Article pubs.acs.org/Langmuir
Thermocapillary Fingering in Surfactant-Laden Water Droplets Raf De Dier,†,§ Wouter Sempels,‡ Johan Hofkens,‡ and Jan Vermant*,†,§ †
Laboratory for Soft Materials, Department of Materials, ETH Zürich, Zürich, Switzerland Department of Chemistry, KU Leuven, University of Leuven, Leuven, Belgium § Department of Chemical Engineering, KU Leuven, University of Leuven, Leuven, Belgium ‡
S Supporting Information *
ABSTRACT: The drying of sessile droplets represents an intriguing problem, being a simple experiment to perform but displaying complexities that are archetypical for many free surface and coating flows. Drying can leave behind distinct deposits of initially well dispersed colloidal matter. For example, in the case of the coffee ring effect, particles are left in a well-defined macroscopic pattern with particles accumulating at the edge, controlled by the internal flow in the droplet. Recent studies indicate that the addition of surfactants strongly influences this internal flow field, even reversing it and suppressing the coffee ring effect. In this work, we explore the behavior of droplets at high surfactant loadings and observe unexpected outward fingering instabilities. The experiments start out with droplets with a pinned contact line, and fast confocal microscopy is used to quantify a radially outward surfactant-driven Marangoni flow, in line with earlier observations. However, the Marangoni flows are observed to become unstable, and local vortex cells are now observed in a direction along the contact line. The occurrence of these vortices cannot be explained on the basis of the effects of surfactants alone. Thermal imaging shows that thermocapillary effects are superimposed on the surfactant-driven flows. These local vortex cells acts as little pumps and push the fluid outward in a fingering instability, rather than an expected inward retraction of the drying droplet. This leads to a deposition of colloids in a macroscopical flower-shaped pattern. A scaling analysis is used to rationalize the observed wavelengths and velocities, and practical implications are briefly discussed.
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and colloids1,4−6 over nanoparticles7 to individual molecules,4,8,9 provided convection dominates over diffusion. This can be desired or undesired, and there is a need to control these phenomena. The bulk diffusivity (D) of the dispersed material plays a crucial role, but this property is determined by the size and shape of the suspended matter and hence cannot be readily changed to avoid the creation of deposition patterns. One way to overcome these ringlike deposits is the creation of Marangoni flows, by temperature gradients or surfactant concentration gradients. Simply introducing surfactants to the bulk can lead to a mismatch in concentration along the free surface of the droplet, establishing a low surface tension at the edge and a higher surface tension at the apex of the droplet.8,9
INTRODUCTION
In 1997, Deegan and co-workers were the first to describe the physical mechanism behind the stain that forms when a simple drop of coffee dries out on a nonadsorbing substrate.1,2 For a droplet with the contact line pinned to the solid surface, the authors observed an axisymmetric, radially outward flow inside the droplet, dragging the suspended particles along. To maintain the pinning and to prevent shrinkage of the droplet, liquid evaporating at the edge is replenished by liquid from the interior, creating the outward capillary flow. The particles that are dragged along concentrate at the edge, leaving behind a distinctive ringlike stain upon complete evaporation, commonly termed the “coffee ring effect”. The mechanisms, the richness of the phenomena, and scaling approaches have recently been reviewed extensively by Larson.3 Not only coffee particles but all suspended matter can concentrate at the edge, ranging from micrometer-sized cells © 2014 American Chemical Society
Received: September 12, 2014 Revised: October 15, 2014 Published: October 15, 2014 13338
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Figure 1. Time evolution of the distribution of tracer particles and observed velocity profiles. A series of confocal images shows the evolution of an evaporating droplet containing a high concentration of surfactant [0.7% (w/v) Triton X-100]. Upon evaporation, particles accumulate at the contact line, indicated by the dotted yellow line (a), and a surfactant-induced Marangoni vortex develops as sketched qualitatively below (b). In a later stage, a nonaxisymmetric flow near the contact line emerges and creates distinct regions containing a higher concentration of particles that move along the edge (c and d) and collide upon encounter and locally undulate the contact line of the droplet (e). The scale bar is 50 μm; tfin is 380 s, and the initial droplet volume is 10 μL.
The resulting gradient in surface tension gives rise to a strong inward Marangoni stress that drags the suspended material back from the edge along the air−liquid interface back to the center of the droplet. The combination of the outward capillary flow and the inward surfactant-induced Marangoni flow leads to the development of a so-called Marangoni eddy or vortex.8 The flow field created by the Maragoni stresses is in the opposite direction of the capillary flow and redistributes the suspended matter. This can lead to a homogeneous deposition of suspended particles. In many circumstances, however, a droplet containing surfactants will not remain pinned to the substrate, and during the final stages of evaporation, a receding contact line is observed.10,11 For polymeric solutions, during the spreading and drying of droplets on a wettable substrate the drying stages can show hydrodynamic instabilities as the viscosity of the polymer solutions will vary in space.10 Hydrodynamic instabilities in droplets are not uncommon. Probably the most striking instabilities are the “viscous fingering” instabilities reported for fusing droplet spreading. When a droplet or a thin film is made to spread on a wetted substrate, the formation of a remarkable pattern can sometimes be observed, with fingers protruding along the edge of the spreading droplet or film. This fingering phenomenon is due to a hydrodynamic instability and arises as a consequence of a competition of the capillary effects with the force that causes the spreading motion. Local fluctuations in curvature give rise to a locally higher Laplace pressure that will modulate the flow fields induced by, for example, a gravitational force,12−14 centrifugal forces,15 or temperature gradients.16 Regions with higher local curvatures will move faster and create subsequent higher curvatures that accelerate the flow locally and make it unstable. In this work, we report on a different type of fingering instability that occurs in water droplets that contain high concentrations of surfactants. In contrast to previous observations and theoretical predictions, where fingering phenomena have been encountered only in either spreading (whatever the spreading driving force is) or receding droplets, our observations occur in a pinned droplet for which the contact line is fixed during the evaporation process. After an incubation period, the drying droplet, whose volume is being
reduced, nevertheless moves outward and the edge of the droplet reveals a regular fingering instability. These fingering phenomena could be relevant for industrial coating processes, as large amounts of surfactants are generally key additives in water-borne coating formulations, functioning as an emulsifier or a dispersant, to improve wetting on substrates or film homogeneity.17−20 The observed instability and the flow profiles inside the droplets are quantified using a combination of bright field and high-speed confocal microscopy. To investigate the possible role of thermal Marangoni stresses, the temperature distributions near the edge of the droplet are visualized using thermal imaging.
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MATERIALS AND METHODS
Experimental Section. Experiments were conducted on aqueous droplets that contained high concentrations of a nonionic surfactant [in the range of 15−250 times the critical micelle concentration (CMC)]. A droplet (of varying size) was placed on a glass substrate, whose initial temperature was controlled using a plate heater and varied from 23.5 to 42.5 °C. The droplet was allowed to evaporate while the internal flow profile was monitored. All droplets remained pinned during the evaporation process, until the final stages when the instability occurred. Ambient temperature and relative humidity (RH) were constant during the experiments and kept at 23 ± 0.5 °C and 38 ± 1%, respectively. The total time for evaporation ranged between 130 and 380 s, depending on the experimental conditions. Different concentrations of surfactant were used, varying in the range of 0.3−5% (w/v) Triton X-100 (Sigma-Aldrich), prepared with Milli-Q water (18.2 MΩ cm, Sartorius Stedim). The surface tension above the CMC of these solutions was measured to be constant and had a value of 29.3 ± 0.1 mN m−1. Similar experiments were conducted using surfactant type Tween 20 (Sigma-Aldrich, surface tension of 33.7 ± 0.1 mN m−1). Tracer particles (Invitrogen) ranging in size from 200 to 1000 nm (yellow-green fluorescent) were used to visualize the flow field. The final particle concentration was adjusted to be approximately 2 × 10−3% (w/v) for flow profile imaging. In other experiments, to reveal the final particle deposition pattern, the particle concentration was increased to 0.2% (w/v). As a substrate, glass coverslips were used in all microscopy experiments (silica #1.5, Menzel-Gläser). These singlemolecule clean coverslips were prepared as reported previously.9 The ratio of the substrate to liquid thermal resistivities is found to be S = (kLhS)/(kShL0) ≈ 0.18−0.22 (for contact angles of 19.4° and 15.3°, respectively) for the droplet height at the onset of drying. A value of S 13339
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Figure 2. Drying droplet fingering outward. A time evolution of top-view images in a reflection of an evaporating surfactant-laden water droplet containing a high surfactant concentration [0.7% (w/v) Triton X-100] shows the propagation of an initial deformation of the contact line along the perimeter of the drop. Representative close-up images (red squares) are shown to emphasize the fingering in detail. The undulations are equally spaced at a well-defined wavelength of 750 ± 57 μm. The scale bar is 1 mm. smaller than unity indicates that the thermal resistance of the substrate does not dominate the droplet temperature. Additionally, it also means that a larger heat path through the liquid will result in a lower temperature at the droplet interface.3 Recondensation effects such as those reported by Poulard et al.10 for water droplets on nearly completely wetting substrates are not observed in our experiments as the contact angles of the aqueous droplets are still on the order of 20°. Fluorescence imaging was conducted using a high-speed multibeam confocal microscope (VisiTech) equipped with 20× and 100× oil objectives (0.85 and 1.4 NA, respectively). Time-lapse optical microscopy experiments were performed using a stereomicroscope stand SZ-61 (Olympus) equipped with a 110LAK0.3x lens and a CCD camera (Basler). The evaporation process was monitored using a white light source and detection in reflection. Thermal imaging was conducted using a FLIR infrared camera (SC6540) equipped with an X3 microscopy lens (FLIR). To analyze the effect of different mechanisms on the internal flow in a droplet and to identify the dominating mechanisms, the relevant dimensionless groups are quantified and discussed briefly. The parameters used for the calculation of all dimensionless groups are liquid viscosity ηL, characteristic velocity inside the droplet U, air− liquid surface tension σ, liquid density ρL, gravitational constant g, initial height of the droplet h0, droplet radius R, and Prandtl number Pr = ηcp/kL (where cp is the specific heat and kL the heat resistivity of the liquid). Strouhal number Sr = Utf/R is calculated using drying time tf. The capillary number Ca = (ηLU/σ) ≈ 3 × 10−7 and the Bond number Bo = (ρLgh0R/σ) ≈ 0.28 demonstrate that internal convection and gravitational sagging do not strongly influence the droplet shape. With respect to momentum transport in the liquid phase, the Reynolds number Re = (ρLUR/ηL) ≈ 2 × 10−2 reveals a laminar flow inside the droplet. The thermal transport dimensionless groups are defined as the dimensionless heat equilibration time theat/tf = (RePr/Sr)(h0/R) ≈ 2.6 × 10−3 and the liquid-phase convective versus diffusive heat transfer RePr ≈ 0.16. As theat/tf is smaller than unity, we expect thermal equilibration to be faster than the overall drying process. A value of RePr < 1 suggests that thermal heat convection can be neglected such that the velocity field inside the droplet can be obtained without accounting for thermal effects. In conclusion, we are in a regime where at least initially the flow field is expected to be dominated by a balance between capillary flow and Marangoni flows.
are simply dragged toward the edge of the droplet by a radially outward capillary flow (Figure 1a), which is the expected behavior based on the magnitude of the different dimensionless groups. As time proceeds, the flow profile changes and particles are pulled upward and back inward toward the center of the droplet by the presence of a so-called Marangoni vortex that finds its origin in the presence of surfactants (Figure 1b), as also observed in earlier work.8,9 This radial vortex redistributes the solutes back to the center of the droplet and hence prevents deposition of suspended matter near the contact line, known as the coffee ring effect. However, we observe that as time increases, a yet unidentified flow regime is found as the vortices are observed to become unstable. Zones with locally higher concentrations of tracer particles develop along the droplet’s contact line. The experiments of Still et al.8 also reported “particle inhomogeneities” in the Marangoni eddies, but the effects are amplified here by the case of higher surfactant concentrations and a better pinning of the contract line. Moreover, these regions of accumulated particles are observed to move toward each other on streamlines parallel to the contact line as shown in Figure 1c. When two of these regions meet (Figure 1d), these form a set of two counterrotating whirls in a plane parallel to the substrate and particles are dragged first along the contact line and then via the counterrotating whirls toward the center of the droplet. Surprisingly, we observe that the contact line locally deforms outward and depins, and a finger protrudes from the drying water droplet (Figure 1e). Hence, the area covered by the droplet is increased, even though the droplet volume is reduced during the drying process. As the surfactant concentrations are well above the CMC, it is not likely that this is a simple wetting phenomenon as surface energies are not expected to vary strongly. Microscopical Lateral Vortices Create Macroscopical Flower-Shaped Droplets. The undulation of the contact line and the outward fingering motion are repeated along the entire edge of the droplet, as illustrated in Figure 2. The initially localized undulation (Figure 2b) in the contact line propagates to fully occupy the droplet edge with deformations (Figure 2c,d), separated by a well-defined length (which is termed wavelength). As long as the droplet can act as a reservoir, the fingers continue to move outward. The effect of droplet volume and surfactant concentration will be discussed below. When the
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RESULTS AND DISCUSSION Vortex Flipping from the Radial to Lateral Direction. Figure 1 and Movie S1 (Supporting Information) show how the internal flow develops in a region near the contact line over time, in an evaporating, surfactant-laden water droplet. During the initial stages of evaporation, the suspended tracer particles 13340
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Figure 3. Thermal imaging. Temperature variations along the contact line of an evaporating surfactant-laden water droplet. The scale bar is 100 μm, and the surfactant concentration is 0.7% (w/v). A corresponding thermal color coding scale is shown.
induced by local enhancement of the convective mass transfer (by gently blowing air on one side of the droplet) the local temperature reduction resulted in advection of water from the neighboring regions. This can be attributed to a temperatureinduced Marangoni effect caused by the enhanced (convective) evaporation and cooling.29 The transfer of liquid along the droplet edge will lead to a local accumulation or depletion of fluid and results in a local increase or decrease in height, respectively. As the temperature of the substrate is kept constant, a local increase in film thickness increases the resistance to heat transfer from the substrate to the interface (and vice versa),30 amplifying the fluctuations and propagating them across the entire perimeter of the droplet. Surface tension acts to annihilate these differences in height of the free surface. In pure water droplets, the high value of the surface tension will lead to a suppression of these variations in height. When surfactant is present, hence lowering the surface tension, our results show that it is possible to generate substantial temperature gradients and trigger an instability in aqueous systems. The ratio of substrate to liquid thermal resistivities (S ≈ 0.18−0.22) indicates that the thermal resistance of the substrate does not dominate the heat transfer. On a microscopic scale, the temperature variations are accompanied by a Marangoni flow that is responsible for the movements observed in panels c and d of Figure 1, where locally distinct higher concentrations and velocities are observed. As the gradients develop further, surfactant- and temperature-induced Marangoni flows superimpose to induce nonaxisymmetric flows within the evaporating droplet, as exemplified by the counterrotating whirls in Figure 1e. The tracer particles are now dragged outward by the capillary flow and subsequently pulled along the droplet’s edge before being moved back inward by the temperature and surfactant concentration gradients. Thermocapillary Effects as the Origin of FlowerShaped Droplets. The origin of these temperature gradients and their dominance over gravitational forces in this case can be understood by comparing these observations with earlier ones for highly evaporative solvents with a relatively low surface tension.28,32,33 The characteristic length scales that govern whether thermocapillary phenomena develop are the capillary length Lcap = [γ(ρg)−1]1/2 ≈ 1.9 mm and the thermocapillary length Lth = Lcap[∂γ/∂T(γβ)−1]1/2 ≈ 3.4 mm, where T is the temperature, ρ the density, g the gravitational constant, γ the surface tension, and β the thermal expansion coefficient. The
reservoir is nearly drained, the droplet dries further and the suspended tracer particles are distributed homogeneously along the contour of the droplet, leaving behind a flower-shaped pattern. Local Thermal Gradients Induce Lateral Marangoni Flows. The phenomenon of fingering instabilities has been encountered in experiments13,21,22 and has been studied theoretically.23,24 For droplets spreading on a liquid or on a solid substrate, the instability is generally thought to be hydrodynamic in nature and occurs because of a local modulation of the spreading velocity by local variations in capillary pressure. Additionally, observations by Senses et al.25 account for a demixing effect responsible for their periodic deposition patterns during the drying process of a retracting droplet, as encountered by Lipson and co-workers.26,27 In this work, the situation is different: the droplet is initially pinned during the evaporation process, and no spreading or receding is observed to occur, indicating that other mechanisms are likely to cause the initial undulations of the contact line. Variations in surfactant concentration can rationalize the Marangoni vortices, but it is not clear how variations of surfactant concentration could break the radial symmetry. More specifically, variations in surfactant concentration are not expected to lead to instabilities, as these variations can be expected to be annealed by changes in the outward capillary flows and there is no obvious autoamplifying mechanism. Therefore, the possibility of thermocapillary effects being superimposed onto the surfactant-induced effects was investigated. The local temperature gradients were measured using thermal imaging experiments, and typical results are shown in Figure 3. As evaporation proceeds, with an evaporative flux diverging near the contact line, especially the droplet edge (left) cools to a temperature lower than that of the substrate. As a result, this influences the substrate directly in front of the contact line to be locally cooled (Figure 3a). As time proceeds, local regions at a lower temperature (ΔT = 0.2 °C) appear along the edge of the droplet and multiply to fully occupy the entire contact line (Figure 3b−d). The spatial modulation of temperature variations matches the wavelength of the undulations and the subsequent fingers as in Figure 2. Such temperature variations have hitherto not been reported in water droplets, yet some evidence is available for highly evaporative solvents (e.g., ethanol, methanol, and FC-72).28 To elucidate how the observed temperature differences can arise in this case, we observed that when a small variation in evaporation rate was 13341
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values of Lcap and Lth for the water surfactant solutions studied are similar to those reported in the literature.28,32,33 It is probably more insightful to study the relevant nondimensional group, which is the dynamic Bond number, defined as the ratio of the Rayleigh number and the Marangoni number Bd = Ra/ Ma = (βgh2ρ)(−∂γ/∂T)−1, which for the surfactant water systems studied here equals Bd ≈ 10−2 and allows us to conclude that thermocapillary forces are expected to dominate over gravitational effects. Thermal imaging of an evaporating droplet as in Figure 3 shows that at a high surfactant concentration [0.7% (w/v) Triton X-100], alternating cold and warm regions appear and propagate over time, at the interface and near the edge of the drop. The positions of the cold zones coincide with the locations of the macroscopically observed undulations of the contact line. The horseshoe shape of the temperature profile in the substrate, with respect to the contact line, is due to differences in the optical path because of reflections. We can conclude that significant thermal gradients on the order of 0.2 °C exist on a length scale comparable with the wavelength of instability. To investigate the thermocapillary nature of this phenomenon in more detail, we studied evaporating droplets of different sizes and quantified the dominant wavelength of the fingering instability, as shown in Table 1. The radius influences
Figure 4. Undulation of the contact line scales with surfactant concentration. Plot of the extent of the deformation (instability) of the contact line (in micrometers) over time (in seconds), during the fingering process in an evaporating droplet containing a large amount of surfactant (Triton X-100). Note that at concentrations lower than 0.5% (w/v) no undulation of the contact line is observed.
Changing the surfactant type (Triton X-100 or Tween 20) allows one to control the wavelength. The thermocapillary effect can be expected to contribute, like the outward capillary flow, to the accumulation of surfactant molecules in the colder regions along the contact line by the temperature-induced Marangoni effect, thus counteracting its own origin. However, in the direction along the contact line, the diffusion of surfactants at the interface (Ds) is on the same order of magnitude as the weaker advection, as indicated by the surface Péclet number Pes = UL/Ds ≈ 2. This implies that diffusion prevents any accumulation of surfactants along the contact line. Hence, the only force acting in the direction parallel to the contact line of the droplet in the current case is the thermocapillary effect. A scaling approach can be used to evaluate the relative importance of the different contributions leading to the observed fingering behavior. In other cases where fingering is observed, a characteristic length scale that describes the distance between two adjacent undulations is predicted from the balance of destabilizing (e.g., gravity) and stabilizing forces (often capillarity) at play.12,15,16,23,24,31 However, as the driving force leading to flow is fundamentally different, the analysis is adapted here to predict the order of magnitude of the length scale of the pattern. As thermocapillary effects are postulated to underlie the formation of the fingers (Bd ≪ 1), a competition between the temperature-induced Marangoni forces (destabilizing) and the capillary effects (stabilizing) suggests that the wavelength is governed by
Table 1. Effect of Droplet Radius, Temperature, Contact Angle, and Surfactant Type on the Wavelength of the Fingering Instability (average ± standard deviation)a R (mm) λ (μm)
7.0 750 ± 57
T (°C) λ (μm) CA (deg) λ (μm) surfactant type λ (μm)
23.5 750 ± 57
5.6 703 ± 40
4.6 571 ± 35 35 341 ± 15
19.4 750 ± 57 Triton X-100 750 ± 57
3.7 473 ± 12 42.5 254 ± 36 15.3 522 ± 33 Tween 20 932 ± 62
a
Unless stated otherwise in every section, the following parameters are kept constant (reference experiment, shown as the first element in every row): T = 23.5 °C, CA = 19.4°, containing 0.7% (w/v) Triton X100, and a droplet radius of 7 mm.
the wavelength significantly for small droplet diameters, indicating that curvature effects play a role. With an increase in temperature, the viscosity decreases while the evaporation rate increases, thus increasing the driving force for spreading. A decrease in contact angle lowers the wavelength of instability. Changing the surfactant type has a direct influence on the driving force for the spreading and the surface tension; it also changes the onset (in time) of the instability, causing the fingers to extend further in space before the droplet completely dries out (Figure 4). The contact line is deformed at concentrations of ≥0.5% (w/v). For lower concentrations, no undulation is observed. For higher concentrations, the fingers emerge from the contact line at approximately an equal velocity (≈0.68 μm/s) and the length of the deformation increases with the concentration of the added surfactant in a manner independent of concentration and equals ≈0.68 μm s−1.
⎛ dγ ΔT ⎞ ⎟ L = f ⎜ dT ⎜ γ ⎟ ⎝ ⎠
(1)
Using the Navier−Stokes equation, describing a unidirectional flow, under the assumption of a thin film and weak surface curvature effects, the wavelength of the fingering instability can be predicted by ⎛ 3ηVs ⎞−1/3 L = h 0⎜ ⎟ ⎝ γ ⎠ 13342
(2)
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deposited on the substrate in a flower-shaped self-assembly pattern along the undulated contact line. The surfactant gradient-induced Marangoni flow has been shown to become unstable. Thermal imaging showed the underlying reason for the instability to be of a thermocapillary nature, as temperatureinduced Marangoni forces add to the surfactant-induced Marangoni vortices. The characteristic wavelengths of the observed temperature gradients match those of the fingering instabilities. A simple scaling analysis suggests that the thermocapillary forces are responsible for the instability. The different fluid and environmental properties that allow one to influence the wavelength of the fingering phenomenon have been identified and varied. The ability to fine-tune this wavelength by changing one or more conditional parameters is key to controlling deposition patterns upon drying.
where Vs is the velocity at which fluid accumulates locally between the vortices and can be measured experimentally from the confocal observations. When the fingering instability is fully developed, conservation of mass dictates that Vs is on the order of the finger spreading velocity Vexp ≈ 0.68 μm s−1, being the velocity of the finger expanding under the effect of a Marangoni force dγ/dr and with a viscous friction within the film of viscosity η and height h0. The latter velocity scales according to Vexp ∼ (h0/2η)(dγ/dr). In agreement with experimental observations, eq 2 now predicts that changing the surfactant concentration should have no significant effect, yet a change in surfactant type alters dγ/dr and γ (see Table 1). Additionally, h0 is influenced by the contact angle. Temperature mainly influences the viscosity and the evaporation rate and therefore influences the spreading velocity. The influence of droplet radius becomes significant only for droplets with radii on order of the capillary length, where a decrease in wavelength is observed with a decrease in droplet size. In our case, for a measured film height of h0 = 0.22 μm, the wavelength is found to be λ ≈ 14L. This value agrees well with a linear stability analysis for the governing equations for these types of problems22 where values ranging from approximately 14L to 18L as dominant wavelengths are predicted. The simple scaling analysis provides good guidelines for how to tune the fingering wavelength. This kind of control of macroscopical structuring has been shown to be useful in many applications4−7 from (bio)colloidal patterning on substrates to the self-assembly construction of photonic crystals and golden plasmonic hot spots. As a proof of principle, Figure 5
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ASSOCIATED CONTENT
S Supporting Information *
Movie S1 shows vortex flipping in surfactant-laden water droplets. Confocal time-lapse imaging showing the internal flow profiles of an evaporating water droplet containing a high concentration of a nonionic surfactant [0.7% (w/v) Triton X100]. The scale bar is 50 μm. The video is played at 10 times real-time speed. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Author Contributions
R.D.D. and W.S. contributed equally to this work. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS R.D.D. and W.S. are grateful for the financial support from the FWO-Vlaanderen and IWT-Vlaanderen, respectively. The Hercules foundation (HER/08/21) is gratefully acknowledged for the funding of the confocal microscope. FWO-Vlaanderen is acknowledged for support through Grants G.0554.10, G.0697.11, G0197.11, and G0990.11. This work was also supported by BELSPO, IAP/micromast. Dr. Robert K. Neely is kindly acknowledged for his critical reading of the manuscript. Koen Jacobs from FLIR is gratefully acknowledged for his assistance with the FLIR infrared camera (SC6540) equipped with an X3 microscopy lens.
Figure 5. Flower-shaped deposition pattern after evaporation of a surfactant-laden water droplet. Confocal imaging of the deposition pattern of a droplet at a high surfactant concentration [0.7% (w/v) Triton X-100] containing a high particle density [0.2% (w/v)]. The particles collect in the fingers of the spreading droplet and, upon drying, assemble in a uniform, flower-shaped deposition pattern on the substrate. The scale bar is 50 μm.
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REFERENCES
(1) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Capillary flow as the cause of ring stains from dried liquid drops. Nature 1997, 389, 827−829. (2) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Contact line deposits in an evaporating drop. Phys. Rev. E 2000, 62, 756−765. (3) Larson, R. G. Transport and Deposition Patterns in Drying Sessile Droplets. AIChE J. 2013, 60 (5), 1538−1571. (4) Wong, T.; Chen, T.; Shen, X.; Ho, C. Nanochromatography driven by the coffee ring effect. Anal. Chem. 2011, 83, 1871−1873. (5) Wang, M. C. P.; Gates, B. D. Directed assembly of nanowires. Mater. Today 2009, 12, 34−43. (6) Kruglova, O.; Demeyer, P. J.; Zhong, K.; Zhou, Y.; Clays, K. Wonders of colloidal assembly. Soft Matter 2013, 9, 9072−9087.
demonstrates the flower-shaped self-assembly and uniform deposition upon evaporation of a surfactant-laden water droplet containing a high concentration of colloidal latex particles.
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CONCLUSION Initially pinned evaporating water droplets containing large amounts of surfactants show remarkable instability. Drying droplets are observed to finger outward. Nanoparticles are 13343
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(7) Bigioni, T. P.; Lin, X.-M.; Nguyen, T. T.; Corwin, E. I.; Witten, T. A.; Jaeger, H. M. Kinetically driven self assembly of highly ordered nanoparticle monolayers. Nat. Mater. 2006, 5, 265−270. (8) Still, T.; Yunker, P.; Yodh, A. G. Surfactant-induced Marangoni eddies alter the coffee-rings of evaporating colloidal drops. Langmuir 2012, 28, 4984−4988. (9) Sempels, W.; De Dier, R.; Mizuno, H.; Hofkens, J.; Vermant, J. Auto-production of biosurfactants reverses the coffee ring effect in a bacterial system. Nat. Commun. 2013, 4, 1757. (10) Poulard, C.; Damman, P. Control of spreading and drying of a polymer solution from Marangoni flows. Europhys. Lett. 2007, 80, 64001. (11) Maheshwari, S.; Zhang, L.; Zhu, Y.; Chang, H.-C. Coupling Between Precipitation and Contact-Line Dynamics: Multiring Stains and Stick-Slip Motion. Phys. Rev. Lett. 2008, 100, 044503. (12) Huppert, H. E. Flow and instability of a viscous current down a slope. Nature 1982, 300, 427−429. (13) Marmur, A.; Lelah, M. D. The spreading of aqueous surfactant solutions on glass. Chem. Eng. Commun. 1981, 13, 133−143. (14) Edmondstone, B. D.; Matar, O. K.; Craster, R. V. Surfactantinduced fingering phenomena in thin film flow down an inclined plane. Physica D 2005, 209, 62−79. (15) Melo, F.; Joanny, J. F.; Fauve, S. Fingering instability of spinning drops. Phys. Rev. Lett. 1989, 63, 1958−1961. (16) Cazabat, A. M.; Heslot, F.; Troian, S. M.; Carles, P. Fingering instability of thin spreading films driven by temperature gradients. Nature 1990, 346, 824−826. (17) Holmberg, K. Role of surfactants in water-borne coatings. Prog. Colloid Polym. Sci. 1998, 109, 254−259. (18) Wilson, I.; Alan, D.; Nicholson, J. W.; Prosser, H. J. Waterborne coatings: Surface coatings 3; Elsevier Applied Science; Elsevier Science Publishers Ltd.: Amsterdam, 1990. (19) Scalarone, D.; Lazzari, M.; Castelvetro, V.; Chiantore, O. Surface monitoring of surfactant phase separation and stability in waterborne acrylic coatings. Chem. Mater. 2007, 19, 6107−6113. (20) Storey, R. F.; Rawlins, J. W. The Waterborne Symposium. Proceedings of the forty-first annual international waterborne, highsolids, and powder coating symposium, New Orleans, LA, February 24−28, 2014. (21) Troian, S. M.; Wu, X. L.; Safran, S. A. Fingering instability in thin wetting films. Phys. Rev. Lett. 1989, 62, 1496−1499. (22) Troian, S. M.; Herbolzheimer, E.; Safran, S. A.; Joanny, J. F. Fingering instabilities of driven spreading films. Europhys. Lett. 1989, 10, 25−30. (23) Troian, S. M.; Herbolzheimer, E.; Safran, S. A. Model for the fingering instability of spreading surfactant drops. Phys. Rev. Lett. 1990, 65, 333−336. (24) Matar, O. K.; Troian, S. M. The development of transient fingering patterns during the spreading of surfactant coated films. Phys. Fluids 1999, 11, 3232−3246. (25) Senses, E.; Black, M.; Cunningham, T.; Sukhishvili, S. A.; Akcora, P. Spatial ordering of colloids in a drying aqueous polymer droplet. Langmuir 2013, 29, 2588−2594. (26) Elbaum, M.; Lipson, S. G. How does a thin wetted film dry up? Phys. Rev. Lett. 1994, 72, 3562−3565. (27) Samid-Merzel, N.; Lipson, S. G.; Tannhauser, D. S. Pattern formation in drying water films. Phys. Rev. E 1998, 57, 2906−2913. (28) Brutin, D.; Sobac, B.; Rigollet, F.; Le Niliot, C. Infrared visualization of thermal motion inside a sessile drop deposited onto a heated surface. Exp. Therm. Fluid Sci. 2011, 35, 521−530. (29) Levich, V. G. Physicochemical Hydrodynamics; Prentice-Hall International Series in the Physical and Chemical Engineering Sciences; Prentice-Hall: Englewood Cliffs, NJ, 1962; pp 384−390. (30) Hu, H.; Larson, R. G. Analysis of the effects of Marangoni stresses on the microflow in an evaporating sessile droplet. Langmuir 2005, 21, 3972−3980. (31) Carles, P.; Troian, S. M.; Cazabat, A. M.; Heslot, F. Hydrodynamic fingering instability of driven wetting films: Hindrance by diffusion. J. Phys.: Condens. Matter 1990, 2, 477−482.
(32) Carle, F.; Sobac, B.; Brutin, B. Hydrothermal waves on ethanol droplets evaporating under terrestrial and reduced gravity levels. J. Fluid Mech. 2012, 712, 614−623. (33) Sobac, B.; Brutin, D. Thermocapillary instabilities in an evaporating drop deposited onto a heated substrate. Phys. Fluids 2012, 24, 032103.
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dx.doi.org/10.1021/la503655j | Langmuir 2014, 30, 13338−13344
