Langmuir 2008, 24, 9889-9897
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Conversion of Surface Energy and Manipulation of a Single Droplet across Micropatterned Surfaces Jing-Tang Yang,*,†,‡ Zong-Han Yang,† Chien-Yang Chen,† and Da-Jeng Yao†,‡ Department of Power Mechanical Engineering and Institute of Nanoengineering and Microsystems, National Tsing Hua UniVersity, Hsinchu, Taiwan 30013 ReceiVed August 12, 2007. ReVised Manuscript ReceiVed April 13, 2008 To clarify a driving mechanism for the self-movement of a droplet across hydrophobic textured surfaces in series and to develop applications for a microfluidic device, we report a theoretical model, a microfabrication technique, and experimental measurements. The contact angle of a droplet on a composite surface, the stable surface energy level, and the energy barrier caused by hysteresis were investigated. With increasing patterned density of the microstructure, the contact angle and stable surface energy decreased gradually, but the energy barrier increased. Both the analytical results and the experimental measurements show that the surface energy for a suspended status is greater than that for a collapsed status, which produces increased energy to generate the movement of a droplet. An analysis of interactions between actuation force, resistive force, and viscous force during the motion of a droplet is based on the equilibrium between forces. From the perspective of energy conversion, the difference in surface energy between a higher state and a lower state would drive a single droplet and make it move spontaneously if it could overcome the static friction force resulting from hysteresis and the kinetic friction force under droplet movement. The mean velocity in the present device, measured to be 62.5 mm s-1, agrees satisfactorily with the theoretical prediction. The model developed for the energy levels enables us to assess the contact mode of a droplet placed on the patterned surface. For a prediction of the transport capability of the designed devices, a theoretical interpretation of the conversion between the surface energy and the kinetic energy of the droplet establishes a criterion that the pattern density of a textured surface should be less than 0.76. The effective rate of energy conversion is estimated to be 20.6%.
I. Introduction Fluid transport is a key issue in the development of microfluidic systems, especially for analytical chemistry and bioassay applications. Surface tension overcomes the inertial force and becomes a dominant force in microscale systems; fluidic actuation driven by surface tension has hence attracted the attention of researchers. Yi et al.1 used electrowetting on a dielectric (EWOD) to cut and transport droplets in a specified direction; their technique is capable of producing tiny droplets (100 nL) and being applied in printers. Satoh et al.2 developed an integrated system of microfluidic transport, mixing, and sensing on a single chip; the operating principle of microfluidic transport was based on electrowetting. Daniel et al.3 showed a net of inertial force acting on the drop to generate the movement of a droplet when a liquid drop was subjected to an asymmetric lateral vibration on a nonwettable surface. They illustrated the integration of several operational units on a chip: drop transport, mixing, and thermal cycling, which were precursor steps to performing advanced biological processes on a microscale domain. Two key factors in the design of a chip for droplet transport are the source of the driving force and the droplet-transporting capability. A gradient of surface wettability has long been applied to control droplet transport. Utilizing chemical deposition to create a transport path with a surface energy gradient was first proposed by Chaudhury and Whitesides4 in 1992; they further * Corresponding author. Current address: Department of Mechanical Engineering, National Taiwan University. E-mail:
[email protected]. Tel: +886-936333218. † Department of Power Mechanical Engineering. ‡ Institute of Nanoengineering and Microsystems.
(1) Yi, U. C.; Kim, C. J. Sens. Actuators, A 2004, 114, 347–354. (2) Satoh, W.; Hosono, H.; Suzuki, H. Anal. Chem. 2005, 77, 6857–6863. (3) Daniel, S.; Chaudhury, M. K.; de Gennes, P. G. Langmuir 2005, 21, 4240– 4248. (4) Chaudhury, M. K.; Whitesides, G. M. Science 1992, 256, 1539–1541.
Figure 1. Schematic of a single droplet in contact with (a) smooth, (b) wetted, and (c) composite surfaces.
demonstrated that such a specified path could make a droplet run uphill spontaneously and move from a more hydrophobic initial state toward a more hydrophilic final state on an inclined substrate. Grunze5 utilized the self-assembled monolayer to make a hydrophobic and hydrophilic pattern on planar gold electrodes. Because those electrodes were conducting, the liquid including surfactant would be pumped along the hydrophilic path and finally collected in the opposite reservoir. The flow phenomenon resulted from the gradient in surface pressure. Daniel et al.6 proposed a novel cooling device in which the surface was arranged to have a radial distribution of the surface energy gradient. The cooling droplets moving spontaneously and collapsing on each other occurred on such specific surfaces on which the saturated vapor condensed. According to his measurement and estimates, the heat transfer coefficient could be substantially increased with the above cooling device. Darhuber et al.7 designed a microfluidic device for the actuation of liquid droplets or continuous streams on a solid surface by (5) Grunze, M. Science 1999, 283, 41–42. (6) Daniel, S.; Chaudhury, M. K.; Chen, J. C. Science 2001, 291, 633–636. (7) Darhuber, A. A.; Valentino, J. P. J. Microelectromech. Syst. 2003, 12, 873–879.
10.1021/la8004695 CCC: $40.75 2008 American Chemical Society Published on Web 08/07/2008
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Figure 2. Illustrations of (a) the hysteresis effect and (b) the energy levels of a single droplet. Figure 2a shows a photograph of a single droplet that slides down a grooved surface of PPFC with a tilt angle of 10°. θA (right) ) 155°, θR(lift) ) 152°. Figure 2b shows that the energy barrier is related to those surface energy levels. If the input energy is less than the energy barrier for case I, then the droplet will have insufficient transport energy on the textured surface but might alter its surface profile and interfacial area, whereas if the input energy is greater than the energy barrier, the droplet would begin to move on those textured surfaces for case II.
means of integrated microheater arrays. In combination with a liquophilic and liquophobic chemically patterned surface, this device can serve as a logistic platform for the parallel and automated routing, mixing, and reacting of multiple liquid samples. Yasuda et al.8 generated and refined the proportion of hydrophilic (SiO2) and hydrophobic (Cytop) thin films on a surface by chemical deposition; the hydrophilic nature of the surface inside a microchannel can be modulated so that a droplet moves gradually toward the other side of the region that is increasingly hydrophilic. Lee et al.9 and Choi et al.10 employed microcontact printing to pattern solid substrates with two self-assembled monolayers; the stamp was fabricated on casting polydimethylsiloxane (PDMS) on a photolithographically prepared master. These authors demonstrated that liquid drops can be delivered laterally along a specified path using patterned surfaces, with a driving force for droplet motion based on molecular adsorption. Ichimura et al.11 proposed a light-driven method; the gradient of surface free energy was generated photochemically on the asymmetric irradiation of a photoisomerizable monolayer covering a substrate surface; the motion of the liquid was manipulated reversibly with UV light. These discoveries reveal that surface tension is controllable when varying either physical or chemical properties of the surfaces. Various mechanisms to manipulate a droplet are based on thermal, electrical, chemical, and photoresponsive principles, but inherent problems, such as chemical compatibility, temperature rise, and electrical potential interference, might induce side effects when manipulating droplets in bioapplications. Therefore, Yang et al.12,13 created gradients of surface wettability by patterning microstructure distributions to develop a dropletmanipulating device based on the varied Laplace pressure of a droplet across distinct hydrophobic surfaces; this mechanism provides a concept that is favorable to the design of microfluidic systems because it features no consumption of external power and no undesirable side effect. With this novel idea, Yang et (8) Yasuda, T.; Suzuki, K.; Shimoyama, I. SeVenth International Conference on Miniaturized Chemical and Biochemical Analysis Systems 2003, 1129–1132. (9) Lee, S. W.; Laibinis, P. E. J. Am. Chem. Soc. 2000, 122, 5395–5396. (10) Choi, S. H.; Newby, B. Z. Langmuir 2003, 19, 7427–7435. (11) Ichimura, K.; Oh, S. K.; Nakagawa, M. Science 2000, 288, 1624–1626. (12) Yang, J. T.; Chen, J. H.; Huang, K. J.; Yeh, A. J. J. Microelectromech. Syst. 2006, 15, 697–707. (13) Yang, J. T.; Yang, T. H.; Chen, C. Y. Surface Energy Transformation of a Moving Droplet across Hydrophobic Textured Surfaces. The Third TaiwanJapan Workshop on Mechanical and Aerospace Engineering, Hualien, Taiwan, November 28-29, 2005.
al.14,15 also proposed a passive microvalve and liquid droplet separator with increased reliability for a microfluidic system. In these inventions, the composite surface was formed with microfabrication. The contact behavior of the droplet with a composite surface is similar to the lotus effect.16 In the present work, we have developed microfabrication techniques to carry out a droplet-transporting device for droplet transport with a textured surface. The related research on static contact phenomena and dynamic transport behavior of the droplet is measured and presented. Furthermore, by integrating our experimental results and theoretical analysis from the perspective of discrete energy levels, the analysis of the energy conversion of a droplet moving on a textured surface is proposed to develop effective criteria for designing such a device and evaluate its functionality. All studies and reports are found in the following sections.
II. Theoretical Analysis When a droplet is placed on a textured surface with varied pattern densities, this droplet moves because of the difference in the Gibbs surface energy between its two sides. On converting the surface Gibbs energy into kinetic energy, a droplet moves spontaneously along a specific path in a transport device without additional energy. The distance of motion and the direction of the droplet can be modulated by the microstructure pattern density on the textured surface. To understand the mechanism of the movement of a droplet, we developed a model of energy levels in an analysis based on the principle of energy conservation. The conversion of droplet energy implies that
∆G - Wf ) EK
(1)
in which EK denotes the kinetic energy of the droplet, which is equal to the difference in surface energy between the initial and the final statuses (∆G) and the friction loss (Wf) between the droplet and the textured surface. When a droplet moves along a composite structure, the surface energy must be correlated with the contact angle of the triple-phase line among gaseous, solid, and liquid phases. In the following sections, we derive and verify the conversion between surface energy and the kinetic energy of a droplet. (14) Yang, J. T. ; Chen, J. H. ; Chen, A. C. ; Huang, K. J. U.S. Patent Publication No. 2005/0045238 A1, 2005. (15) Yang, J. T. ; Chen, C. Y. ; Yang, T. H. ; Chen, A. C. U.S. Patent Publication No. 2007/0034270 A1, 2007. (16) Barthlott, W.; Neinhuis, C. Planta 1997, 22, 1–8.
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A. Contact Angle of a Single Droplet on the Textured Surface. The surface wettability and the contact states of a droplet on a solid surface are defined through the contact angle of a droplet. When the contact angle is greater than 90°, the solid surface is called a hydrophobic surface; otherwise, it is called a hydrophilic surface. The contact angle also varies with the roughness of the solid surface; the contact states of a droplet on a solid surface are also classified mainly as collapsed and suspended states.17 For a droplet on a smooth solid surface, as shown in Figure 1a, the intrinsic contact angle, θ0, of a liquid droplet on a flat homogeneous solid surface is given by Young’s equation18
cos θ0 ) (γSV - γSL) ⁄ γLV
(2)
in which γSV, γLV, and γSL are the surface tensions of the solid-vapor, liquid-vapor, and solid-liquid interfaces, respectively. For a rough surface, Wenzel19 proposed a theoretical model to describe the contact angle, θw, of a liquid droplet on the rough surface by modifying eq 2 as follows,
cos θw ) rf cos θ0
(3)
rf)Aact ⁄ Apro
(4)
in which rf is a roughness factor defined as the ratio of the actual surface area of a rough surface, Aact, to the geometric projected area, Apro; its value is invariably greater than unity. The larger the roughness factor, the more hydrophobic the surface becomes. A droplet collapsed on the surface is properly described by eq 3. In the collapsed state, this contact area is the noncomposite surface, also called the wetted surface. The most notable feature is a layer of air not existing in the interfacial contact surface between the bottom of the droplet and those microstructures, as shown in Figure 1b. The composite interface beneath a suspended droplet contains both liquid-gas and liquid-solid interfaces, as depicted in Figure 1c. Cassie and Baxter20 proposed an equation to describe the apparent contact angle on a composite surface as follows,
cos θc ) f1 cos θ1 + f2 cos θ2
(5)
f1 + f2 ) 1
(6)
in which θ1 is also the intrinsic contact angle of a droplet in contact with a flat homogeneous solid surface; f1 and f2 are defined as the area fractions of solid-liquid and liquid-vapor contact interfaces with respect to the total composite interface, respectively. The sum of f1 and f2 invariably equals unity, as shown in eq 6. The contact angle of a droplet in air, θ2, is defined as 180° according to Miwa et al.21 Hence, eq 5 is simplified to
cos θc ) f1 cos θ1 + (1 - f1)cos 180o ) f1 cos θ1 + f1 - 1 (7) In our work, we fabricated uniform microstructures on the surface of a silicon wafer and modulated the values of f1, also called the pattern density, by varying the number of microstructures per unit area. After completing a series of microfabrication processes, we measured the static contact angles of a droplet suspended on those variably textured surfaces, defined (17) Bachmanna, J.; Elliesb, A.; Hartgea, K. H. J. Hydrol. 2000, 231-232, 66–75. (18) Young, T. Philos. Trans. R. Soc. London, Ser. A 1805, 95, 65–87. (19) Wenzel, R. N. Ind. Eng. Chem. 1936, 28, 988–994. (20) Cassie, A. B. D.; Baxter, S. Trans. Faraday Soc. 1944, 40, 546–551. (21) Miwa, M.; Nakajima, A.; Fujishma, A.; Hashimoto, K.; Watanabe, T. Langmuir 2000, 16, 5754–5760.
Figure 3. (a) Schematic of an analysis of force equilibrium during the motion of a droplet and (b) illustration of droplet-transporting devices. Figure 3a shows a schematic of the kinematics and mechanics for the motion of a single droplet on a hydrophobic textured surface. Figure 3b shows the patterned microstructure density on the surface of each groove pad and the geometric parameters of the type B droplet-transporting device.
as θC,m; those experimental values are compared with theoretical values of the static contact angle estimated with eq 7, defined as θC,t. The satisfactory agreement of experimental and theoretical results demonstrates that the droplet is indeed suspended on those textured surfaces. In addition, the stable surface energy corresponding to those contact angles on textured surfaces, Gs, was analyzed and evaluated and is presented in the next section. (The measured data and theoretical values of static contact angles are listed in Table S-1 of Appendix I in Supporting Information.) B. Stable Surface Energy of a Single Droplet. In attaining a naturally stable state in air, a droplet forms a spherical shape with a minimum surface area that has a minimum surface Gibbs energy, estimated as follows,
G0 ) γLV × ΩLV - min
(8)
in which γLV represents the surface tension of a liquid-vapor interface and ΩLV - min is the surface area of the liquid-vapor interface of a droplet. In the present experiment, the volume of a droplet of deionized water for these measurements was 3 µL. The equivalent diameter of a spherical droplet in air was assumed to be about 1.79 mm. The temperature of the droplet was controlled at 20 °C, and the corresponding surface tension, γLV, had a value of 72.75 × 10-3 N m-1. According to eq 8, the initial surface energy, G0, of the droplet not in contact with the textured surface adopted in our experiments was about 7.32 × 10-7 J. Considering the wall effect, Patankar22 described the stable surface free energy, Gs, of a droplet in contact with a textured surface in a stable state as
Gs 3
√9πΓ2⁄3γLV
) (1 - cos θr)2 ⁄3(2 + cos θr)1 ⁄3
(9)
in which θr corresponds to the contact angle θw arising in Wenzel’s theory from a wetted surface as shown in Figure 1b; in contrast, θr becomes θc in the theory of Cassie and Baxter for a droplet suspending on a composite surface as shown in Figure 1c; and V is the volume of the droplet. According to eq 9, the surface energy of a droplet in the stable state (Gs), also called the stable energy level, is hence predictable whereas the droplet is suspended on a textured surface. (A detailed derivation of eq 9 appears in Appendix I in Supporting Information.) C. Hysteresis Effect and Surface Energy Barrier. In the instant before a droplet begins to move from static status on a textured surface, the process of altering the contour of a droplet surface can be known by the hysteresis effect or the static friction effect. The contact angles at opposite sides of a dropletsthe advancing angle (θA) and the receding angle (θR) shown in Figure (22) Patankar, N. A. Langmuir 2003, 19, 1249–1253.
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2asare asymmetric, thus serving to define the direction of droplet motion. In nature, before beginning to move, a stable droplet must acquire sufficient energy to overcome the static friction caused by interfacial contact. Such additional energy per unit area is defined as an energy barrier per unit area, Eb (J/m2). According to Albenge et al.,23 Eb could be further expressed as
Eb ) γLV(cos θR - cos θA)
(10)
Therefore, the total required energy for a droplet, called the total energy barrier (i.e., Gb(J)), is required to raise the Gibbs surface energy of a droplet before motion is initiated from a static state. Furthermore, Gb is defined as a product of the barrier energy per unit contact area (Eb) and the effective contact area (Ac,eff) between a droplet and a textured surface with a specific pattern density. Rb is the base radius of the droplet in contact with the solid. A metastable energy level (Gm) is defined as the sum of the steady-state surface energy (Gs) and the energy barrier (Gb). Those calculations are described by the following equations.
Ac,eff ) f1πRb2 ) f1π(R
cos(θC - 90 ))
o 2
(11)
Gb ) EbAc,eff
(12)
Gm ) Gs + Gb
(13)
In our present experiment, a series of dynamic images of droplet motion were recorded with a high-speed camera; the advancing and receding contact angles on all textured surfaces with varied pattern density, f1, were measured when a single droplet began to slide on the platform with a certain tilt angle at that moment. The static, advancing, and receding contact angles of each textured surface were obtained with this experimental measurement so that the stable and metastable energy levels of each textured surface with the specified pattern density were determined according to eqs 9 and 13. A droplet with a smaller surface energy is more likely to remain stable on a surface; in contrast, a droplet with a greater surface Gibbs energy tends to be in an unstable state, and a little extra energy might lead to the profile alteration of the droplet or to motion on the surface as shown in Figure 2b. These analyses of energy levels might thus provide an approach to predicting whether a moving droplet would proceed across a textured surface with a particular pattern density and how far the droplet might be transported. (The concept of mobility of transport of a droplet are referred to and discussed in detail in Appendix III in Supporting Information.) D. Analysis of Mechanics. Equation 14 results from an analysis of force equilibrium for the motion of a droplet on a textured surface. As shown in Figure 3a, the actuation force, Fact, to move a droplet across a textured surface comes from the variable wetting property (or surface energy) of the liquid-solid interface, whereas the resistance force comes from two sources: one is the hysteresis force, Fhys, resulting from the hysteresis phenomenon before a droplet begins to move, and the other is the viscous force, Fvis, of a liquid during the motion of a droplet.
∑ F ) Fact - Fhys - Fvis ) ma
(14)
The actuation force is equal to the gradient of surface energy24
Fact ) -
d cos θ d∆G = πRb2γLV dx dx
(
)
(15)
in which γLV represents the surface tension of a droplet, Rb is the base radius of the droplet in contact with the solid, and θ is (23) Albenge, O.; Lacabanne, C.; Beguin, J. D.; Koenen, A.; Evo, C. Langmuir 2002, 18, 8929–8932.
the position-dependent contact angle of the liquid droplet on the solid surface, which decreases in the same direction that the droplet moves. Before a droplet begins to move, it must overcome the moving barrier caused by contact angle hysteresis. The hysteresis force (i.e., Fhys) is expressed as25
Fhys ) γLV(cos θR - cos θA)wc,eff
(16)
wc,eff ) 2f1Rb
(17)
in which cos θA and cos θR are the dynamic advancing and receding contact angles at the instant at which a droplet begins to move, respectively, and wc.eff is the effective contact length for a droplet suspended on the each textured surface with a specified patented density, f1. As the droplet moves on those textured surfaces, the resistance resulting from the viscous force is expressed as26
( )
Fvis = 3πηRbV ln
Xmax Xmin
(18)
in which η is the viscosity of the liquid and V is the velocity of the moving droplet. Xmax and Xmin are the characteristic lengths of a liquid: in general, Xmin is the length of a molecule in the liquid phase, and Xmax can be represented as the radius of the droplet. When the droplet is moving steadily, the driving force acting on the droplet is assumed to equal the viscous force (i.e., Fact ) Fvis); the velocity of the moving droplet is calculated as25
V=
γLVRb d cos θ 3η ln(Xmax ⁄ Xmin) dx
(
)
(19)
This equation reveals that the velocity is proportional to surface tension γLV and the surface energy gradient d cos θ/dx but inversely proportional to the viscosity coefficient η of the liquid. For a droplet moving on those droplet-transporting device, the j , and viscous force, F j vis, are estimated with eqs mean velocity, V 18 and 19, respectively; these two equations are modified by the j b. The primary objective for which we average base radius, R seek to utilize such theoretical equations is to provide a preliminary prediction of mobility for a droplet-transporting device. E. Analysis of the Conversion of Surface Energy. The mechanism of the motion of a droplet may also interpreted from the perspective of conservation of energy. The average kinetic energy of the moving droplet is calculated as the difference in surface energies of the droplet between initial and final states and the energy loss caused by friction. Besides, the droplet would halt when its kinetic energy obtained from the surface energy gradient is unable to surpass the energy barrier existing on the surface. The energy state of the droplet transfers from a higher metastable status to a lower stable one by virtue of altering its contour. For a type-B droplet-transporting device, for instance, a droplet would be transported from pad 1 to pad 4 because the surface energy difference of the droplet between each two adjacent pads is converted into the kinetic energy to drive the droplet and overcome friction loss during motion. The total converted energy (∆G) is assumed to be the difference between the initial and final energy states. The initial energy level (Gini) represents the energy threshold for a droplet beginning to move and is greater than the sum of Gs1 and Gb1. When this droplet arrives at the end pad (i.e., the fourth pad) and lacks enough kinetic energy to continue moving, the final energy level for the droplet to halt at that instant (Gfin) must be greater than the stable energy level of the (24) Daniel, S.; Chaudhury, M. K. Langmuir 2002, 18, 3404–3407. (25) Furnidge, G. J. Colloid Interface Sci. 1962, 17, 309–324.
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Figure 4. (a) Profile of a textured surface obtained with a scanning electron microscope (SEM), (b) illustration of the measurement platform, and (c) experimental processes. The dark bars on the silicon wafer substrate are called microstructures, and the patterned density (f1) in the left and right half-regions are 0.25 and 0.50, respectively. The patterned density (f1) is also defined as the ratio of microstructure width to the sum of microstructure width and the separation between two microstructures (e.g., f1 = A/(A + B)0.25). All measurement platforms and components are assembled as shown in part b. Those experimental measurements of contact angle on those varied textured surfaces are shown in part c.
droplet on the fourth pad (i.e., Gs4). Then the remaining surface energy of the droplet becomes consumed via the vibration of its outer profile until the droplet attains a stable state. Such a surface energy difference between Gfin and Gs4, also defined as Gosc, represents the energy dissipation of the droplet during the oscillation. According to those energy levels, the total converted energy (∆G) is approximately estimated as
∆G ) (Gini - Gfin) = (Gs1 + Gb1) - (Gs4 + Gosc) (20) In combination with eq 20, eq 1 may be rewritten as
1 (Gs1 + Gb1) - (Gs4 + Gosc) - Wf ) mV¯2 2
(21)
j represent the mass of the droplet and the mean in which m and V velocity of the moving droplet, respectively. During the period from the moving droplet instantly halting to staying stable on the final pad, the friction energy loss, Wf, is estimated to be a product of the average friction force and the total distance of motion as follows.
Wf ) F¯vis∆x
(22)
∆x is the total distance moved. Gosc represents the energy loss of that droplet resulting from the oscillating profile of the droplet. On the basis of the measured data such as the contact angles required to establish an energy-level analysis and related calculations such as the dynamic friction loss and the kinetic energy of the droplet, the energy dissipation, Gosc, might be roughly estimated with eq 21. According to concepts outlined above, our theoretical analysis has integrated the perspectives of kinematics and energy conservation. Accordingly, we have designed experiments on textured surfaces with varied pattern density to verify the actuation and kinematics of a droplet. (26) Suda, H.; Yamada, S. Langmuir 2003, 19, 529–531.
III. Microfabrication and Experimental Measurement To fabricate specially textured surfaces with a gradually varying patterned microstructure density (f1) is the primary design ideal of a device used to transport a droplet. Therefore, how to determine the geometry parameters of microstructures, how to manufacture the textured surfaces, and how to carry out those experiments are illustrated in detail in the following sections. A. DesignCriteriaoftheTexturedSurfaceandMicrofabrication. Designing and to fabricating textured surface are critical operations. The experimental devices mentioned in this text are arranged with respect to controlling the specific height and width of patterned microstructure on a silicon wafer.27,28 According to an analysis of the energy state and the measurement of the contact angle of a droplet, we suggest the approximate geometric dimensions of the microstructure to be 1000 µm length, 5 µm width, and 10 µm height. Microstructures were fabricated on silicon wafers as follows. Photoresist AZ5214 (PR) was first spun on silicon substrates, followed by a standard lithographic process to create the tested pattern and to define those locations on the microstructures. We then used the inductively coupled plasma to etch the bare surface of the silicon substrate partially without the protection of the PR. After terminating the etching and removing the residual PR, we fabricated the textured surface with microstructures. To enhance the hydrophobic wettability, the hydrophobic material, either Teflon or PPFC, was coated on the textured surface. PPFC, a polymer chemical compound of formula C4F8, was deposited using plasma-enhanced chemical vapor deposition. Teflon was spin coated onto the substrates, followed by baking at 200 °C. The microstructure-textured surface was eventually completed as illustrated in Figure 4a, and f1 is also defined as the patterned (27) Johnson, R. E.; Dettre, R. H. AdV. Chem. Ser. 1963, 43, 112–144. (28) Yoshimitsu, Z.; Nakajima, A.; Watanabe, T.; Hashimoto, K. Langmuir 2002, 18, 5818–5822.
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Table 1. Contact Angle Measurement Data and Estimations of Energy Levelsa PPFC f1 1 0.67 0.5 0.25 0.14 0.1
θA/deg
θR/deg
θC/deg
128 135 139 152 155 156
102 122 134 147 152 153
125 135 141 154 159 160
Aeff/m2
Gs/J
Gb/J
Gm/J
1.687 × 10-6 8.425 × 10-7 4.980 × 10-7 1.208 × 10-7 4.522 × 10-8 2.942 × 10-8
7.021 × 10-7 7.174 × 10-7 7.233 × 10-7 7.300 × 10-7 7.310 × 10-7 7.312 × 10-7
5.006 × 10-8 1.086 × 10-8 2.176 × 10-9 3.892 × 10-10 7.684 × 10-11 4.824 × 10-11
7.521 × 10-7 7.282 × 10-7 7.255 × 10-7 7.304 × 10-7 7.311 × 10-7 7.312 × 10-7
a All data are listed in Table 1, in which the pattern density affecting the hysteresis effect is explored. The energy variations of a droplet suspended on a textured surface corresponding to the varied pattern density are also listed. Taking the PPFC hydrophobic surface as an example, we substitute the intrinsic contact angle, advancing angle and receding angle into the theoretical formulae, Eq. 9 - 13, to derive all parameters of the surface energy levels.
Figure 5. Moving droplet on a type-B droplet-transporting device.
Figure 6. Variation of surface energy in a stable state with a varied microstructure pattern density for a droplet on hydrophobic textured surfaces.
Figure 7. Images of two contact behaviors of textured surfaces with varied microstructure statures.
density of a microstructure. (Design and fabrication details appear in Appendix II in Supporting Information.) B. Measurement of Contact Angle. The entire measurement system and test platform are illustrated in Figure 4b. The sessile drop method was used to measure contact angles with a meter
(OCA 20 Dataphysics Instruments, Germany). We adopted as hydrophobic surfaces two kinds of coating materialssPPFC and Teflonsto measure the contact angle for a droplet suspended stably on a hydrophobic textured surface with varied patterned density (f1) as depicted in Figure 4c. As θc increases with decreasing f1, the hydrophobicity of the composite surface is enhanced through a decreased area of solid-liquid contact. The strategy to measure the contact angle hysteresis on each textured surface is to place a sessile droplet there and then to tilt the surface until the droplet begins to slide. The angle subtended at the front of the droplet is the advancing contact angle (θA), whereas that at the rear is the receding contact angle (θR). With such an instrument, the dynamic advancing and receding contact angles of a droplet on the slanted platform were measured to enable an estimate of the hysteresis effect of a droplet on the textured surface with varied microstructure density. The contact angle hysteresis ∆θ (∆θ ) θA - θR) decreases with decreasing f1 for PPFC; these contact angles measurement results appear in Table 1. C. Visualization of Droplet Motion. The basic principle of a droplet transport device on a textured surface is to utilize the arrangement of the patterned density of the surface microstructures so that a droplet has a continuous variation of surface energy when in contact with the surface. A droplet is transported on the textured region at a particular velocity. We thus designed the droplet-transporting device on a silicon wafer as depicted in Figure 3b; each path consisted of four textured regions with a gradually increasing patterned density. We designed and fabricated transport devices of two types, A and B. Two sequences of patterned density were arranged as (A) 0.25, 0.5, 0.8, and 1 and (B) 0.2, 0.35, 0.65, and 1. These microstructures in four regions of two types were fabricated with a groove shape of 1000 µm length, 5 µm width, and>10 µm pattern depth. A highspeed video camera (IDT X-Stream, 1024 pixels × 1280 pixels at 1000 frames s-1) recorded images of the dynamic motion of droplet transport on a textured surface as shown in Figure 5. A dynamic analysis was conducted with these continuous video images so captured. The mean velocity and acceleration of the transport phenomenon on the textured surface were solved from the total distance of motion and the duration of the images.
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Table 2. Analysis of the Conversion of Gibbs Surface Energy for Types A and B type A f
θC/deg
cos θR - cos θA
0.25 0.50 0.80 1.00
154 141 131 125
4.43 × 10-2 6.01 × 10-2 2.45 × 10-1 4.08 × 10-1
0.20 0.35 0.65 1.00
156 148 136 125
2.83 × 10-2 4.14 × 10-2 1.11 × 10-1 4.08 × 10-1
Gs/J 7.30 × 10-7 7.23 × 10-7 7.12 × 10-7 7.02 × 10-7 type B 7.31 × 10-7 7.28 × 10-7 7.19 × 10-7 7.02 × 10-7
IV. Results and Discussion A. Estimation of Surface Gibbs Energy of a Droplet Suspended on the Textured Surface. On the basis of measured contact angle results and a theoretical model following eq 9, the estimated values of Gibbs surface energy Gs in the stable state of a droplet suspended on a textured region with various f1 values are depicted in Figure 6. A droplet exposed to air and not in contact with the solid surface has a surface energy, G0 ) 7.32 × 10-7 J, that decreases with increasing patterned density when a droplet comes into contact with the textured surface. Because of the increased patterned density, the gas-liquid interface in the bottom contact area decreases, resulting in a smaller contact angle and decreased Gibbs surface energy, hence degenerating the hydrophobicity of the textured surface. B. Droplet Collapse and Suspension on a Textured Surface. The contact behavior of a droplet deposited on a textured surface is described as in a suspended mode, on a composite surface, or in a collapsed mode, on a wetted surface, as depicted in Figure 7. In each mode, a droplet exhibits a distinct contact angle and surface Gibbs energy. In our experiments, the microstructure statures were fabricated to be 3.2 and 24.1 µm with the same pattern density, f1 ) 0.25. We measured the contact angle of a droplet on a textured surface for such two cases and estimated the corresponding Gibbs surface energy to be 7.03 × 10-7 and 7.31 × 10-7 J, respectively; the results are also shown in Figure 6. When a droplet is placed on a textured surface with a smaller stature, the contact mode might convert to a wetted surface, which has a decreased contact angle. Through the droplet collapsing inside the gaps of the structures and even contacting the wafer surface, little air can exist between the contact interfaces.
Figure 8. Analysis of energy levels and prediction of mobility for types A and B.
Gb/J
dGs/J
Gm/J
3.89 × 10-10 2.18 × 10-9 2.04 × 10-8 5.01 × 10-8
NA 6.69 × 10-9 1.12 × 10-8 1.00 × 10-8
7.30 × 10-7 7.25 × 10-7 7.33 × 10-7 7.52 × 10-7
1.71 × 10-10 7.44 × 10-10 6.37 × 10-9 5.01 × 10-8
NA 2.70 × 10-9 9.27 × 10-9 1.64 × 10-8
7.31 × 10-7 7.29 × 10-7 7.25 × 10-7 7.52 × 10-7
This phenomenon makes the Gibbs surface energy smaller than for a droplet suspended on the surface. Before a droplet can move from static status, an additional actuation force and energy must be applied to overcome the work done by the static friction force. According to Figure 6, a collapsed droplet has a state of lower energy than does a suspended droplet; more energy is thus required for a collapsed droplet to move on a textured surface, or a greater external force must be applied to overcome the static friction force. C. Hysteresis and the Total Energy Barrier on a Textured Surface. With decreasing patterned density, effective contact area (Aeff) and the total surface energy barrier (Gb) all decrease as shown in Table 1. Because of the larger contact angle of the droplet and more strongly hydrophobic effect of a surface with a smaller pattern density, the area of the solid-liquid interface in the bottom contact area decreases so that the droplet was intrinsically apt to be suspended on the textured surface. The difference between advancing and receding angles at the instant of motion also decreased. These results indicate that a smaller energy barrier must be overcome before a droplet can move across a textured region. The hysteresis effect is hence less dominant and facilitates the transport of a droplet on a textured surface. In contrast, with increasing patterned density, the ratio of the solid-liquid interface of the contact area increases; a droplet must overcome a larger static surface friction force and energy barrier before moving on the textured surface. D. Analysis of Energy Levels and Prediction of Mobility for the Droplet-Transporting Device. When a droplet is placed across two textured regions, the gradient of the Gibbs surface energy might be converted into kinetic energy, which allows the droplet to move on the surface. The droplet would halt when its kinetic energy obtained from the surface energy gradient is unable to overcome the energy barrier existing on the surface. The energy state of the droplet transfers from a greater metastable status (Gm) to a less-stable status (Gs) by virtue of altering its contour. If the droplet has sufficient kinetic energy to overcome the energy barrier and the energy loss caused by the friction force, then the droplet moves continuously until reaching the next interface. The method of analysis that we developed might also yield a criterion to design a device to transport droplets along a surface. (Other examples and an analysis of energy states appear in Appendix III in Supporting Information.) Designed surface transport devices of types A and B were used in our experiment, for which the evaluated data are listed in Table 2. For type A, the total energy accumulated from the first two regions is ∆Gs13 ) 1.79 × 10-8 J, which is smaller than the energy barrier Gb3 ) 2.04 × 10-8 J at the third interface; the droplet is thus unable to overcome the barrier and halts at the third interface with f1 ) 0.8. For type B, although the energy barrier at the third interface f1 ) 0.65 is a little greater than the energy difference provided at the prior interface, the total energy difference accumulated from the first interface to the third is
9896 Langmuir, Vol. 24, No. 17, 2008
Yang et al.
Figure 9. Droplet moving on a surface and its varying shape.
about ∆Gs13 ) 1.20 × 10-8 J, which is greater than the energy barrier Gb3 ) 6.37 × 10-9 J at the third interface; the droplet thus moves continuously to the end interface. The energy states for stable and metastable status on a textured surface with four patterned densities were estimated, and the results are plotted in Figure 8. The trends in variation of the two devices of both stable and metastable status were closely matched. The energy states at the stable status on the first interface of the two textured surfaces were similar. In Figure 8, line AB represents the initial status of the energy state of the droplet. The lengths of red and blue lines indicate the accumulated energy obtained from the difference, ∆Gs13, in energy states when the droplet moves from the first to the third interface and the energy barrier, Gb3, respectively. We evaluated the mobility of a droplet on the two surface-transport devices by comparing energy variations ∆Gs13 and Gb3. Although the stable energy state (Gs) decreases gradually with increasing patterned density, the metastable energy state increases because of the increased energy barrier. Especially when the pattern density exceeds 0.76, the metastable energy state is above that of the initial state, marked as point C in Figure 8. The accumulated energy ∆G s at all points after pattern density 0.76 is hence much less than the increasing energy barrier Gb on the PPFC surface, which results in the termination of continuous motion for the droplet on that textured surface. A criterion for a device for droplet transport is thus that the pattern density of the textured surface should not exceed 0.76. After our theoretical analysis of energy conversion, we fabricated and tested devices for the surface transport of types A and B. According to the experimental results, a droplet can travel to the third interface on the surface only with the design parameters of type A and to the fourth interface with the textures arranged as for type B. The dynamic moving progress of the droplet on the surface was recorded with a camera, as shown in Figure 5. The results of experimental observation and prediction according to energy conversion have a satisfactory consistency. E. Dynamic Analysis and Conversion of Surface Energy of a Single Droplet. During the transport of the droplet, instantaneous images of the dynamic variation of the movement and the profile alteration were captured with a high-speed camera (1000 frame s-1), shown in Figure 9. As mentioned above, the attenuation of surface energy from a higher level to a lower level
is converted into the sum of the kinematic energy of the droplet and the energy loss due to overcoming the energy barrier and friction force. As the droplet moves to the end of the patterned surface, it is unable to move across the final interface, and the remaining energy becomes the internal energy of the droplet, which appears as the unstable profile altering so as gradually to consume the energy. As shown in the temporal images after 0.048 s, the outer surface of the droplet reaches the end of the patterned surface. The remaining energy is consumed via the trembling of its profile during a gradual return to a stable state. We also inspected the phenomenon of droplet transport from the perspective of force equilibrium. For type A, for instance, the estimated results of actuation and friction forces at the interface with fl ) 0.25 and 0.5 are 4.91 and 2.46 µN respectively, according to eqs 15-17. The droplet is thus able to move across the interface between the first pad and the second pad and then proceed through the second pad with f1 ) 0.5 as the actuation force exceeds the friction force. j vis, After the droplet begins to move, the mean viscous force, F is estimated according to eq 18. For example, the droplettransporting device for type B is divided into four identical areas, of which the total transport path is approximately 4 mm long. The contact angles corresponding to four textured surfaces decline from 156 to 125°. The related parameter data are Xmax ) 0.9 mm, j b) 0.486 mm. The mean viscous Xmin ) 0.1 nm, η ) 1 cp, and R force is thus equal to 4.58 µN during droplet motion. The mean j , is estimated with eq 19 to be 62.6 mm s-1 in the velocity, V theory for type B, which is near the experimental result of 62.5 mm s-1 obtained from the photographs (at which distance ∆x of motion is 2.5 mm and interval ∆t is 0.04 s). The dynamic energy of the moving droplet, Ek, is about 5.85 × 10-9 J, whereas the energy loss caused by the friction force, Wf, is estimated to be 1.15 × 10-8 J according to eq 22. It is impossible to measure the loss of surface energy, Gosc, caused by the profile changing when the droplet transfers from a metastable state to a stable state as depicted in Figure 9. Estimating the energy loss resulting from the interfacial shape of a droplet vibrating is difficult, but on the basis of ∆Gs14, Gb1, Wf, and Ek obtained from our experimental measurements and theoretical analysis, the loss of internal energy caused by the changing profile of the droplet, Gosc, is evaluated to be 1.21 × 10-8 J according to eq 21. The
Manipulation of a Droplet across a Surface
effective rate of energy conversion, β, is defined as the fraction of kinetic energy with respect to the difference in stable surface energy from the initial to the final state and is thus estimated to be 20.6% in this case. According to the theory of energy states and the present experiments, the kinematic processes and energy conversion of a moving microdroplet on a hyperhydrophobically textured surface have been successfully investigated and verified.
V. Conclusions Learning from nature and imitating the lotus effect, we designed and fabricated a device for droplet transport that utilizes the surface energy gradient on a textured surface as the driving mechanism; no external power is required for this device. The initiation and progress of the self-moving phenomenon of a droplet on a textured surface are interpreted successfully with a theoretical model of energy conversion between surface energy and kinematic energy. The proposed model can also be proven according to thermodynamic principles. The static and dynamic characteristics of a droplet deposited on a PPFC hydrophobic surface were investigated with experimental measurements; the results provide valuable references for the design of a device for the transport of a single droplet. The transport capability of such a device is predictable with methods that we developed. The dynamic motion and the energy conversion are analyzed theoretically according to perspectives of energy conservation and force equilibrium. The analytical and experimental results are summarized as follows. The contact angle decreases with increasing pattern density of the textured surface. For a PPFC hydrophobic surface as an example, the contact angle decreased from 160 to 125° as the patterned density increased from 0.1 to 1.0. The results also indicate the degeneration of the hydrophobicity of the surface. From our analysis of the surface energy in a stable state, the energy level of a droplet in a suspended mode on the textured surface is verified to be greater than that in a collapsed mode. The droplet with a lower energy state tends to be more stably deposited on the surface. A suspending droplet hence has greater mobility than a collapsed one on the textured surface. With increased pattern density, the difference between advancing and receding angles increases from 3 to 26°. This result shows that the increased pattern density results in a greater energy barrier that must be overcome before a droplet can move on the surface.
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On the basis of our theoretical analysis of surface energy and experimental measurements, we implemented these ideas with microfabrication. A device for the surface transport of a single droplet on a textured surface has been fabricated and tested. The gradient of surface energy is generated on arranging the pattern density of the textured surface so that the droplet moves in a desired direction. According to our theoretical analysis of the energy level, the design parameter for the pattern density on a textured surface should be less than 0.76. The course of motion of a droplet on a textured surface has been recorded and analyzed with a high-speed video camera. For those PPFC hydrophobic textured surfaces of type B, the mean velocity, measured to be 62.5 mm s-1, is in satisfactory agreement with the theoretical prediction. The effective rate of energy conversion was estimated to 20.6%. Our analysis of the dynamic mechanism and energy conversion assists the understanding of transport phenomena of a droplet on the microscale and promotes the effective control of a liquid droplet. On the basis of this theoretical analysis and fabrication technology, three novel microfluidic devices to transport, mix, and separate liquid droplets with varied physical and dynamic properties are derived. Further practical biodetection chips and devices will be realized on combining techniques related to biomedical science and analytical chemistry. Acknowledgment. The National Science Council of the Republic of China partially supported this work under contracts NSC 93-2218-E-007-048 and NSC 96-2218-E-007-015. We express appreciation to Professor Wen-Hwa Chen of the Department of Power Mechanical Engineering, National Tsing Hua University, Taiwan, for providing the experiment apparatus for the contact angle measurement. Supporting Information Available: Estimation and measurement of contact angles and a derivation of the surface Gibbs energy of a single droplet on a textured surface. Details and criteria of the design, microfabrication procedure, and measurement of contact angles on the test platform. Analysis of the energy barrier and criteria of transport mobility for surface transport devices. This material is available free of charge via the Internet at http://pubs.acs.org. LA8004695
