Anal. Chem. 2006, 78, 5192-5197
Control of Particle-Deposition Pattern in a Sessile Droplet by Using Radial Electroosmotic Flow Sung Jae Kim,*,† Kwan Hyoung Kang,‡ Jeong-Gun Lee,§ In Seok Kang,| and Byung Jun Yoon|
Department of Electrical Engineering and Computer Science, RLE, MIT, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, Department of Mechanical Engineering, Division of Mechanical and Industrial Engineering and Department of Chemical Engineering, Division of Mechanical and Industrial Engineering, Pohang University of Science and Technology, San 31, Hyoja-Dong, Pohang, 790-784, Korea, and Bio laboratory, Samsung Advanced Institute of Technology, San 14-1, Nongseo-ri, Giheung-eup, Yongin-si, Gyunggi-do, 449-712, Korea
In this technical note, we report an experimental investigation of radial electroosmotic flow (EOF) as an effective means for controlling particle-deposition pattern inside an evaporating droplet, which has a potential application to biochemistry and analytical chemistry especially for sample preparation steps. Using the microelectrode, which consists of the circular electrode around the rim of droplet and the point electrode at the center of the droplet, we generate the radial electric field at the bottom of the electrolyte droplet. The electric field developed between the center electrode and the circular electrode causes a radial EOF in the vicinity of the bottom of the droplet. By changing the applied voltage, the strengths and directions of the radial EOF are controlled at one’s own discretion, and thus, we can modify the solute distribution inside the droplet during evaporation. When the radial EOF compensates the natural outward flow at a suitable choice of electrical voltage, the particles are uniformly distributed at the entire droplet spot. Moreover, with strong radial EOF, all the particles are deposited at the center rather than at the rim. We also carry out a simple theoretical investigation of flow field inside the droplet with Smoluchowski slip velocity condition to show how the particles travel during evaporation. The dynamics of an evaporating droplet on a solid substrate have been emphasized in the scientific field, such as heat-transfer applications. In addition, these dynamics are commonly observed in everyday life, for example, a ringlike stain after an evaporating coffee droplet. Recently, this simple phenomenon has shown to be an essential mechanism in the field of biochemistry and analytical chemistry applications, especially in the case of environments open to the atmosphere. The evaporation process as a highly important step for precise detection in protein chip and genomic DNA microarray1 has been demonstrated. This process * To whom correspondence should be addressed. E-mail:
[email protected]. Phone: +1-617-253-2516. Fax: +1-617-258-5846. † MIT. ‡ Department of Mechanical Engineering, Pohang University of Science and Technology. § Samsung Advanced Institute of Technology. | Department of Chemical Engineering, Pohang University of Science and Technology.
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has also been successfully applied to analysis of DNA and protein using MALDI-TOFMS.2 However, the unexpected ring-patterned stain formation after complete evaporation of a droplet has become a key obstacle for an efficient and automatic analysis. Such localization of solute may need the time required to search for a sample spot that yields an abundant signal. This search to reduce the automation concept of the analysis is labor-intensive and timeconsuming. Thus, it is desirable to devise a method for controlling the solute distribution inside a droplet after complete evaporation. The physicochemical mechanism of the drop stain phenomenon has yet to be completely developed, but the contact line pinning due to the hydrophilic surface and the nonuniform evaporation from the edge of the droplet might contribute to the outward migration of solute.3 As the droplet remains pinned on the substrate and the liquid is removed from the edge of the droplet first, the outward flow from the interior must replenish the mass loss. The spotlighted explanation for the evaporation from the edge is that the probability of escaping an evaporating molecule at the edge is higher than at the center due to the geometrical curvature of the droplet.4 One way to improve spatial stain homogeneity is to develop a system that uses a substrate other than bare metal or chemical surface treatments. The uses of the poly(tetrafluoroethylene)5 and polymer/Nafion substrate6 were reported to produce a relatively homogeneous solute distribution. Another possibility is the control of the outward radial flow inside the droplet. Stirring7 and spin-coating8 sample preparation methods were reported to achieve the control. However, the surface treatment and the mechanical techniques have shortcomings that gave rise to an uncontrollable deposition pattern during the experimental processes. Simple controllable deposition schemes, thus, are required depending on sample droplet properties. (1) Blossey, R.; Bosio, A. Langmuir 2002, 18, 2952-2954. (2) Guo, B. Anal. Chem. 1999, 71, 333R-337R. (3) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Nature 1997, 389, 827-829. (4) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Phys. Rev. E 2000, 62, 756-765. (5) Hung, K. C.; Ding, H.; Guo, B. Anal. Chem. 1999, 71, 518-521. (6) Kim, Y.; Hurst, G. B.; Doktycz, M. J.; Buchanan, M. V. Anal. Chem. 2001, 73, 2617-2624. (7) Westman, A.; Demirev, P.; Huth-Fehre, T.; Bielawski, J.; Sundqvist, B. U. R. Int. J. Mass Spectrom. Ion Processes 1994, 130, 107-115. (8) Perera, I. K.; Perkins, J.; Kantartzoglou, S. Rapid Commun. Mass Spectrom. 1995, 9, 180-187. 10.1021/ac0601866 CCC: $33.50
© 2006 American Chemical Society Published on Web 05/27/2006
Figure 1. Schematic illustration of (a) simplified fabrication processes, (b) mask 1 for center electrode patterning, (c) mask 2 for silicon deposition to prevent short circuit, (d) mask 3 for circular electrode patterning, and (e) the completed electrode.
In this work, we study the utility of radial electroosmotic flow (EOF) as an effective means for controlling liquid flow inside the droplet. We devise the circular electrode system, which also has a point electrode in the center of the circle. The electric field developed between the center point electrode and the circular electrode placed along the droplet rim causes a radial EOF in the vicinity of the bottom of the droplet. By changing the polarities and the strengths of applied voltage, we can control the radial direction (inward and outward) and magnitude of the radial EOF, and thus, we can modify the solute distribution inside the droplet at one’s own discretion. With this device, the almost homogeneous deposition on a substrate is possible and the solutes are even collected into the center of the droplet according to the applied voltage. EXPERIMENTAL SECTION Preparation of Electrode. The present investigation used a 4-in. silicon wafer to fabricate the circular electrode system. Prior to microfabrication of the silicon wafer, the wafer was cleaned to remove contamination. Figure 1 provides the schematic illustration of the simplified fabrication process, together with the masks used. First, the surface of the silicon wafer was oxidized to prevent a short circuit. The thin layer of positive film was then used as a mask, shown as Figure 1b, for the sputtering of the center aluminum electrode. The patterned aluminum was sputtered to form a 1-µm-height electrode. We designed the center electrode such that it could be buried beneath the circular electrode. Thus, the silicon insulation layer was deposited to prevent the short circuit using the negative film mask shown in Figure 1c. Finally,
the circular patterned aluminum electrode and its pod were redeposited to a 1-µm height using the positive mask shown in Figure 1d. We fabricated the circular electrodes at various radii, 1, 2, and 5 mm in the single silicon wafer. Completed electrode systems are shown in Figure 1e. System Setup including Sample Liquid. Colloidal suspension of surfactant-free, 50-nm polystyrene microspheres in 0.01 M NaCl electrolyte solution was used as the deposition pattern tracer (A Johnson Matthey Co.). The electrical double layer thickness is less than 10 nm at this concentration. Although the polystyrene particles have a slightly negative charge, we regarded them as neutrally charged particles. The electrophoretic motion of the polystyrene particles was extremely small, enough to assume that we can neglect the electrophoretic effect. The experiment without electrolyte solution, i.e., in deionized (DI) water, was carried out to test the electrophoretic motion of the polystyrene particle itself. In DI water, the resulting deposition pattern was identical to the pattern in the natural evaporation case, even though we applied either the inward-radial or the outwardradial electric field. These results also indicate that the Joule heating effects that make temperature variation on the droplet do not play an important role in the migration of the polystyrene particles. The flow velocity due to the natural convection is ∼40 µm/s. Since the external applied voltage has a maximum value of 1.2 V in this system, the electrophoretic mobility of the polystyrene particles with slightly negative charge is less than 1 µm/s. Therefore, we regard the polystyrene particles as neutrally charged particles. Although gravitational force and temperature gradient did not play an important role in formation of the ring stain,4 we kept horizontality of the substrate during the experiments at room temperature. The diffusion of the particles can be neglected because the Peclet number is far greater than 100 (Pe ) UL/D ) 40 µm/s × 1 mm/10-12 m2/s ) 4 × 104). The performance of the circular electrode was captured using a digital camera (Optio4, Pentax) every 30 s. A micropipet was used to drip 1 µL of solution on a 1-mm-radius circular electrode. Under the assumption that the shape of the droplet is a spherical cap, an initial contact angle is 60°. With those conditions, the droplet completely evaporated within 20 min. The experiments were performed at various strengths and polarities of electrical voltage to investigate the effects of radial EOF. THEORETICAL MODELING Scale Statement. The droplet shape is controlled by the Bond number, Bo ) FgRh0/σ, which is the ratio of surface tension and gravitational force on the droplet, and by the capillary number, Ca ) µu/σ, which is the ratio of viscous force to capillary force. Here, F represents the fluid density, µ the fluid viscosity, σ the interfacial tension at the air-water interface, g the constant of gravitational acceleration, R the contact-line radius; h0 the initial height of the droplet, and u the average radial velocity induced by evaporation. The contact-line radius of the droplet system is ∼1.0 mm, and the flow velocity inside of the droplet is less than 40 µm/s. Consequently, the Bond number is ∼0.07 and the capillary number is ∼10-8, so that the droplet shape can be regarded as a spherical cap. Furthermore the flow field inside a droplet is governed by the unsteady Stokes equation, ∂u/∂t ) -∇p + µ∇2u and the continuity equation, ∇‚u ) 0. The flow Analytical Chemistry, Vol. 78, No. 14, July 15, 2006
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u ˜r ) u ˜z )
(
)
˜z 2 2z˜ 3 1 1 [(1 - ˜r 2) - (1 - ˜r 2)-λ(θ)] 2 8 1 - ˜t r˜ h˜ h˜
(
)
(5)
3 1 ˜z 2 3 1 ˜z 3 + [1 + λ(θ)(1 - ˜r 2)-λ(θ)-1] 2 [ 4 1 - ˜t h ˜ 2 1 - ˜t 3h˜
(
(1 - ˜r 2) - (1 - ˜r 2)-λ(θ)]
2
)
˜z ˜z 3 h˜ (0,t) (6) 2h˜ 2 3h˜
where the dimensionless variables are defined as follows: Figure 2. Schematic diagram of an evaporating droplet in cylindrical coordinate system (r, z). R, h0, and θ are droplet radius, center height, and contact angle, respectively. J(r, t) is the nonuniform evaporation rate on the droplet surface as a function of radial position and time, and h(r, t) is local droplet height. The black bars under the z ) 0 at r ) 0 and at r ) R are center and rim electrode, respectively. φ0 and φR are the electrical potential at the center and at the rim electrode, respectively.
boundary conditions are the no-slip condition for the natural evaporation case and the Smoluchowski slip conditions for the radial EOF. Analytical Solution of 2D Flow Field in an Evaporation Droplet. Consider the small spherical cap-shaped droplet of water sitting on a solid substrate with center and rim electrode (see Figure 2). We introduce a (r, φ, z) cylindrical coordinate system, which has its origin at the center of the base circle of the droplet. Due to the axial symmetry, there is no change of parameters in φ-direction, i.e., ∂/∂φ ) 0. Then, the continuity and the unsteady Stokes equation are written, in the cylindrical coordinate system, as follows:
∂uz 1 ∂ (rur) + )0 r ∂r ∂z
(1)
(( ) ) ( ( ) )
∂2ur ∂ur ∂p ∂ 1 ∂ ) -µ (ru ) + 2 + ∂t ∂r r ∂r r ∂r ∂z
(2)
∂uz ∂2uz ∂p 1 ∂ ∂uz r + 2 + ) -µ ∂t r ∂r ∂r ∂z ∂z
(3)
where ur and uz represent the velocity component in r and z direction, respectively. The local height h(r, t) of a spherical droplet is determined from the contact angle θ, which is a linearly decreasing function of time, as well as the contact radius R as follows:9
h(r,t) ) x{R2}/{sin 2θ} - r2 - R/tan θ,
r eR
(4)
In previous studies done by Deegan et al.3 and Larson et al.,10 two-dimensional velocity fields inside the droplet are (9) Hu, H.; Larson, R. G. J. Phys. Chem. B 2002, 106, 1334-1344. (10) Chopra, M.; Li, L.; Hu, H.; Burns, M. A.; Larson, R. G. J. Rheol. 2003, 47 (5), 1111-1132.
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r ˜r ) , R
˜z )
z , h0
h˜ )
h , h0
t ˜t ) , tf
u ˜r )
urtf R
u ˜z )
uztf h0
and λ(θ) is the experimental parameter reflecting the nonuniformity of evaporation and is given by 0.5 - θ/π and tf is the total drying time. The equations 5 and 6 satisfy the zero-shear-stress boundary condition on the free air-liquid surface (∂ur/∂z|interface ) -∂uz/∂r|interface) and the no-slip boundary condition on the substrate (ur|z)0 ) uz|z)0 ) 0). Natural flow inside a droplet due to evaporation satisfies the no-slip flow condition at the liquid/substrate interface. However, the slip flow condition is applicable as long as the EOF is induced inside the droplet. The electroosmotic slip condition is valid in the case of the thin electrical double layer. The thickness of the electrical double layer is determined by various factors, and the most important factor is the concentration of bulk electrolyte (higher electrolyte concentration gives thinner electrical double layer). We use 0.01 M electrolyte, which gives the electrical double layer thickness of 3 nm. The droplet dimension is much greater than the thickness, so we can use the slip velocity approximation. To apply the slip velocity boundary condition due to electroosmosis, we should determine the electrical field distribution in the vicinity of the substrate surface. If the electrolyte concentration is uniform inside the droplet, the electric field satisfies ∇‚E ) 0, which is merely the current conservation requirement, and the electric potential follows the Laplace equation in the polar coordinate with two boundary conditions (at r ) 0, φ ) φ0 and at r ) R, φ ) φR). Then the electric potential has the form of a logarithmic function. Because the electric field is equal to the negative gradient of electrical potential, E ) -∇φ, we can approximately represent that the nonuniform electrical field distribution is proportional to 1/r under the lubrication assumption that the derivation in z-direction can be neglected. With this property, we consider the radial velocity, u ˜r first. We insert a constant times 1/r term into eq 5 to obtain u ˜r with the electroosmotic slip velocity on the substrate surface as follows:
u ˜r )
(
)
R ˜z 2 2z˜ 3 1 1 + [(1 - ˜r 2) - (1- ˜r 2)-λ(θ)] 2 (7) 8 1 - ˜t ˜r h ˜ ˜r h˜
where R is the strength parameter of the electroosmotic velocity determined from the following equation:
R)
ζ|E| av /ue µ
(8)
Figure 3. (a) Cross-sectional streamline inside the evaporating droplet at natural drying condition of ˜t ) 0.0 and ˜t ) 0.5. And the experimental results of droplet evaporation without electroosmosis when (b) ˜t ) 0.0 and (c) ˜t ) 1.0 on 1-mm-radius electrode of polystyrene droplet and (d) ˜t ) 1.0 on 2-mm-radius electrode of coffee droplet.
where uav e is the radial average electroosmotic velocity, which can be obtained by integrating 1/r from the center to the rim of the droplet. On the substrate, the radial velocity is exactly proportional to the electrical field and its strength is controlled by the surface ζ potential and the external electric field strength. The axial velocity, u ˜ z, is obtained using the continuity eq 1 and has the same formula as eq 6. And also the 1/r term in eq 7 satisfies the governing equations and the zero-shear-stress boundary condition because the differentiation of r×R/r with respect to r vanishes to zero. Finally, we can use the full two-dimensional radial and axial electroosmotic velocity field given by eqs 7 and 6, respectively. RESULTS AND DISCUSSION Natural Evaporation. The cross-sectional streamlines inside the droplet at natural drying condition are theoretically computed by eqs 7 and 6 and are shown in Figure 3a. Figure 3a shows that the flow near the center dominantly has the vertical component and the magnitude of flow near the rim is strongest due to the maximum evaporation rate at the edge. Also, the magnitude of outward radial flows is accelerated as evaporation time proceeds. Consequently, a polystyrene particle that starts from the liquid/ gas interface goes down and then moves toward the rim of the droplet. Figure 3b-d shows the experimental results of the evaporating drop stain without EOF; i.e., R is zero in eq 7. The initial dripped droplet is shown in Figure 3b, and the ringlike stain is clearly observed after complete evaporation as shown in Figure 3c. The coffee stain on the 2-mm-radius electrode is also shown in Figure 3d. While many unknown substances are contained in coffee particles, we can also observe the ring-shaped deposition pattern around the rim. Effect of Radial EOF. Figure 4a shows the streamlines inside the droplet when the outward radial EOF helps the outward natural flow. The strength parameter of EOF, R, is 0.025 (|E| ) 600 V/m). Since the EOF is stronger at the center than at the
edge of the droplet, the total flow field (sum of natural flow and EOF) at the center has a horizontal velocity component toward the edge of the droplet. And it helps to transport the solute to the edge. Consequently, depositions thicker than the natural evaporation case are experimentally observed with various outward EOFs as shown in Figure 4b-d. The value of R is (b) 0.025 (|E| ) 600 V/m) and (c) and (d) 0.050 (|E| ) 1200 V/m). Figure 4d is the case of the coffee stain on the 2-mm-radius electrode. In those cases, denser depositions are observed at the stronger outward EOF condition than at the natural evaporation condition. In contrast to outward flow, Figure 5a shows the streamlines when there is an inward radial EOF with R ) -0.025 (|E| ) 600 V/m). The streamlines separate around ˜r ) 0.4 also due to the stronger inward EOF near the center. As time goes by, the separate position moves closer to the center of the droplet as shown in the second part of Figure 5a, and it gives raise the separated solute deposition pattern in experimental results. In this inward case, important features are observed depending on the strength of EOF. The ring-shaped solute deposition around the edge is fairly similar to the case of natural drying at the weak inward EOF. However, the solute moves together into the center of droplet as the strength of the inward electric field increases. By this operation, we easily notice that there is the specific strength of the electric field, which gives uniform solute deposition. Figure 5b-e shows the experimental particle deposition patterns at various EOF strengths. When R is -0.025 (|E| ) 600 V/m), we obtain the almost homogeneous deposition pattern shown in Figure 5b and d. In our recent work, we do not provide quantitative analysis of stain homogeneity such as the method of using fluorescent dye particle because the digital image of the stain can suitably describe the homogeneity. With stronger inward EOF, the solute would rather concentrate in the center than Analytical Chemistry, Vol. 78, No. 14, July 15, 2006
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Figure 4. (a) Streamline inside the droplet at ˜t ) 0.0 and ˜t ) 0.5 when the outward radial EOF is induced (R ) 0.025). And the experimental results of drop stain patterns after complete evaporation at various strengths of outward EOF: (b) R ) 0.025, (c) R ) 0.050, and (d) R ) 0.050. (d) The case of coffee stain on the 2-mm-radius electrode.
Figure 5. (a) Streamline inside the droplet at ˜t ) 0.0 and ˜t ) 0.5 when there is an inward radial EOF (R ) -0.025). And the experimental results of drop stain patterns after complete evaporation at various strengths of inward EOF: (b) and (d) R ) -0.025 and (c) and (e) R ) -0.050. (d) and (e) the case of the coffee stain on the 2-mm-radius electrode.
around the edge as shown in Figure 5c and e (R ) -0.050 and |E| ) 1200 V/m). Panels d and e in Figure 5 are the particle deposition patterns of coffee on the 2-mm-radius electrode. Panels c and e in Figure 5 show the separated deposition pattern, which results from the strong inward electroosmosis. Since the radial flow is separated around ˜r ) 0.4 which is predicted by Figure 5a, the solutes are deposited at not only the center but also the rim of the droplet. With these results, one can control the solute deposition pattern by modifying the strength and magnitude of external applied voltages. 5196 Analytical Chemistry, Vol. 78, No. 14, July 15, 2006
CONCLUSIONS In this technical note, employing a microelectrode system that consists of the circular electrode around the rim and the point electrode at the bottom center of the droplet, we induce the radial EOF at the bottom surface of a droplet to control the solute distribution. When the outward radial EOF is induced, it helps the migration of solutes toward the edge of the droplet. As a result, overflowed deposition at the rim is observed. However, almost uniform solute distributions are obtained with the inward radial EOF field, which compensate for the natural outward flow at an
optimal value of R, -0.025. Over this value, the polystyrene solutes flock together near the center of the droplet, which can represent the remarkable effects of radial EOF. The concept of controlling particle deposition using radial EOF can be valuably applied for the sample preparation step, especially for the process that includes the evaporation of a sample droplet such as DNA microarray and MALDI-TOFMS. The micro- or nanoparticles such as DNA or other proteins used for biochemistry and analytical chemistry applications are not electrically neutral particles. DNA usually has a negative charge, and the optimal electrical condition for uniform deposition may be changed. Recently, we have tried to test the effects of charged particles including DNA, proteins, and functionalized magnetic beads, and the effect of the ac electrical field is also
being investigated. The numerical study of the two-dimensional mass-transfer problem is in progress with the EOF field given by eqs 7 and 6 for resolving the deposition profile and the optimal value of the electric field. Those results will be reported soon. ACKNOWLEDGMENT This work was supported by Grant R01-2004-000-10838 (2004) from the Korea Science and Engineering Foundation, the Ministry of Education under the BK21 program, and also by Samsung Advanced Institute of Technology. Received for review January 27, 2006. Accepted April 29, 2006. AC0601866
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