Cheerios Eﬀect Controlled by Electrowetting Junqi Yuan, Jian Feng, and Sung Kwon Cho* University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States S Supporting Information *

ABSTRACT: The Cheerios eﬀect is a common phenomenon in which small ﬂoating objects are either attracted or repelled by the sidewall due to capillary interaction. This attractive or repulsive behavior is highly dependent on the slope angles (angles of the interface on the wall or ﬂoating object with respect to a horizontal line) that can be mainly controlled by the wettability of the wall and ﬂoating object and the density of the object. In this paper, electrowetting on dielectric (EWOD) is implemented to the wall or ﬂoating object in order to actively control the wettability and thus capillary interaction. As such, the capillary force on buoyant and dense ﬂoating objects can be easily switched between repulsion and attraction by simply applying an electrical input. In addition, the theoretical prediction for the capillary force is veriﬁed experimentally by measuring the motion of ﬂoating particle and the critical contact angle on the wall at which the capillary force changes from attraction to repulsion. This successive veriﬁcation is enabled by the merit of EWOD that allows for continuous change in the contact angle. Finally, the control method is extended to continuously move a ﬂoating object along a linear path and to continuously rotate a dumbbell-like ﬂoating object in centimeter scales using arrays of EWOD electrodes. A continuous linear motion is also accomplished in a smaller scale where the channel width (3 mm) is comparable to the capillary length.

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INTRODUCTION The Cheerios eﬀect is an everyday phenomenon coined after observations of cereal ﬂakes ﬂoating in milk tending to aggregate and stick to the wet sidewall of the bowl.1,2 In fact, not only cereal ﬂakes but also most small ﬂoating objects (even bubbles and foams in Figure 1a) have a tendency to move away

from or toward the sidewall depending on the properties of interfaces, the wettability of sidewall, and the properties of ﬂoating objects. When a ﬂoating object is placed on the air− liquid interface, the interface is distorted, which generates a horizontal force (capillary force) against the sidewall enabling the ﬂoating object to move toward or away from the sidewall. Surprisingly, some water-dwelling creatures harness this phenomenon to climb up the inclined meniscus forming at the water bank.3,4 Instead of sliding their limbs to climb the meniscus, these small animals have developed special tricks for which they change their posture and distort the adjacent interfaces to generate a horizontal force. In Figure 1b, for example, the water-lily leaf beetle simply bends its back and distorts the adjacent interfaces to climb the slippery meniscus.4 Inspired by meniscus climbing insects, Hu et al.5 and Yu et al.6 used a bent plastic or metal sheet to distort the air−liquid interface to climb the inclined meniscus. In addition, the Cheerios eﬀect governs a variety of capillary interactions between ﬂoating objects in the self-assembly processes of 2dimensional array or monolayer on the ﬂuid−ﬂuid interface.7−9 A simple and common understanding of the Cheerios eﬀect is that attraction or repulsion between walls and ﬂoating objects solely depends on surface wetting properties.10−12 For example, objects with similar wettability (i.e., both interacting objects are hydrophobic or hydrophilic) attract each other; otherwise, they repel away. However, this understanding is true for the limited Received: April 22, 2015 Revised: June 28, 2015 Published: July 6, 2015

Figure 1. Cheerios eﬀect. (a) Bubbles migrate to the sidewall. (b) A water lily leaf beetle climbs up the meniscus by arcing its back.4 © 2015 American Chemical Society

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Figure 2. Conﬁgurations and capillary interactions of ﬂoating spherical particles with an adjacent vertical wall. The contact angles at the wall and sphere are θw and θf separately. (a) Buoyant sphere close to a hydrophobic wall; (b) dense sphere close to a hydrophilic wall; (c and d) Horizontal force vs separation in the wall-sphere capillary interaction for various wall contact angles for (c) buoyant sphere (ρf = 0.58 kg/m3, R = 1 mm, θf = 45°) and (d) dense sphere (ρf = 1.18 kg/m3, R = 1 mm, θf = 45°); (e and f) Eﬀect of density on the capillary force in (e) hydrophobic wall condition (θw = 120°, R = 1 mm, θf = 45°) and (f) hydrophilic wall condition (θw = 80°, R = 1 mm, θf = 45°). The thin dotted lines show the smallest separation possible between the particle and wall.

ﬁrst two conﬁgurations, the surface wettability is most critical for determining the direction of the horizontal force (attraction or repulsion) because the meniscus proﬁles near the vertical walls or vertical cylinders is mainly determined by the contact angle of the surfaces. For the latter two conﬁgurations, however, the vertical force balance determines the vertical position of the ﬂoating objects as well as the contact line positions on the ﬂoating objects. The surface wettability is no longer the sole parameter to determine the capillary force direction. Other parameters such as the density of the ﬂoating objects become important as well. In addition to the above four conﬁgurations, Mansﬁeld et al.20 studied mutual attraction or repulsion of 2-dimensional strips. Some researchers17,21,22 studied the conﬁgurations of two horizontally ﬂoating inﬁnite

conﬁgurations (for example, when two inﬁnite vertical walls or inﬁnite vertical cylinders are not very close to each other). It may not be true for other conﬁgurations such as interaction between a ﬂoating object and a vertical wall or between two ﬂoating objects. Vella and Mahadevan1 challenged this common understanding through a simple experiment. By maintaining the wettabilities of two ﬂoating objects similar but changing the weight of one object, it was shown that the force between the objects could be reversed. To better understand the Cheerios eﬀect, many theoretical models have been reported for a variety of conﬁgurations: (1) between two inﬁnite vertical walls;1,13 (2) between two inﬁnite vertical cylinders;14,15 (3) between two ﬂoating spheres;16,17 (4) between a sphere and an inﬁnite vertical wall.18,19 For the 8503

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Langmuir cylinders. The interaction between horizontally ﬂoating small cylinders with a ﬁnite length was also investigated.23 Among the various conﬁgurations, the major focus in this paper lies on the capillary interaction between a ﬂoating object and a vertical wall, which is one of the most common and practical conﬁgurations. In particular, our scope is placed on the boundary condition of predetermined contact angle. Paunov et al.18 studied capillary interaction in the similar conﬁguration and found that the meniscus between the particle and the wall (only when the wall contact angle θw = 90°) is identical to a half of the meniscus between two identical particles: each half is the mirror image of the other half with respect to the wall. Krachelvsky et al.19 extended the concept of mirror image and derived the capillary force for the interaction between a ﬂoating sphere and a vertical wall with arbitrary contact angles. A general rule of the capillary interaction for this conﬁguration is that, as long as the vertical wall and the ﬂoating object are not very close to each other, they attract each other when the slope angles of the wall and the object have the same signs. On the contrary, they repel when the slope angles of the wall and the object have the opposite signs. Here, the slope angle denotes the angle of interface slope on the ﬂoating object or wall. When the slope is downward (viewed from the object or wall), the slope angle is deﬁned to be positive.24 In this paper, the ﬁrst major contribution is to implement ondemand control to the Cheerios eﬀect (more speciﬁcally, the capillary interaction between a ﬂoating object and a vertical wall). To the authors’ best knowledge, active control of Cheerios eﬀect has rarely been done up to date. Electrowetting on dielectric (EWOD) is applied to alter the surface wettability of the wall and/or the ﬂoating object and thus their slope angles. As a result, attraction and repulsion (horizontal capillary force) between the ﬂoating object and wall can be switched in a controlled fashion. The controlling behavior in experiment is in good agreement with theoretical prediction (Krachelvsky et al.19). As the second major contribution of this paper, a quantitative veriﬁcation of the Cheerios eﬀect between experiment and theory is made by measuring the motion of the ﬂoating particles and the critical contact angle at which the horizontal component of capillary force is reversed in direction. EWOD allows for continuous change in the contact angle, which makes it able to measure the critical contact angle in the Cheerios eﬀect. The third major contribution is that the present control method is extended in order to continuously propel a ﬂoating object along linear and circular paths using arrays of EWOD electrodes. The preliminary results of this work were reported in the conference.25 Here, the working ﬂuid is limited to electrically conductive liquid (water). Similarly, however, the control scheme can be extended to nonconductive liquid.26

the contrary, the object moves toward the wall when the wall is hydrophilic since the interface level becomes higher as approaching the wall. The same argument can be applied to a dense ﬂoating object (ρf > ρl, Figure 2b). The interface near the dense ﬂoating object is depressed due to its overwhelming weight. The upward component of surface tension at the contact line prevents the dense object from sinking. The dense object tends to move downward along the downhill meniscus due to its dominant weight. As a result, the behavior of attracting and repelling with the wall is opposite to the case of the buoyant object: the dense object would be repelled by the hydrophilic wall (Figure 2b) and attracted by a hydrophobic wall. By solving the linearized Young−Laplace equation and introducing capillary image force, Kralchevsky et al. 19 quantitatively derived the horizontal force Fx for the given contact angle: Fx = −πσ[2qQ 2K1(2qs) + 2QqH e−qs + q(rqH e−qs)2 ] (1) −1

where σ is the air−liquid interfacial tension, q = Lc ≈ (σ/ ρlg)1/2 the capillary length, g the gravitational acceleration constant, Q = r sin ψf the capillary charge of spherical particle, r the radius of the contact line on the sphere surface, ψf the meniscus slope angle at the contact line, K1 the modiﬁed Bessel function, and s the separation between the center of the sphere and the vertical wall. H in eq 1, the contact line elevation on the vertical wall for a given contact angle θw, can be expressed as follows:12 H=

sin ψw |sin ψw|

Lc 2(1 − cos ψw)

(2)

For the vertical wall, ψw = 90° − θw. H is positive for the hydrophilic surface (θw < 90°) and is negative for the hydrophobic surface (θw > 90°). By solving the vertical force balance and assuming small meniscus slopes, the capillary charge Q for a ﬂoating sphere can be expressed as17,24 Q = r sin ψf ≈ −

3r 2h ⎞ ⎟ R3 ⎠

q2R3 ⎛ 3 ⎜2 − 4D + 3 cos θf − cos θf 6 ⎝ (3)

where R is the radius of sphere, θf the contact angle of sphere surface, and h the elevation of the contact line with respect to the interface level at inﬁnity. Here, the density correlation of the sphere D is ρ − ρa D= f ρl − ρa (4)

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THEORETICAL BACKGROUND A relatively simple and qualitative explanation for horizontal capillary force between a ﬂoating object and wall can be made as follows.1,27 When a buoyant object (ρf < ρl) is ﬂoating at the free surface (Figure 2a), there is a force acting upward on the object due to the buoyancy force, which tends to push the object out of the liquid. Here, ρ is the density, and subscripts f, l, and a denote the ﬂoating object, liquid, and air, respectively. Due to interface constraints, however, the object cannot simply rise up vertically but stays at the interface and climbs up along the meniscus of uphill slope. As a result, the object moves away from the wall when the wall is hydrophobic since the interface level becomes lower as approaching the wall (Figure 2a). On

where ρa is the density of air. In eq 1, the ﬁrst term in the right-hand side represents the capillary image force; the second term originates from the superposition of the particle weight and the buoyancy force; the third term takes into account the pressure jump across the interface.19 If the second term is divided by the third term, the absolute value yields |(2 sin ψf/rq2H)eqs|, which is large for a moderate or large separation s. In addition, the ratio of the second term to the ﬁrst term reads |(He−qs/QK1(2qs))|, which is also large for large s because the modiﬁed Bessel function (K1(2qs)) decreases much faster than e−qs as s increases. For 8504

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Langmuir large s, the last term in eq 3 is negligible because the contact line elevation on the sphere is very small. As a result, for the moderate or large separation s, the second term in eq 1 is dominant to determine the overall direction and magnitude of the horizontal capillary force. For example, the force is attractive if Q and H have the same signs, but is repulsive if Q and H have the opposite signs. Since ψf and ψw are the sole parameters to determine the signs of Q and H, one can make a general argument that for the moderate or large separation s the force between a ﬂoating sphere and a vertical wall is attractive when ψf and ψw have the same signs and is repulsive when they have the opposite signs. It can be inferred from eq 3 that, in addition to the contact angle (θf), the density correlation D (or particle density ρf) is another important parameter to determine the signs of ψf and Q. For a given sphere of known size along with known interfacial tension and densities of air and liquid, the contact angles at the wall and of the sphere (θw and θf) and the density of the f loating sphere ρf eventually become the critical parameters that determine the horizontal capillary force between a f loating sphere and a vertical wall. As shown in Figures 2c and d, the horizontal capillary force between a ﬂoating sphere (buoyant or dense) and a vertical wall is calculated for diﬀerent wall contact angles. The radius of the sphere R is ﬁxed at 1 mm, and the contact angle θf is 45°. For a buoyant ﬂoating sphere (ρf = 0.58 kg/m3, Figure 2c), the force is attractive for θw < 90° while it becomes repulsive for θw > 90°. When θw = 90°, the horizontal capillary force is small almost in the entire range of separation s. In this case, the force is attributed to the pure capillary image force.19 Note that the capillary image force is slightly attractive at the small separation. For a dense ﬂoating sphere (ρf = 1.18 kg/m3, Figure 2c), however, this trend is generally reversed: repulsion for θw < 90° and attraction for θw > 90°. Note that at a certain wall contact angle (e.g., θw = 89.5° in Figure 2d) the force curve may intercept the s axis at position s0, where the sphere experiences a zero horizontal force. This means that the hydrophilic wall does not always generate the attractive force on a hydrophilic ﬂoating sphere. In addition, the capillary force does depend on the density of the ﬂoating object, as clearly shown in Figures 2e and f. The horizontal capillary force is calculated for the interaction of a sphere for three diﬀerent densities with two types of vertical walls (hydrophobic and hydrophilic). Note that the size (R = 1 mm) and surface wettability (θf = 45°) of the sphere is ﬁxed. For both cases of θw = 120° and 80°, the direction of F can be reversed by changing the density.

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Figure 3. (a) Typical EWOD conﬁguration with a sessile droplet. The solid droplet outline shows the original droplet shape with no voltage applied; the dashed line indicates the droplet shape when EWOD signal turns on; (b and c) control concept of Cheerios eﬀect by EWOD. EWOD electrodes are installed on vertical wall. (b) The ﬂoating sphere has a positive slope angle. (c) The ﬂoating sphere has a negative slope angle; (d and e) control concept of Cheerios eﬀect by EWOD. An EWOD electrode is installed on ﬂoating object. (d) Hydrophobic wall (θw > 90°). (e) Hydrophilic wall (θw < 90°).

RESULTS

Control of Cheerios Eﬀect by EWOD. Among many, the contact angles are a critical yet easy parameter for controlling the direction of the horizontal capillary force. EWOD (electrowetting on dielectric) is embedded on the wall or the ﬂoating object to actively change the contact angles and thus control the direction of the horizontal capillary force. Figure 3a shows a common EWOD setup with a sessile droplet that sits on the dielectric-covered EWOD electrode. EWOD is typically arranged horizontally to manipulate droplets or bubbles.28,29 The surface is initially hydrophobic. When a voltage Vd is applied to the dielectric layer, the contact angle θ in the droplet is decreased according to the Lippmann−Young equation:

cos θ = cos θ0 +

εrε0Vd 2 2σalt

(5)

where θ0 is the initial contact angle with no voltage applied, εr the relative permittivity of the dielectric layer, ε0 the permittivity of vacuum (8.854 × 10−12 F/m), σal the air−liquid interfacial tension, and t the thickness of dielectric layer. For the 8505

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electrical ground. Two types of resin spheres (R = 1 mm, solid and hollow) are manufactured by the 3-D printing technology (3D Systems Viper si2 SLA). The density of the spheres is varied by changing the shell thickness. The solid sphere has density of 1.18 kg/m3 resulting in a negative slope angle when placed on the air−water interface. The hollow sphere has a 200 μm thick shell, which leads to the reduced sphere density of 0.58 kg/m3 and the positive slope angle. The contact angles of both spheres are measured equal to be ∼45°. As sequential snapshots (see the supplementary movie clip, movie 1) are shown in Figure 4a, when EWOD is turned oﬀ, the hollow (buoyant) sphere (positive slope angle) is repelled and the dense one (negative slope angle) is attracted since the vertical wall is hydrophobic (θw ≈ 120°). But when EWOD is turned on (150 VDC, Figure 4b), the wall surface changes to hydrophilic (θw ≈ 80°) and thus the forces are reversed. These results agree with the theoretical predictions in Figures 2c and d. EWOD electrode can also be installed on a ﬂoating object to actively control the Cheerios eﬀect. Figure 3d and e show the schematic with EWOD electrode installed on the buoyant ﬂoating object. Initially when EWOD is turned oﬀ, the surface of EWOD electrode is hydrophobic (θf > 90°), so the slope angle of the object is negative (ψf < 0). As a result, the ﬂoating object is attracted by a hydrophobic vertical wall (ψw < 0, left in Figure 3d) and is repelled by a hydrophilic wall (ψw > 0, left in Figure 3e). When EWOD is switched on, the EWOD surface becomes hydrophilic, which generates a positive slope angle (ψf > 0). So the ﬂoating object is repelled by a hydrophobic wall (ψw < 0, right in Figure 3d) and is attracted by a hydrophilic wall (ψw > 0, right in Figure 3e). Experimental veriﬁcations are shown in the overlapped snapshots in Figure 5 (see the supplementary movie clips, movie 2 and movie 3). A boat

typical air−water EWOD system with parylene/Teﬂon dielectric layers, θ0 ≈ 120°, εr ≈ 3, and σal = 0.072 N/m. Note that the droplet serves as a conductor closing the EWOD electric circuit. Typically, the surface wettability can be changed from hydrophobic to hydrophilic states by EWOD. When the voltage is removed, the contact angle returns to the initial value. By simply toggling the applied voltage, EWOD surface can be repeatedly switched between hydrophobic and hydrophilic states (typical contact angle change ∼40°). When a vertical EWOD electrode is partially submerged in water as shown in Figure 3b and c, the wettability (contact angle) of the electrode wall also changes according to the Lippmann−Young equation. By changing the wettability of vertical wall by EWOD, attraction and repulsion between the wall and ﬂoating objects can be controlled, as illustrated in Figures 3b and c. When EWOD is oﬀ, the wall surface is initially hydrophobic, so the meniscus slope angle at the wall is negative (ψw < 0). As a result, the wall would repel the object when the object slope angle is positive (ψf > 0, left in Figure 3b) and attract the object when the object slope angle is negative (ψf < 0, left in Figure 3c). When EWOD is turned on, the wall will be switched from hydrophobic to hydrophilic states. This results in a positive slope angle (ψw > 0) at the wall. So the wall would attract the object of the positive slope angle (ψf > 0, right in Figure 3b) and repel the object of the negative slope angle (ψf < 0, right in Figure 3c). Figure 4 shows experimental veriﬁcations of the above control concept. For the EWOD electrode wall, a silicon wafer covered with a 2.5 μm thick parylene layer and a ∼200 nm thick Teﬂon AF layer is vertically and partially submerged in water. A rectangular piece of bare aluminum foil is attached to the interior surface of the water container bottom and used for

Figure 5. Snapshots of ﬂoating object motions. An EWOD electrode is installed on the ﬂoating object. (a and b) Hydrophobic wall (θw > 90°). When EWOD is OFF (a), the ﬂoating object is attracted toward the wall. When EWOD is ON (b), the object is repelled from the wall; (c and d) hydrophilic wall (θw < 90°). When EWOD is OFF (b), the object is repelled from the wall. When EWOD is ON (d), the object is attracted toward the wall. The yellow dashed line represents the initial position, while the red dashed line is the ﬁnal position. See the supplementary movie clips (movie 2 and movie 3).

Figure 4. Snapshots of particle motions controlled by EWOD. EWOD electrode is installed on vertical wall. (a) When EWOD is OFF, the buoyant object is repelled from but the dense object is attracted to the EWOD electrode; (b) When EWOD is ON, the buoyant object is attracted to but the dense object is repelled from the EWOD electrode. The sphere circled by the dashed line is the dense sphere. See the supplementary movie clip (movie 1). 8506

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Figure 6. Comparison between eq 1 and experiment. (a) The displacement of the ﬂoating sphere is measured by high-speed images when EWOD voltage is applied. (b) The velocity of the particle is obtained by taking the ﬁrst derivative of the measured displacement. The horizontal component of capillary force obtained by using eqs 6 and 7 and the velocity is compared with theory eq 1. The thin dotted line denotes the smallest separation possible between the sphere and wall.

(ﬂoating object) is made of Styrofoam (density ∼0.02 kg/m3) and has dimensions of 15 (L) × 10 (W) × 10 (H) mm3. The ﬂexible EWOD electrodewhich is made of DuPont Pyralux ﬂexible Cu product covered with an 18 μm thick Cu layer, a 2.5 μm thick parylene layer, and a ∼200 nm thick Teﬂon AF layer on the top surfaceis glued on one sidewall of the boat. The total weight of the boat with the EWOD electrode is 0.1 g. Aluminum foil is attached to the interior surface of the water container bottom for electrical grounding. Copper wires as small as 30 μm in diameter are used for electrical connection with minimal mechanical disturbance. For a hydrophobic vertical wall, the ﬂoating object is attracted when EWOD is turned oﬀ (Figure 5a) and is repelled when EWOD is turned on (Figure 5b). For a hydrophilic wall, the forces become repulsion when EWOD is turned oﬀ (Figure 5c) and attraction when EWOD is switched on (Figure 5d). The force direction in these experimental results is in qualitative agreement with theoretical predictions by eq 1. Veriﬁcation of Theory. Since the capillary force is very small (typically, < tens of μN), the direct measurement of the force is diﬃcult in many conﬁgurations, as reviewed in more detail in Yuan and Cho.30 In particular, it is even more diﬃcult in the conﬁguration with ﬂoating objects. Nevertheless, many attempts have been made to measure the capillary force between vertical cylinders, between spheres, and between a sphere and a vertical wall.31−33 In particular, Dushkin et al.33 measured the horizontal force for the ﬁxed contact angle condition by using torsion balance to verify eq 1. However, their results had large errors for small separation, even though they were in good agreement for large separation. Possible reasons for the errors at small separation may be as follows. (i) Equation 1 is derived based on the linearized Young−Laplace equation with an assumption of small meniscus slope. In many measurements, however, the contact angle of the wall was set to be 0°, which easily violated the assumption of the small meniscus slope. As a result, nonlinear eﬀects become substantial for small separation. (ii) During the torsion balance experiments, the vertical position of the ﬂoating object was ﬁxed, which alters the original conﬁguration. In this paper, two methods are used to experimentally verify eq 1: (1) measurement of ﬂoating particle motion and (2) measurement of the critical contact angle. Petkov et al.34 investigated the drag coeﬃcient of moving ﬂoating spheres under capillary forces with a vertical wall that has the ﬁxed

contact line boundary condition. By measuring the velocity of the ﬂoating spheres, the drag coeﬃcient was obtained. Vassileva et al.35 made the similar experiment to investigate the viscous drag on ﬂoating spheres that were driven by the particle-toparticle Cheerios eﬀect. Similar to the above two methods, the dynamic motion of the ﬂoating particle is experimentally measured and analyzed to obtain the capillary force. The detailed experimental procedure is as follows. An EWOD electrode (shown in Figure 4) is vertically and partially submerged in water. A ﬂoating sphere (R = 1 mm, θf = 75°, ρf = 8 kg/m3) is initially in contact with the electrode because of the initial negative slope angles of the sphere and the wall. When a 160 VDC voltage is applied to the EWOD, the contact angle on the electrode wall reduces from 120° to 80° and the slope angle of the wall becomes positive. As a result, the sphere is repelled departing from the wall. The dynamic motion is recorded by a high-speed camera. The displacement of the sphere is digitized in each time frame and is curve-ﬁtted to a rational polynomial function, as shown in Figure 6a. The velocity v and acceleration a are obtained by taking the ﬁrst time-derivative and second time-derivative of the displacement, respectively. The velocity of the sphere is shown in Figure 6b. The capillary repulsive force initially accelerates the sphere. As the distance between the sphere and the wall increases, the capillary force becomes weaker while the drag force becomes larger because of the increased velocity. As the sphere further moves away from the wall, the sphere decelerates due to weak capillary force and dominant drag force. The force balance34 in the horizontal direction is given as Fx = ma + Fdrag

(6)

where m and Fdrag are the mass of the sphere and the drag force acting on the sphere, respectively. Since the present Reynolds number is not small (>20) and the sphere is partially submerged, the Stokes drag expression may not be correct. So the following expression (more general for moderate Reynolds number and partially submerged) is used to describe the present drag:36 Fdrag =

1 Cdρl v 2A 2

(7)

where Cd is the drag coeﬃcient and A is the projection area (0.84πR2) of the submerged part of the sphere. By substituting v and a into eq 6 and eq 7, the capillary force on the sphere Fx 8507

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Langmuir can be calculated and compared with eq 1. In this calculation, Cd is assumed 1.07. As shown in Figure 6b, the experimental result is in good agreement with eq 1. In this veriﬁcation, the sphere (chrome coated steel bearing ball) is carefully selected to minimize the eﬀect of surface roughness and thus contact angle hysteresis. In the meantime, Velev et al.37 presented an interesting method to partially verify eq 1 by measuring the stable position of zero force for the boundary condition of ﬁxed contact line. Within a certain range of contact angle or contact line elevation at the wall, eq 1 (or a similar equation for the ﬁxed contact line boundary condition) allows us to ﬁnd a zero-force position s0 where the sphere experiences a zero net horizontal force. This position may or may not be stable depending on the boundary condition on the wall. For the ﬁxed contact line at the wall, the zero-force position is stable because the force is repulsive for s < s0 while the force is attractive for s > s0. As a result, the ﬂoating object always stays at the zero-force position even under some disturbances. For the ﬁxed contact angle at the wall, there may also exist a zero-force position (for example, the thick dashed vertical line in Figure 2d). However, this position is not stable because the horizontal force between the wall and ﬂoating object is attractive for s < s0 and repulsive for s > s0. That is, the object has tendency to move away from the zero-force position. As a consequence, the experimental measurement of the zeroforce position for the ﬁxed contact angle at the wall (present boundary condition) is very diﬃcult. The second method (critical contact angle method) for theory veriﬁcationwhich uses EWOD as wellis inspired by the above work.37 EWOD allows us to continuously change the contact angle on the wall. Given an EWOD voltage, however, it creates the boundary condition of the ﬁxed contact angle at the wall, not ﬁxed contact line. This means it is very diﬃcult to verify eq 1 by directly measuring the zero-force position since the zero-force position is unstable. So, an alternative way is to experimentally measure the critical contact angle (θw,cr) at the wall at which the force is changed from attraction to repulsion for a given separation s. Initially, the ﬂoating object (sphere) is attracted and stays in contact with the wall by the Cheerios eﬀect. In this case, the separation s between the wall and object is equal to the radius of the sphere. Then, the EWOD voltage is gradually increased until the sphere starts repelled and separated from the wall. At this moment, it can be assumed that the force on the object crosses the zero line. The critical EWOD voltage at the onset of sphere separation is recorded and converted to the critical contact angle by the Young− Lippmann equation. This critical contact angle is compared with that the theoretical results obtained from eq 1. Figure 7 shows a comparison between experimental results and theoretical predictions of the critical contact angle (θw,cr). The theoretical calculations and experimental results are in excellent agreement. Since the critical contact angles in the experiment are very close to 90° which results in small meniscus slopes near the wall, the assumption of small meniscus slope for the linearized Young−Laplace equation is satisﬁed. As a result, the nonlinear eﬀect in small separation that commonly occurred in other experiments33 is negligible in the present experiment. In calculation, the density of the sphere changed from 1.00 kg/m3 to 1.20 kg/m3 with a step of 0.001 kg/m3, while the radius, initial separation, and contact angle of the sphere are ﬁxed at 1 mm, 1 mm, and 45°, respectively. For experiments, resin spheres of three diﬀerent densities are also fabricated by the 3-D printing technology. The solid sphere has

Figure 7. Critical contact angle at which the horizontal component of capillary force is reversed in direction. Contact angle θf and radius r of sphere are 45° and 1 mm for both experiment and calculation.

the density of 1.18 kg/m3, which is the same as the density of the bulk resin. Two hollow spheres with the shell thicknesses of 500 and 600 μm have the densities of 1.03 kg/m3 and 1.10 kg/ m3, respectively. All the spheres have the same contact angles of 45° and negative slope angles at the horizontal air−water interface. The EWOD wall is fabricated using the same method and condition as that shown in Figure 4. Continuous Motion. The previous sections have shown that attraction and repulsion of the ﬂoating objects can be controlled by EWOD. However, simply toggling EWOD with a single EWOD electrode restricts the motion of ﬂoating objects within a limited distance toward or far away from the wall, as illustrated in Figure 8a. In order to achieve continuous motions along a predeﬁned path, arrays of EWOD electrodes are attached to each of two vertical walls and partially immersed in water, as shown in Figure 8b and c. When a pair of EWOD electrodes (one in the left wall and the other in the right wall) are activated, the surfaces of electrodes change from hydrophobic to hydrophilic states. As a result, the adjacent free

Figure 8. Concept of continuous propulsion. (a) Single actuation: the boat is attracted toward or repelled from the wall; (b and c) continuous actuation using EWOD electrode arrays. The boat has a positive slope angle to stay in the middle of the two vertical walls. 8508

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Figure 9. (a) A boat with a positive angle is propelled along a 15 mm wide channel. Pairs of electrodes are activated sequentially from right to left with duration of 1 s. The white bars indicate activated EWOD electrodes. (b) Rotation of the ﬂoating dumbbell in a circular container (24 mm in radius). Pairs of diagonal electrodes are activated clockwise with duration of 1.5 s. The white bars indicate activated EWOD electrodes. (c) A boat is propelled left and right in the channel of smaller width (3 mm wide, comparable to the capillary length). The boat has a positive slope angle. Duration of activation was 0.5 s for each pair of electrodes. See the supplementary movie clips (movie 4, movie 5 and movie 6).

surface is distorted with an elevation. The elevated interface simulates the wall eﬀect illustrated in Figure 4 and generates a pulling force on the ﬂoating object of positive slope angle. Due to symmetry, the forces on the object that are perpendicular to the walls are canceled out by each other. Only a net force on the object is generated toward the elevated interface, so the object is pulled along the channel path. By shifting the EWOD activation from one pair to the next pair, a continuous movement can be made along the channel. Figure 8c shows a perspective view of the setup. Note that the sidewalls of the boat in Figures 8b and c need to have positive slope angles. In the initial state, the surfaces of EWOD electrodes are hydrophobic, repulsive forces from both sides of the channel act on the boat but are canceled out. As a result, the boat aligns its axis along the channel direction and stay in the center of the channel. Even when EWOD electrodes are activated, no net lateral force is generated, so the boat still maintains the position in the center. On the contrary, if the boat sidewalls have negative slope angles, forces from sidewalls are attractive. There exists an equilibrium position (zero-force position) in the center of the channel, but it is not stable. So the boat is easily attracted toward either of the sidewalls.

Figure 9a shows the buoyant object with positive slope angle is propelled in the 15 mm wide channel with two arrays of EWOD electrodes (5 mm width). The boat is made of styrofoam (∼0.02 kg/m3, 30 (L) × 10 (W) × 10 (H) mm3). All channel sidewalls with EWOD electrodes are coated with Teﬂon AF in order to be initially hydrophobic, so the object with positive slope angle automatically aligns and stays in the middle of the channel. A bare aluminum foil for electric grounding is attached to the interior surface of the channel bottom. Upon shifting activation of EWOD electrode pairs to the left (160 VDC of EWOD voltage) with duration of 1 s, the object is step-by-step propelled to the left (see the supplementary movie clip, movie 4). A sequential signal is provided by a microcontroller (ATMEL ATtiny24A) and relays (Panasonic AQW614EH). Note that the mechanism of this propulsion is diﬀerent from that of AC EWOD propulsion38,39 in which the Stokes drift induced by surface capillary waves40 generates a propulsion force. A rotational motion (ﬂoating motor) is achieved by arranging 10 mm wide EWOD electrodes along the circular path (24 mm in radius, Figure 9b). A mini Styrofoam dumbbell with positive slope angle is held in the center. As sequential activations of 8509

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which the capillary force is transitioned from attraction to repulsion. This veriﬁcation is accomplished by EWOD that allows for continuous change in the contact angle. Finally, the above control scheme is extended to generate continuous propulsions of ﬂoating objects along linear and circular paths. Arrayed EWOD electrodes are sequentially activated to continuously propel a ﬂoating object between two vertical walls and continuously rotate a ﬂoating dumbbell object. Similar linear motions are accomplished in a smaller channel, whose width is comparable to the capillary length. This control scheme does not need any physical contact, possibly bringing a new method to handle (separate, self-assemble, and so on) with micro particles and structures.

diagonal electrode pairs shift clockwise (100 VDC EWOD voltage with duration of 1.5 s), a torque is generated that continuously rotates the ﬂoating dumbbell (see the supplementary movie clip, movie 5). When the two walls are suﬃciently close, the capillary interaction between the walls is signiﬁcantly strong. The channel width (15 mm) tested in Figure 9a is much larger than the capillary length for the air−water interface (2.7 mm). In order to validate this continuous motion in the scale comparable to or smaller than the capillary length, two linear arrays of smaller EWOD electrodes (1.5 mm width) are microfabricated on a SiO2 plate and an ITO (indium tin oxide) glass plate separately (Figure 9c). The transparent ITO electrodes allow us to visualize motions of objects. A thin layer of Al is sputter-coated on the SiO2 substrate for the EWOD electrode array. Photoresist (AZP4210) is spin-coated on the top. After exposure by UV light, unwanted photoresist and Al are removed by an alkaline-based developer simultaneously. As a result, the traditional acid wet etching process is not needed. For the ITO electrodes, an 18% HCl solution is used to etch conductive ITO layer after a standard photolithographic process. A 2.5 μm-thick parylene layer is coated on both plates for the EWOD dielectric layer. Two plates with arrays of EWOD electrodes are partially immersed into water and vertically and parallel aligned to form the small channel. The gap between the plates can be adjusted by a linear traversing stage. In Figure 9c, the spacing between the two arrays is reduced to 3 mm, which is comparable to the capillary length of air−water interface. The ﬂoating object is made of Styrofoam and measured at 5.4 (L) × 0.8 (W) × 0.8 (H) mm3. Sequential images in Figure 9c show that the object is moved left ﬁrst and then right with synchronization with the electrode activation shifts (80 VDC EWOD voltage with duration of 0.5 s). See the supplementary movie, movie 6.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.5b01479.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] Notes

The authors declare no competing ﬁnancial interest.

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ACKNOWLEDGMENTS This research is supported by NSF Grant No. ECCS-1029318. REFERENCES

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CONCLUSION This paper describes control of the Cheerios eﬀect (capillary force between objects) using electrowetting on dielectric (EWOD). A particular interest is placed in the conﬁguration between a vertical wall and a ﬂoating object. When the object and the wall is at moderate or large separation, a general rule in the capillary interaction between them is that, the slope angles (angle of the interface on the wall or the object with respect to a horizontal line) are the major parameters to determine the direction of the capillary force. When the slope angles on the wall and object have the same signs, the force between them is attractive, but it changes to be repulsive if the slope angles have the opposite signs. For the vertical wall, the contact angle of the wall is the sole parameter to determine the slope angle. For the ﬂoating object, however, both density and contact angle are critical to determine the slope angle. Based on this interaction rule, we implemented electrowetting-on-dielectric (EWOD) on the vertical wall or ﬂoating objects in order to on-demand control the Cheerios eﬀect. By applying EWOD, the wettability of the wall or the ﬂoating object can be switched between hydrophobic and hydrophilic states. As a result, the slope angles on the wall or objects can be changed, which reversibly switches the capillary force between attraction and repulsion in a controlled fashion. Then, a theoretical model for the wall− sphere interaction with the boundary condition of ﬁxed wall contact angle is experimentally veriﬁed by measuring the dynamic motion of the ﬂoating particle. The model is further validated by measuring the critical contact angle on the wall at 8510

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DOI: 10.1021/acs.langmuir.5b01479 Langmuir 2015, 31, 8502−8511