air after drying under ambient conditions. Further increase in the ethanol concentration in the surrounding solution leads to the dissolution of the droplets.

4.3. Characterisation

The flow velocity profiles in the surrounding phase were acquired using microparticle tracking with 2 μm diameter melamine particles (Sigma-Aldrich Pty. Ltd, Castle-Hill, NSW, Australia). Video footage of the flow and the evolution of the droplet shape was acquired using a standard contact angle measurement setup (OCA 20, DataPhysics Instruments GmbH, Filderstadt, Germany) from which, at a given time, two subsequent individual still frames were analysed using ImageJ and plotted through Matlab. The ImageJ code is similar to the PIV (particles image velocimetry) Image J plugin and relies on a three-step iterative scheme that calculates the displacement through a normalised correlation coefficient algorithm. Each iteration assumes an interrogation window that is half that of the previous step, e.g., starting from 64 to 32 and then 16 pixels, with an average of five beads per interrogation window for the smallest (final) iteration step. The time interval between two consecutive images is 0.1683 s. It should be noted that these velocity measurements were carried out not for long-term quantification, but to examine the qualitative dependence of the droplet dissolution process on external parameters. The toroidal structures were imaged optically (HRM-300, Huvitz BD, Gyeonggi-do, Republic of Korea) as well as using scanning electron microscopy (SEM; Philips XL-300, SEMTech Solutions Inc., North Billerica, MA, USA).


We are grateful for inspiring discussions with Detlef Lohse on the Korteweg force and valuable comments from Helmuth Moehwald on the manuscript preparation. XHZ and LY gratefully acknowledge support from the Australian Research Council (FT120100473, FT130100672 and DP140100805). AR is the recipient of the RMIT University Vice-Chancellor's Postdoctoral Fellowship. The authors acknowledge equipment and facilities access as well as technical support at the MicroNano Research Facility and the Microscopy & Microanalysis Facility at RMIT University.


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Electronic supplementary information (ESI) available. See DOI: 10.1039/C7NR02704D

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