Anal. Chem. 2009, 81, 8256–8259
Behavior of Particles in an Evaporating Didisperse Colloid Droplet on a Hydrophilic Surface Jung-Yeul Jung,*,†,§ Young Won Kim,† and Jung Yul Yoo†,‡ Institute of Advanced Machinery and Design, Seoul National University, Seoul 151-744, Korea, and School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-742, Korea It is well-known that the liquid and the nanoparticles in an evaporating colloid droplet on a hydrophilic surface move radially outward for the contact line to maintain its position. However, the motion of micro/nanoparticles in an evaporating didisperse colloid droplet has not been reported to date. In this study, an experiment on an evaporating didisperse colloid droplet on the hydrophilic surface is carried out. It is found that nanoparticles move radially outward and remain at the contact line while microparticles move inward toward the center of the droplet. Furthermore, the mechanism of the microparticles moving toward the center of the droplet is found to be due to the surface tension force of the liquid. We commonly encounter various kinds of “coffee stains,” where the residue is left after a coffee drop dries. Nanoparticles (on the order of 10-100 nm) contained within the droplet are moved by liquid flow and stacked at the contact line. It is wellknown that the liquid in an evaporating colloid droplet with a fixed contact line must flow radially outward for the contact line to maintain its position.1 Theoretical studies on the outward capillary flow and contact line deposits in an evaporating droplet are in good agreement with experimental results.1-3 The self-pinned contact line of the evaporating droplet is of great interest in the field of patterning and separation of particles and biocells.4-9 There are various applications of the optical mapping of DNA molecules, the making assembly associated with patterned hydrophobicity, and the separation of microparticles and biocells associated with DEP (dielectrophoresis).5,7,10 However, the behaviors of micro/nanoparticles in an evaporating didisperse colloid * To whom correspondence should be addressed. E-mail: jungjy73@ khu.ac.kr. Phone: +82-31-201-3682. † Institute of Advanced Machinery and Design, Seoul National University. ‡ School of Mechanical and Aerospace Engineering, Seoul National University. § Present address: Department of Mechanical Engineering, Kyung Hee University, Gyunggi 446-701, Korea. (1) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Nature 1997, 389, 827–829. (2) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Phys. Rev. E 2000, 62, 756–765. (3) Hu, H.; Larson, R. G. J. Phys. Chem. B 2002, 106, 1334–1344. (4) Adachi, E.; Dimitrov, A. S.; Nagayama, K. Langmuir 1995, 11, 1057–1060. (5) Fan, F.; Stebe, K. J. Langmuir 2004, 20, 3062–3067. (6) Popov, Y. O. Phys. Rev. E 2005, 71, 036313. (7) Jung, J.-Y.; Kwak, H.-Y. Anal. Chem. 2007, 79, 5087–5092. (8) Kim, I.; Kihm, K. D. Langmuir 2009, 25, 1881–1884. (9) Sommer, A. P.; Rozlosnik, N. Cryst. Growth Des. 2005, 5, 551–557. (10) Chon, C. H.; Paik, S.; Tipton, J. B.; Kihm, K. D. Langmuir 2007, 23, 2953– 2960.
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Figure 1. Experimental setup.
droplet were not reported yet while only Jung and Kwak7 simply reported that the didisperse particles of 1 µm diameter and 6 µm diameter polystyrene beads in an evaporating colloid droplet could be separated without additional forces near the contact line. Here, we report for the first time a phenomenon where microparticles (on the order of 1 µm) in the dilute didisperse colloid droplet on a hydrophilic surface move toward the center of a droplet. There are three steps in which the fluid and particles flow inside the evaporating droplet. In the first step, a self-pinned contact line is maintained and the fluid and micro/nanoparticles flow toward the contact line. In the second step, micro/nanoparticles self-assemble near the contact line, as reported by Jung and Kwak.7 In the final step, only microparticles are advected toward the center of the droplet due to the receding contact line where the surface tensile force is most dominant in the didisperse colloid droplet on the hydrophilic surface. EXPERIMENTAL SECTION Figure 1 shows the experimental setup. A mixture of 0.5 µm diameter (excited by 532 nm of light) and 5.0 µm diameter (excited by 488 nm of light) polystyrene particles (Polyscience, PA) in distilled water is prepared. Then, using a micropipet (in the range of 0.2-10 µL, Biohit Inc., NJ), a droplet of a 0.4 µL volume is pumped from the mixture and dropped on the slide glass. The total time needed to dry out the droplet is ∼315 s. The photos of the side view and the bottom view are taken using an epifluorescence microscope and CCD camera. All the particle images are captured in black and white, which are converted to green for color presentation. 10.1021/ac901247c CCC: $40.75 2009 American Chemical Society Published on Web 09/09/2009
Figure 2. Behavior of particles after evaporation at the particle concentration of 0.005%: (a) 5 µm particles; (b) 0.5 µm particles, where 532 nm of light was used for imaging small particles. The dashed circle in (a) corresponds to the measured diameter of the droplet in the beginning of the evaporation. The diameter of the circle in (b) made by 0.5 µm particles, due to the evaporation, corresponds to that of the initial droplet diameter before the evaporation.
RESULTS AND DISCUSSION To study the self-assembly mechanism of the particles in an evaporating didisperse colloid droplet, we use a droplet of distilled water which contains surfactant-free polystyrene beads having different sizes of 0.5 and 5.0 µm diameters. To easily distinguish the different-sized particles, fluorescein-labeled particles are used in such a manner that 0.5 µm diameter and 5.0 µm diameter particles are excited, respectively, by 532 and 488 nm of light. Unless otherwise noted, we use the 488 nm light source to image particles, so that 5.0 µm diameter particles would appear comparatively brighter than the small ones. We first test the behavior of particles for the monodispersed system. In the case of liquid containing only 5.0 µm diameter particles as shown in Figure 2a, most particles move inward toward the center, at an early stage. Later, however, particles lean to one direction because, due to the absence of nanoparticles, the contact line was not fixed. In the other case of liquid containing only 0.5 µm diameter particles as shown in Figure 2b, all particles contribute to maintaining the contact line so that they do not move to the center. Figure 3 shows the self-assembly of polystyrene particles in the droplet after it is dried out. At a relatively high volume fraction (Figure 3a), mixed particles are not easily separated. However, at a low volume fraction (Figure 3b), this is possible. Dispersed particles move under Brownian motion to be stably suspended in the droplet. It is conjectured that, at a high volume fraction, the evaporating liquid does not leave sufficient space for the particles to move without colliding with the substrate and other particles. As shown in Figure 3a, it was observed that particles settled down disorderly. Therefore, in a previous study, Deegan et al. used the monodisperse droplet of the volume fraction of 10-4 as an ideal solution.1 For the other case, what mechanism could separate different-sized particles as shown in Figure 3b? Droplets dropped onto a glass slide form a spherical cap with a radius R of 730 µm and an initial height of 418 µm. Then, the droplets are dried at ambient temperature and humidity while the drying process is recorded by the use of a CCD camera connected to a microscope. Figure 4 shows the time-lapse images of an evaporating droplet, taken near the top of the glass slide (Figure 4a), where 5.0 µm diameter particles appear bright, and taken at the corresponding side views (Figure 4b). As shown in Figure
Figure 3. Self-assembly of small particles (0.5 µm diameter) and large particles (5 µm diameter) in a dried-out droplet. (a) For a relatively high volume fraction of particles, the mixture consists of 0.005 vol % of 0.5 µm diameter and 0.05 vol % of 5 µm diameter polystyrene beads. Mixed particles are not separated easily from each other. Bright strings are 5 µm particles, while 0.5 µm diameter particles accumulate around the contact line. (b) For the mixture consisting of 0.005 vol % of 0.5 µm diameter and 0.005 vol % of 5 µm diameter particles, one can see the quasi-perfect separation of 0.5 µm diameter particles and 5 µm diameter particles. The ring corresponds to 0.5 µm diameter particles, while 5.0 µm diameter particles accumulate around the center.
4a, initially at t ) 0 s, all particles move under Brownian motion so that each particle appears to be of different intensity due to light diffraction. However, at t ) 230 s, while the microscope is still focused on the top of the glass slide, all particles appear clearly and their sizes look uniform, which means that all particles sedimented on the glass slide. This also means that the particles are no longer affected by the Brownian motion. At t ) 268 s, 5.0 µm diameter particles are shown to have moved toward the center. Chon et al.10 reported that, during the evaporation, strong pinning of nanoparticles acts to congregate them to the contact line. However, with further evaporation of liquid, the contact angle exceeds the critical angle so that the thin core liquid region begins to break away from the contact line.10 Therefore, particles moving toward the center can be attributed to the receding contact line toward the center of the droplet. Figure 5 shows a result of PTV (particle-tracking velocimetry) analysis. For 5 s (260 s e t e 265 s), most particles move radially inward or outward. Some particles move toward the contact line in accordance with Stokes’ flow caused by evaporation, while other particles near the contact line move inward due to the receding contact line, as shown in Figure 5b. All particles moving inward are those of 5.0 µm diameter. Analytical Chemistry, Vol. 81, No. 19, October 1, 2009
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Figure 4. Time-lapse images of didispersed particles, which show a scenario of the particle separation according to their sizes at the same volume fraction of 0.005% for each size particle. (a) Behavior of 5.0 µm diameter particles in the droplet, as imaged near the slide glass top. There are three steps in which the fluid and particles flow inside the evaporating droplet: the pinned contact line is maintained while the fluid and particles flow to the contact line (t ) 0 s); different-sized particles self-assemble at the near-side contact line (0 s e t e 230 s); only relatively larger particles are advected to the center of the droplet (230 s e t e 309 s). (b) Respectively, corresponding side views of the changing droplet shape.
Figure 5. Motions of 5 µm particles during evaporation. (a) Streaks of 5 µm particles due to multiple exposures over 5 s (260 s e t e 265 s), where 0.5 µm particles accumulate around the contact line. (b) Particle-tracking velocimetry (PTV) results obtained from the left image using only the large particles. Some particles move toward the contact line in accordance with Stokes’ flow caused by evaporation, while other particles near the contact line move toward the center of the droplet due to the receding contact line.
To account for the experimental results, we carried out a theoretical analysis using the equations proposed by Deegan et al.,1,2 whose theory is valid at the pinned contact line. The radial velocity v of the fluid inside the evaporating drop as a function of radial distance r and time t is given as follows:
v(r, t) ) -
1 Frh
∫ drr(J (r, t)1 + ( ∂h ∂r ) r
0
s
2
+F
∂h ∂t
)
(1)
where F is the density of the liquid and Js is the rate of mass loss per unit surface area per unit time from the drop by evaporation. The time dependent height of the droplet during evaporation is given as follows:
h(r, t) )
[
]
h(0, t)2 + R2 R2 - h(0, t)2 - r2 2h(0, t) 2h(0, t)
(2)
where h(0,t) is the droplet height at r ) 0. Based on their theory, we can predict various parameters such as the height of the droplet and vertical and radial flow velocities in the droplet without knowing the chemical nature of the liquid, solute, or substrate. 8258
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Estimated results are in good agreement with measured ones, within 5% of deviation. For instance, at t ) 0.5 s, the measured height of the droplet is about 418 µm and the estimated height is 410 µm, so the deviation between these two values is about 2%. At 215 s, the measured height of the droplet is about 140 µm and the estimated height is 134 µm, so the deviation between these two values is less than 5%. From the theoretical and experimental results, at the moment of depinning of the contact line, larger particles rise above the liquid layer, as schematically shown in Figure 6b. After depinning, the contact line moves to the surface of 5.0 µm diameter particles so that individual particles are surrounded with liquid film since the particle volume fraction is very low, as shown in Figure 4. The body force (which is proportional to the maximum friction force) Fb ) mg (where m is the mass of the particle and g is the gravitational acceleration) of an individual particle (5.0 µm diameter) is on the order of 10-12 N, while the surface tension force Fst ) 2πRσ (where R is the particle radius and σ is the surface tension) of water semisurrounding the particle is on the order of 10-6 N. Therefore, the particles are induced to move to the center of
given in Xu et al.11 These forces are greater than the body force and drag force. However, they are not strong enough to overcome the surface tension force of the liquid layer. The sum of the body force, drag force, van der Waals force, and electrostatic force acting on each particle is smaller than the surface tension force of the liquid film. Therefore, due to the evaporation, the contact line moves to the center of the droplet such that the particles are advected to the center of the droplet by the receding contact line. Lastly, it is remarked that, as was shown in Figure 3a (for the case of high volume fraction of 5.0 µm diameter particles), different-sized particles can be separated in the vicinity of the rim of the droplet. However, large particles do not move to the center of the droplet, which is attributed to the increase of various forces, as mentioned above (such as body, drag, electrostatic, and van der Waals forces), due to the aggregation of the particles.
Figure 6. At t ) 230 s, the contact line seems to be depinning. (a) Theoretically estimated droplet shape. (b) Schematic diagram of particle positions in the droplet, deduced from the experimental results (see t ) 230 s in Figure 3a.). (c) Depinned contact line moves to the surface of 5 µm diameter particles, where surface tensile forces (Fτ) act on individual particles.
the droplet because they can not overcome the tensile strength of the liquid. Outward-moving particles, as shown in Figure 5b, are subject to the drag force. From the obtained outward velocity of 5 µm diameter particles, the drag force acting on the particles can be calculated using Stokes’ formula, Fd ) 6πRµvp (where µ is the dynamic viscosity of water and vp is the particle velocity). The order of magnitude of the drag force in our case is about 10-12 N, which is not strong enough to overcome the tensile strength of the surrounding water film. Also, when the particles embedded in the carrier fluid are in contact with a substrate, there are two forces,11 the van der Waals force and the electrostatic force between the particle and the substrate. In our case, based on Hamaker’s theory, the van der Waals force is on the order of 10-8 N, and the absolute value of the electrostatic force based on a constant surface-charge model is on the order of 10-8 N. The detailed theoretical approach is (11) Xu, K.; Vos, R.; Vereecke, G.; Doumen, G.; Fyen, W.; Mertens, P. W.; Heyns, M. M.; Vinckier, C.; Fransaer, J. J. Vac. Sci. Technol., B 2004, 22, 2844– 2852.
CONCLUSION In summary, we report the first-observed phenomenon wherein microparticles in a colloid droplet containing micro/nanoparticles move toward the center of the droplet. Nanoparticles contained in the colloid droplet fix the contact line, where the volume fraction of the microparticles is sufficiently low to move the particles toward the center of the droplet by the receding contact line. This work provides a passive methodology to separate and/or concentrate large particles when they are contaminated in small particles. In other words, this method does not require external forces, such as dielectrophoretic force, ultrasonic/acoustic waves, photophoretic force, pressure-driven hydrodynamic force, etc., which have been widely adopted in the field of chemical/biomedical engineering. One possible application of the present concept toward biological engineering is the separation/concentration of biological particles in the situation when these particles are specially designed to bind with microparticles, or when they have strong affinity with microbeads (such as the phenomenon observed between bacteria and polystyrene particles). On the other hand, the present method may not hold for a highly viscous droplet, because it takes a long time for the droplet to be evaporated. In addition, we consider that the surface wettability, determining a rule of droplet evaporation, may play a critical role in the separation. ACKNOWLEDGMENT This work was supported in part by the Brain Korea 21 Project in 2007 under the auspices of the Ministry of Education and Human Resources Development and by the Korea Research Foundation Grant (MOEHRD) (KRF-0420-20070058).
Received for review June 9, 2009. Accepted August 7, 2009. AC901247C
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