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Langmuir 2007, 23, 918-924
Electrowetting of Nonwetting Liquids and Liquid Marbles G. McHale,* D. L. Herbertson, S. J. Elliott, N. J. Shirtcliffe, and M. I. Newton School of Biomedical and Natural Sciences, Nottingham Trent UniVersity, Clifton Lane, Nottingham NG11 8NS, United Kingdom ReceiVed July 4, 2006. In Final Form: October 14, 2006 Transport of a water droplet on a solid surface can be achieved by differentially modifying the contact angles at either side of the droplet using capacitive charging of the solid-liquid interface (i.e., electrowetting-on-dielectric) to create a driving force. Improved droplet mobility can be achieved by modifying the surface topography to enhance the effects of a hydrophobic surface chemistry and so achieve an almost complete roll-up into a superhydrophobic droplet where the contact angle is greater than 150°. When electrowetting is attempted on such a surface, an electrocapillary pressure arises which causes water penetration into the surface features and an irreversible conversion to a state in which the droplet loses its mobility. Irreversibility occurs because the surface tension of the liquid does not allow the liquid to retract from these fixed surface features on removal of the actuating voltage. In this work, we show that this irreversibility can be overcome by attaching the solid surface features to the liquid surface to create a liquid marble. The solid topographic surface features then become a conformable “skin” on the water droplet both enabling it to become highly mobile and providing a reversible liquid marble-on-solid system for electrowetting. In our system, hydrophobic silica particles and hydrophobic grains of lycopodium are used as the skin. In the region corresponding to the solid-marble contact area, the liquid marble can be viewed as a liquid droplet resting on the attached solid grains (or particles) in a manner similar to a superhydrophobic droplet resting upon posts fixed on a solid substrate. When a marble is placed on a flat solid surface and electrowetting performed it spreads but with the water remaining effectively suspended on the grains as it would if the system were a droplet of water on a surface consisting of solid posts. When the electrowetting voltage is removed, the surface tension of the water droplet causes it to ball up from the surface but carrying with it the conformable skin. A theoretical basis for this electrowetting of a liquid marble is developed using a surface free energy approach.
Introduction A small droplet of water naturally either sits upon a smooth solid surface as a spherical cap or it spreads across the surface and forms a film.1 Which of these tendencies occurs is due to the balance of the interfacial interactions between the solid, liquid, and vapor, and for a flat surface the range of contact angles, θ, is between 0° and ∼120°. The maximum contact angle can be increased toward complete nonwetting (i.e., θ ) 180°) by roughening or topographically structuring the surface.2 Such roughness or structure to create a superhydrophobic surface can either reduce or increase contact angle hysteresis and so make it easier or more difficult to actuate droplet motion.3-7 Reducing a given contact angle on a smooth solid surface can be achieved in a controllable manner by electrostatically charging the solidliquid interface (i.e., electrowetting).8,9 With well-designed electrode configurations it is then possible to move liquids along capillaries to create, e.g., voltage configurable X-ray filters,10 alter the curvature of a meniscus to create a tunable lens11,12 and by altering the contact angle by different amounts on the opposite * To whom correspondence should be addressed. Phone: +44 (0)115 8483383. E-mail:
[email protected]. (1) Le´ger, L.; Joanny, J. F. Rep. Prog. Phys. 1992, 55, 431-486. (2) Blossey, R. Nat. Mater. 2003, 2, 301-306. (3) Cassie, A. B. D.; Baxter, S. Trans. Faraday Soc. 1944, 40, 546-551. (4) Johnson, R. E.; Dettre, R. H. Contact angle, Wettability and Adhesion. AdV. Chem. Ser. 1964, 43, 112-135. (5) Wenzel, R. N. Ind. Eng. Chem. 1936, 28, 988-994. (6) Wenzel, R. N. J. Phys. Colloid Chem. 1949, 53, 1466-1467. (7) Que´re´, D.; Lafuma, A.; Bico, J. Nanotechnology 2003, 14, 1109-1112. (8) Berge, B. C. R. Acad. Sci. Paris II 1993, 317, 157-163. (9) Mugele´, F.; Baret, J. C. J. Phys.: Condens. Matter 2005, 17, R705-R774. (10) Prins, M. W. J.; Welters, W. J. J.; Weekamp, J. W. 2001. Science 2001, 291, 277-280. (11) Berge, B.; Peseux, J. Eur. Phys. J. 2000, E3, 159-163. (12) Kuiper, S.; Hendriks, B. H. W. Appl. Phys. Lett. 2004, 85, 1128-1130.
sides of a droplet actuate motion and create droplet-on-a-chip microfluidic systems.13-15 Since there is no reason the capacitive charging effect should be restricted to a smooth/nonstructured surface, the mechanisms of superhydrophobicity and electrowetting are complementary, and fully tunable wetting through contact angles of 0-180° appears to be a possibility. Torkkeli et al. attempted to use these combined effects to create a droplet-on-a-chip system with fully programmable motion of the droplets on a superhydrophobic surface with low contact hysteresis and, hence, low requirements for actuating force. 16,17 However, application of the electrowetting voltage caused the liquid to penetrate into the surface features and so transformed the droplet from the “slippy” Cassie-Baxter state to a completely immobile “sticky” Wenzel state. While the transformation from a “slippy” state into a “sticky” state is a problem for droplet actuation applications, Krupenkin and coworkers have shown that the irreversible switching of a droplet from a Cassie-Baxter to a Wenzel state can be exploited to create reserve batteries.18 However, there have been few other attempts to combine these two physical mechanisms due to the (13) Pollack, M. G.; Fair, R. B.; Shenderov, A. D. Appl. Phys. Lett. 2000, 77, 1725-1726. (14) Wapner, P. G.; Hoffman, W. P. 2000. Sens. Actuators, B 2000, 71, 6067. (15) Lee, J.; Moon, H.; Fowler, J.; Schoellhammer, T.; Kim, C. J. Sens. Actuators, A 2002, 95, 259-268. (16) Torkkeli, A.; Saarilahti, J.; Haara, A.; Harma, H.; Soukka, T.; Tolonen, P. Electrostatic transportation of water droplets on superhydrophobic surfaces. In 14th IEEE International Conference on Micro Electro Mechanical Systems. Technical Digest 2001, 475-478. (17) Torkkeli, A.; Haara, A.; Saarilahti, J.; Harma, H.; Soukka, T.; Tolonen, P. Droplet manipulation on a superhydrophobic surface for microchemical analysis. In Transucers ‘01: Eurosensors XV, Digest of Technical Papers; Springer-Verlag: Berlin, 2001; Vols. 1 and 2, pp 1150-1153. (18) Krupenkin, T. N.; Ashley Taylor, J.; Schneider, T. M.; Yang, S. Langmuir 2004, 20 3824-3827.
10.1021/la061920j CCC: $37.00 © 2007 American Chemical Society Published on Web 11/22/2006
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problems caused by the lack of reversibility in the contact angle when the electrowetting voltage is removed.19 Of course, as reported by Krupenkin et al., a transformation back to a CassieBaxter state can be achieved by, for example, using a current to vaporize the water between surface features,20 but this is not reversibility in the sense of simply removing the electrowetting voltage. In this report, we demonstrate a nonwetting system which can be subject to electrowetting but also recovers its initial contact angle and contact radius on removal of the voltage. The fundamental new idea in our approach is to perform electrowetting on a system in which the solid surface structure providing the superhydrophobicity has been attached to the liquid rather than to the substrate. In the following section we outline this concept and show how a liquid marble21-24 may be regarded as a special type of superhydrophobic system whose “skin” forms a conformable surface structure. We then set up and minimize the energy functional for model cylindrical- and spherical cap-shaped nonwetting droplets, including gravitational energy and capacitive energy terms. Numerical solutions are used to understand the relationship between observed contact angle and contact radius and their dependence on the droplet volume and the applied electrowetting voltage. Proof-of-concept experiments using water droplets coated with hydrophobic silica and hydrophobic lycopodium are presented, and it is shown that over a restricted range of contact angles electrowetting of a highly nonwetting droplet (θ > 150°) can be achieved with full recovery to the initial contact angle and contact radius on removal of the voltage. Liquid Marbles as Droplets on Superhydrophobic Surfaces. To develop the concept of electrowetting of a liquid marble we first review some simple ideas due originally to Que´re´ and coworkers.24 Consider the attachment of a particle (which in this work is also referred to as a “grain”), initially in air, to the surface of a droplet of water. If the particle is spherical, then as it attaches it replaces a solid-vapor surface area of 2πRs2(1 + cos θe), where Rs is the radius of the grain and θe is the intrinsic (Young’s law) contact angle, with an equivalent amount of solid-water surface area. Simultaneously, the droplet loses a water-vapor interfacial area of πRs2 sin2 θe, so that the net change in surface free energy is ∆F ) 2πRs2(1 + cos θe)(γSL-γSV) - πRs2 sin2 θeγLV, where γij are the interfacial tensions. Using Young’s law
cos θe )
γSV - γSL γLV
(1)
this gives
∆F ) -πRs2γLV(1 + cos θe)2
(2)
Equation 2 is either zero (θe ) 180°), which is physically impossible because the maximum obtainable contact angles by surface chemistry alone are around 120°, or negative (the practically achieved case). Equation 2 is a form of the YoungDupre´ equation and suggests that it is always favorable for grains to spontaneously attach to the liquid-vapor interface, even if they are hydrophobic. As the equilibrium contact angle is increased, each grain will protrude further from the liquid into the air. If the grains are spherical with a radius Rg, the length (19) Herbertson, D. L.; Evans, C. R.; Shirtcliffe, N. J.; McHale, G.; Newton, M. I. Sens. Actuators 2006, 130, 189-193. (20) Krupenkin, T. N.; Taylor, J. A.; Kolodner, P.; Hodes, M. Bell Labs Technol. J. 2005, 10, 161-170. (21) Mahadevan, L.; Pomeau, Y. Phys. Fluids 1999, 11, 2449-2453. (22) Aussillous, P.; Que´re´, D. Nature (London) 2001, 411, 924-927. (23) Que´re´, D. Rep. Prog. Phys. 2005, 68, 2495-2532. (24) Aussillous, P.; Que´re´, D. Proc. R. Soc. 2006, A462, 973-999.
Figure 1. (a) Superhydrophobic droplet on micropost surface, (b) lithographic microposts, (c) liquid marble on a flat surface, and (d) electrowetting with a conformable skin.
of a grain protruding into air, dg, is
dg ) Rg(1 - cos θe)
(3)
Thus, a droplet of water with a complete powder or granular coating will form a liquid marble with a deformable skin and that skin will provide a gap of thickness dg between the liquid and any surface upon which the marble rests. We emphasize that the grains in the skin will not usually be close-packed but will adopt some distribution with an equilibrium separation between each grain so that the gap is a combination of the grains and the air between them. The concept behind the present work is that when a liquid marble sits upon a flat surface, the contact region will effectively possess a set of protruding grains upon which the water rests. In the contact region, this situation will be similar to the way a set of hydrophobic posts fabricated on a solid surface suspend a droplet to give a superhydrophobic Cassie-Baxter surface. Figure 1a shows a side profile image of a droplet of water in a Cassie-Baxter state on a set of lithographically fabricated microscopic posts (Figure 1b). In comparison, Figure 1c shows a side-profile image of a liquid marble, formed using hydrophobic grains, on a completely flat surface; conceptually, the water within the marble is supported by a set of grains (posts) in the contact region (Figure 1d). However, the difference between the liquid droplet on a surface consisting of posts and the liquid resting on the grains (posts) attached to the liquid-air interface is that the system of grains is able to conform to the shape of the liquid. Moreover, providing the grains are not electrically conducting, the water will be separated from any surface by an electrically insulating gap. Thus, placing a marble onto a metal surface and applying a voltage between the (conducting) water in the marble and the metal surface will cause changes in the contact of the marble with the surface due to the capacitive charging of the interface (e.g., an electrowetting-on-dielectric-type effect). There is a danger that a sufficiently high voltage will cause sufficient electrocapillary pressure for the water to intrude between the grains and eventually come into direct contact with the metal surface, thus causing a large current to flow. Experimentally, this can be avoided by including a thin insulating layer on the metal. Experimental Method In the experiments reported here, two types of powders, lycopodium grains of size 17 ( 3 µm and silica particles with an approximate size of 6 nm, were hydrophobized by immersing a
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small quantity, typically 5 g, in a 40 mL solution containing 2% trimethylsilyl chloride TMSCl (Aldrich 95%) in cyclohexane (Fisher) in a polypropylene centrifuge tube. The tube was placed on a vortex mixer for 1 h and then allowed to stand overnight. The liquid was then decanted off, and the remaining solid was air-dried before being placed in a vacuum oven at 80 °C for 3 h. To create the liquid marbles, a copper sheet was shaped to create a steep slope at one end and a shallow slope at the other with a horizontal section between them; this central section was spin coated with amorphous fluoropolymer Teflon AF 1600 (DuPont Polymers) of around 10 µm thickness to provide an area suitable for the electrowetting experiments. The hydrophobic powders were placed on the shallow slope upon which droplets of 0.01 M aqueous KCl were deposited from a syringe. These droplets immediately became coated with particles and rolled between the slopes two or three times before coming to rest on the insulated section as liquid marbles; these marbles were highly mobile. The marbles created with lycopodium appeared to have a coating consisting of individual grains with water clearly visible between them, but the silica-coated marbles appeared to have a thicker multilayer coating which prevented water being observed between grains. A thin metal contact wire was then brought into contact with the water within the marble from above, and a dc voltage was applied using a Keithley 2410 source/meter under the control of a microcomputer between the copper and the liquid. The profile of the drop was captured in silhouette illumination (e.g., Figure 1c) and analyzed using the drop shape analysis software on a Kru¨ss DSA-10 contact angle meter using placement of a baseline and the tangent 1 method, which fits the profile to a general conic section equation. The derivative of the equation at the baseline gives the slope at the three-phase contact point and thus the contact angle. In principle, this type of measurement for nonwetting sessile droplets on flat surfaces can provide a contact angle accurate to around (0.1°. However, for almost spherical droplets with small to vanishing contact areas, the reported contact angles depend sensitively on the baseline determination, which can introduce systematic error. In the case of the liquid marbles, the blurring of the silhouette profile caused by the coating of grains also further complicates the measurements; these issues are discussed in detail in the Results section. Theory of Electrowetting of a Nonwetting Droplet. To understand the effect of charging of the substrate-marble interface of a liquid marble we will use a surface free energy approach and consider two idealized cases; for generality we will formulate the problem using nonwetting droplet contact angles rather than just the liquid marble contact angle of 180°. In the first case, the droplet is large compared to the capillary length κ-1 ) (γLV/Fg)1/2, where F is the density of the liquid and g ) 9.81 m s-2 is acceleration due to gravity, and so this becomes a puddle with a shape approximating a flat cylinder. In the second case, the droplet is small compared to the capillary length, so that the shape is approximated by a spherical cap with a small flat spot in the region of contact. By approximating the droplet shape to either a cylinder or a spherical cap, an energy functional can be set up and solved to obtain a defining equation between the contact angle and the contact radius or any other geometric parameter. (i) Cylindrical/Puddle Case. The energy functional, E, for a cylinder with a height h and a contact radius r, including surface energy, gravitational potential energy, and electrostatic energy from the charging of the lower surface by an applied voltage V, is given by E ) (γSL - γSV)πr2 + γLVπr2 + γLV2πrh + gF
∫
h
0
πr2(z)z dz -
1 2 2 cV πr (4) 2
where the capacitance per unit area is c ) sro/d, o and r are the permittivity and relative permittivity of free space, and d is the separation between the conducting metal plate and the liquid. The
parameter s is a simple empirical correction factor to take into account the complexities of charging the lower surface of the droplet when it is formed by grains attached to a liquid-vapor interface. It may also be used to take into account any insulating layer coating a conducting surface; to a first approximation we assume s ≈ 1. Evaluating the gravitational energy term, using Young’s law and rearranging gives
[
E ) γLVπr2 1 - cos θe +
2h 1 2 2 cV2 + κh r 2 2γLV
]
(5)
To obtain the equilibrium configuration of the puddle, we minimize eq 5 subject to the constraint that the volume, Vo ) πr2h, remains constant, i.e.
[
cV2 1 h(V,θe) ) 2κ-1 (1 - cos θe) 2 4γLV
]
1/2
(6)
and this can also be written as h(V,θe) ) 2κ-1 sin
( )[
θe 12 4γ
cV2 2 LV sin (θe/2)
]
1/2
(7)
where h(0,π) ) 2κ-1 is the expected result when there is no voltage applied and the droplet is completely nonwetting (i.e., θe ) 180°).21-24 While for a liquid droplet-on-solid system, Young’s law does not allow θe ) 180°, a liquid marble with a grain coated droplet does correspond to θe ) 180° in eq 7. This is because a liquid marble with widely separated hydrophobic grains can be viewed as sitting upon a layer of vapor and the first term in eq 4 becomes γLVπr2 with γLV taking on an effective value for the surface tension between the marble and the vapor. It should also be noted that for a droplet in a Wenzel or Cassie-Baxter state, θe in eq 7 would be replaced by the Cassie-Baxter or Wenzel contact angles, respectively. Equation 7 can also be written in terms of the contact radius r by equating the volume, 4πRo3/3 of sphere of radius Ro to the volume of the cylinder πr2h, so that h ) 4Ro3/3r2, i.e. r(V,θe) ≈
x
( )[
θe 2 1/2 3/2 cV2 κ Ro sin 13 2 4γLV sin2(θe/2)
]
-1/4
(8)
where r(0,π) ) (2/3)1/2Ro3/2κ1/2. Thus, the first-order effect of an applied voltage is expected to be to thin and spread out the puddle as would be expected for a droplet in an electrowetting-on-dielectric experiment. When no voltage is applied and the droplet is assumed to be completely nonwetting (i.e., θe ) 180°), eq 8 recovers previously published results.21-24 The capillary length, and hence the surface tension, of a marble can be deduced experimentally from measurement of the limiting thickness of a puddle as the volume is increased (i.e., h(0,π) ) 2κ-1).22-24 Equations 7 and 8, which can be expanded in powers of V2, should also allow an estimate of the capacitance per unit area to be obtained. (ii) Flat Spot Spherical Case. When volume decreases, the forces of surface tension begin to dominate gravity and a droplet adopts a more spherical shape. For a spherical cap shape with a flat spot lower surface contact region, the height h, base contact radius r, spherical cap radius R, and contact angle θ are related by r ) R sin θ, h ) R(1 - cos θ),
R)
( ) 3Vo πβ
1/3
(9)
where β ) 2 - 3 cos θ + cos3 θ ) (1 - cos θ)2(2 + cos θ)
(10)
The surface free energy, F, of the spherical cap sat upon a solid surface is given by F ) (γSL - γSV)Abase + γLVAcap
(11)
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where the base and cap surface areas are Abase ) πr2 and Acap ) 2πR2(1 - cos θ)
(12)
Due to the constant volume constraint, eq 9, any variation in the contact angle can be related to the variation in base radius by ∆θ )
- (2 + cos θ)(1 - cos θ) ∆r r tan(θ/2)
( )
(13)
Thus, performing a variation of Acap subject to constant volume and rewriting the result in terms of ∆(πr2), we obtain the following relationship between changes in the surface area of the spherical cap and that of the base ∆Acap ) cos θ∆Abase
on the right-hand side represents the effect of surface free energy, and for a completely nonwetting droplet or liquid marble with θe ) 180° this would give -1. The third term is the usual capacitive energy in electrowetting-on-dielectric systems arising from the electrostatic charging that occurs along the base area of the marble. The second term gives the correction due to the weight of the marble creating a flat spot, and this introduces the coupling between the contact angle and the contact radius. Indeed, the combination r tan(θ/2) is simply the maximal height, h, of the marble, and the length scale for gravitational effects to be important is set by κh, which to a first approximation is expected to be of the order 2κR. To compare our analytical result to previous work on liquid marbles, we consider θe ) 180° and V ) 0, multiply both sides of eq 19 by R4/r2, and then rearrange using R4 ) r4/sin4θ
(14) r)
The change in surface free energy, ∆F, subject to the constant volume constraint is then ∆F ) [cos θ - cos θe]γLV∆Abase
(15)
where θe is the contact angle given by Young’s Law (eq 1). For a spherical cap with an angle θ at the contact with the flat spot, the gravitational energy term G can be evaluated and is given by G)
(
)
2πγLVκ2R4 (3 + cos θ)sin6(θ/2) 3
(16)
The limit θ f 0° gives G ) 0, and the limit θ f 180° gives G ) msgR, where ms ) 4πR3/3 is the mass of the sphere. An equivalent form of eq 16 for the gravitational energy of a spherical cap droplet has also been given by Shapiro et al.25 Taking into account the volume constraint and after some simplifying algebra a variation in the base area gives ∆G )
(
)
- γLVκ2r2 tan2(θ/2)∆Abase 6
(17)
Thus, the variation in total energy, including the surface free energy, gravitational potential energy, and capacitive energy is
(
∆E ) γLV cos θ - cos θe -
)
κ2r2 tan2(θ/2) cV2 ∆Abase 2γLV 6
(18)
Setting the change in total energy to zero we obtain an equation defining the observed equilibrium contact angle θ and contact radius r cos θ ) cos θe +
κ2r2 tan2(θ/2) cV2 + 6 2γLV
(19)
It should be noted that the parameters θ and r (or, equivalently, h and θ) are linked via the requirement that the volume, Vo, remains constant, and so they are not independent variables. As in the cylindrical/puddle case, while Young’s Law does not allow θe ) 180°, a liquid marble does correspond to θe ) 180° in eq 19. This is again because a liquid marble can be viewed as sitting upon a layer of vapor and the first term in eq 11 becomes γLVAbase with γLV taking on an effective value for the surface tension between the marble and the vapor. For droplets in Wenzel or Cassie-Baxter states, θe in these equations would be replaced by the Wenzel or Cassie-Baxter contact angles. Equation 19 is a generalization of the key experimental linear relation between the cos θ and V2 observed in electrowetting-ondielectric problems. To interpret eq 19, we note that the first term (25) Shapiro, B.; Moon, H.; Garrell, R. L.; Kim, C. J. J. Appl. Phys. 2003, 93, 5714-5811.
( ) () 2κR2 θ sin3 2 x3
(20)
Using the angle ξ ) π - θ to represent deviations from a spherical shape we can then rewrite eq 20 and expand it as r)
( )
( )(
)
2κRo2 2κR2 3ξ2 cos3(ξ/2) ≈ 18 x3 x3
(21)
where Ro is the radius of an equivalent volume sphere; the volume conservation equation (eq 9) shows that the spherical radius can be approximated by R ≈ Ro(1 + ξ4/16). Equation 21 for r is greater by a factor of x2 than the result given by Aussillous and Que´re´,24 although the power law dependencies on the capillary length and spherical radius are the same. In their work, this factor appears to arise from an extra factor of 2 in the surface energy term compared to the gravitational energy term. When the voltage vanishes and θ ) 180°, the marble contact radius (eq 21) gives the same result as the puddle radius (eq 8) when Ro ) κ-1/2. Numerical Results. To numerically evaluate eq 19 subject to volume conservation (eq 9), we can rewrite it as cos θ ) cos θe +
(
)
21/3(2κRo)2 c 1V 2 sin4(θ/2) + 3 2 (1 - cos θ)4/3(2 + cos θ)2/3 (22)
where Ro is the radius of a sphere of equivalent volume to the droplet and c1 ) sro/dγLV. Equation 22 allows a contact angle, θ, to be deduced as a function of four parameters: the Young’s Law (or 180° marble, Wenzel, or Cassie-Baxter) contact angle, θe, the dimensionless size κRo, the electrowetting strength constant c1, and the applied voltage V. In electrowetting-on-dielectric experiments, the typical thickness of the insulator is in the range of a micrometer to tens of micrometers and the liquid is water. Thus, for numerical work we rewrite c1 ) ao/(γW × 10-6), where γW ) 72.8 mN m-1 is the surface tension of water. The new parameter a is the ratio of the relative permittivity to effective insulator thickness in micrometers scaled by any shape factor, s, and the ratio of the surface tension of water to that of the marble. In ref 22 the effect of coating a droplet of water with silane-treated lycopodium was to reduce its surface tension to 51 mN m-1 based upon the maximal height of a lycopodium marble/puddle. Figure 2 shows the effect of drop size and applied voltage on the contact angle for a completely nonwetting droplet with θe ) 180°. This value of θe gives a perfect liquid marble whereby the grains effectively allow the liquid to sit on the solid surface but separated from it by a thin cushion of air. The dotted curve with κRo ) 0 shows the effect of neglecting the gravitational term in eq 22. As expected, the cosine of the contact angle is linear with voltage squared (Figure 2a), but less obvious is the linearity of the contact angle with voltage rather than voltage squared (Figure 2b). Analytically this linearity can be deduced from eq 22 using an expansion in the angle ξ ) 180° - θ, about θ ) 180°. The effect of including the gravitational term
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Figure 2. Theoretical curves for electrowetting of a nonwetting liquid marble with κRo ) 0.0 (dotted curve) and κRo ) 0.3 and 0.6 (solid curves): (a) linearity of cos θ with square of voltage and (b) decrease of contact angle with increasing drop size and applied voltage.
Figure 3. Fits of the standard electrowetting relationship (eq 22 with κRo ) 0.0, a ) 0.965, and θe )144.7°) to data points generated using eq 22 with κRo ) 0.3, a ) 1, and θe ) 150°, representing a superhydrophobic droplet subject to gravity.
and increasing drop volume κRo is to uniformly shift the cos θ curves upward as illustrated in Figure 2a by the solid curves for κRo ) 0.3 and 0.6 over the voltage range 0-100 V. Figure 2b shows the corresponding curves to Figure 2a for the contact angle, θ. The effect of gravity is to reduce the angle below 180° even before a voltage is applied (solid curves in Figure 2b); the larger the droplet volume, the lower the initial contact angle. As the voltage is increased, the curves asymptotically mirror the slope for the κRo ) 0 straight line. For a completely nonwetting liquid marble (θe ) 180°), κRo adjusts the initial contact angle at V ) 0 and the value of xc1 gives the slope in Figure 2b. The curves in Figure 2b look identical to the curves we would expect to observe with increasing voltage when electrowetting with a superhydrophobic droplet. Consider a theoretical set of data generated from eq 22 using a ) 1, κRo ) 0.3, and θe )150° representing an initial Cassie-Baxter contact angle at V ) 0 (data points in Figure 3). The effect of the finite size is to give an initial observed angle of 144.7°, which further decreases as the voltage increases. These theoretical data points can be fitted with the usual electrowetting equation (eq 22 with κRo ) 0.0) as shown by the solid curves in Figure 3 provided a ) 0.965 and θe )144.7° are used. The net result of such an analysis ignoring the droplet size would therefore be a good fit to the data but with a slight underestimate of the value of the (Cassie-Baxter) contact angle θe and a slight overestimate of the insulator thickness.
grains and come into contact with the substrate, and if the voltage was increased too high, the marble burst. When liquid penetrated through the grains, the marble irreversibly attached itself to the substrate and became immobile. Liquid marbles resting directly on a metal substrate without the amorphous Teflon insulating layer were more susceptible to bursting when the electrowetting voltage was applied. We did not seek to determine any characteristic voltage related to drop size for the drop bursting effect. At high applied voltages some of the lycopodium grains were ejected from the surface of the liquid marble, indicating charging and high electric fields; this coincided with experiments where the marble did not return to its initial contact radius when the voltage was removed. However, by restricting the range of the applied voltage, a marble could be taken through an electrowetting cycle and a reversible change in contact angle achieved. One experimental problem encountered in dealing with liquid marbles was in determining accurate contact angles given their extremely high contact angles and the skin created by the powder coating. In side profile, small marbles appear as almost perfect circles with a rapid change in curvature occurring close to the solid upon which they rest. Accurate measurement of the spherical radius from images is possible, but any errors in the vertical location of a baseline can significantly alter the exact values recorded for the contact area and contact angle. Since the droplet shape is strongly curving inward as the contact line is approached and this is compounded by a slightly “fluffy” profile caused by the powder skin, absolute measurements of contact radius and contact angle are relatively inaccurate; we believe the contact angles we report may be underestimates by around 5-10°. However, the purpose of our measurements are to illustrate the
Results Figure 4 shows examples of a front- and back-illuminated lycopodium liquid marble and a silica liquid marble. As expected, creating liquid marbles with larger volumes caused a reduction in the observed contact angles, and as the voltage was increased, the contact radius increased and the observed contact angle decreased. At higher voltages liquid appeared to penetrate through
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Figure 4. Examples of liquid marbles created using hydrophobic lycopodium (a and b) and hydrophobic silica (c).
0.0356, κRo ) 0.45, and θe )180° (solid curves in Figure 5). While the relative permittivity is unknown for the silica used in the experiment, taking r ≈ 2 and the surface tension of the marble as γM ≈ γW gives an order of magnitude estimate of the effective insulator thickness of d ≈ 50 µm, indicating that the silica is a relatively a thick layer. The volume of the marble gives Ro ≈ 1.3 mm, and using the surface tension of water, this gives Roκw ) 0.49, which is the same order of magnitude as the fitted value. However, we would expect a lower surface tension for the marble and, hence, a higher value of Roκ. If the second term in eq 19 (and eq 22) was reduced by a factor of 2 to agree with Aussillous and Que´re´,22 the fitted value of κRo would increase by a factor of 21/2 to 0.64, and this would then require γM ) 43 mN m-1 for Ro ) 1.3 mm.
Figure 5. Fitting to electrowetting of silica-based liquid marble. Squares show increasing voltage half-cycle, and triangles show decreasing voltage half-cycle. Solid curves are fits to eq 22 with a ) 0.0356, κRo ) 0.45, and θe ) 180°.
trends in these parameters with voltage, and so provided the baseline is not moved during a series of measurements on a liquid marble, we believe the data obtained is useful to illustrate the general trend and reversibility; repeated measurements on a given marble provide contact angles consistent to within (0.5°. We would, however, caution against the use of the reported values beyond the purpose of establishing the general trend and reversibility of the electrowetting process. Figure 5 shows an example of data for a silica-based liquid marble; the squares indicate the increasing voltage half-cycle and the triangles the decreasing half-cycle. The trend of the data with increasing voltage is well described by the minimum energy formula eq 22, and the hysteresis on decreasing the voltage is small. Quantitatively, the data can be fitted to eq 22 using a ) (26) Newton, M. I.; Herbertson, D. L.; Elliott, S. J.; Shirtcliffe, N. J.; McHale, G. J. Phys. D: Appl. Phys. 2006, in press.
While further work is needed to improve the accuracy of absolute measurements of contact angle and clarify the quantitative fitting of the data, these experiments nonetheless demonstrate the principle that electrowetting can be performed on liquid marbles in a manner similar to electrowetting-on-dielectric of simple water droplets. Moreover, our liquid marbles are in a highly mobile state and have high initial contact angles equivalent to droplets on superhydrophobic surfaces. Over a limited range of applied voltage the liquid marbles also recover their original state when the voltage is removed. The lack of recovery is one of the main difficulties presented when attempting to perform electrowetting of a water droplet on a superhydrophobic surface and so usually limits applications in, for example, droplet microfluidics. Development of the liquid marble concept may provide one method to overcome this limitation, and indeed, we have already reported initial promising results showing controllable voltage-actuated movement of liquid marbles.26 For labon-a-chip applications, controllable movement would need to be complemented by development of methods to dispense, coalesce, separate, and mix liquid marbles and separate the liquid from the marble. If such control could be achieved, the liquid marble concept might provide a route to reducing the surface fouling effects experienced in the electrowetting of biological fluids.
Conclusion In this work we considered the electrowetting of liquid marbles composed of lycopodium and silica-coated droplets of water. We argued that a liquid marble can be viewed as equivalent to a liquid droplet resting on a superhydrophobic surface but with the surface structure providing the superhydrophobicity conformal to the liquid surface rather than the underlying solid substrate. The spreading and decrease in contact angle caused by an electrowetting voltage is therefore expected to be reversible provided no penetration between the grains of the droplet coating
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occurs. The energy functional including surface free energy, gravitational energy, and electrostatic energy has been minimized and numerical solutions plotted for a range of droplet sizes and applied voltages. Experimentally, we have shown that the observed contact angles of these highly mobile nonwetting droplets can be reduced in a reversible manner by application of an electrowetting voltage. The initial contact angle is
McHale et al.
determined by the total mass of the droplet, and the cosine of the contact angle changes linearly with the square of the applied voltage. Acknowledgment. We acknowledge the financial support of the UK EPSRC and MOD/Dstl (Grant GR/S34168/01). LA061920J
