- Email: [email protected]
Resonance induced wetting state transition of a ferrofluid droplet on superhydrophobic surfaces
Accepted Manuscript Resonance induced wetting state transition of a ferrofluid droplet on superhydrophobic surfaces P. Poesio, E.N. Wang PII: DOI: Reference:
S0894-1777(14)00043-0 http://dx.doi.org/10.1016/j.expthermflusci.2014.02.012 ETF 8160
To appear in:
Experimental Thermal and Fluid Science
Received Date: Revised Date: Accepted Date:
29 December 2013 7 February 2014 7 February 2014
Please cite this article as: P. Poesio, E.N. Wang, Resonance induced wetting state transition of a ferrofluid droplet on superhydrophobic surfaces, Experimental Thermal and Fluid Science (2014), doi: http://dx.doi.org/10.1016/ j.expthermflusci.2014.02.012
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
AIP/123-QED
Resonance induced wetting state transition of a ferrofluid droplet on superhydrophobic surfaces P. Poesio1, a) and E.N. Wang2 1)
Universit` a degli Studi di Brescia, via Branze 38, 25123 Brescia,
Italy 2)
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307
(Dated: 9 June 2014)
We investigated manipulating wetting transitions of ferrofluid droplets on planar superhydrophobic surfaces by electromagnetic stimulation. We showed that even if magnetic forces are small at small liquid volumes (1 to 10 μl) , they can be effectively used to induce Cassie to Wenzel transition when the exciting frequency is close to the resonant frequency. We related the wetting transition to the increase of the Laplace pressure as a consequence of the large deformation that occurs close to the resonant frequency; on the contrary, inertia forces were not able to induce such a transition. This study promises a new approach to manipulate ferrofluid droplets for various microfluidic and lab-on-chip technologies. Keywords: Wetting transition; superhydrophobic surface; ferrofluid
a)
Electronic mail: [email protected]
1
I.
INTRODUCTION
Many microfluidic applications utilize continuous-flow silicon, polymer, or glass-based microchannels equipped with valves, mixers, pumps, and sensors to perform rapid reactions, detection, and analyses1–3 . While these devices have demonstrated significant promise, the integration of various components is often challenging and a bottleneck in lab-on-a-chip technologies. In addition, the adaptability of these devices to new applications or to the addition of new components is limited; typically, the devices have to be redesigned and newly fabricated, which can have significant lead times. More recently, discrete dropletbased approaches where a liquid plug is suspended in an inert carrier fluid have received interestFair 4 owing to the ability to control individual droplets independently and to perform complex tasks in nano- to pico-liter volumesNiu et al. 5 , Rastogi and Velev 6 . However, challenges due to contamination of isolated plugs by diffusion through the carrier fluid can occur and accurate volume conservation is difficult to achieve. In contrast to closed channel microfluidic architectures, recent interests in controlling discrete liquid droplets on surfaces have emerged to help eliminate the need for microchannels. Mechanisms for droplet manipulation include electrowetting4,7–9 , dielectrophoresisGascoyne et al. 10 , thermocapillarity11 , surface acoustic waves12,13 , magnetic forces in combination with superparamagnetic particles14,15 . In particular, magnetic actuation has demonstrated several unique advantagesPamme 16 . An updated review on micro magnetofluidics can be found in Nguyen17 . For example, superparamagnetic particles can be remotely manipulated by permanent magnets or electromagnets located off-chip, which provides the possibility to decouple the substrate in contact with the droplets from the actuation stage. In such a case, the surface can be low cost and disposable which eliminates cross-contamination, 2
while the actuation stage (more expensive and complex) can be repeatedly used since it is not in direct contact with the fluid sample. In addition, the magnetic interaction is weakly dependent on pH, ionic strength, and temperaturePamme 16 , which promises a more robust platform. Furthermore, magnetic actuation is particularly suitable for biological and biomedical applications since low frequency magnetic fields do not harm biological tissuesPamme 16 . However, in contrast to the other actuation mechanisms mentioned above, the magnetic force is a body force, i.e., the magnetic moment is proportional to the volume. As droplets decrease to microscale sizes, the actuation mechanism is less effective. For example, in the case of a droplet sliding on a surface, the smaller the droplet, the larger the frictional force is compared to the driving body force. Combining the use of superhydrophobic surfaces with magnetic actuation, however, promise a platform to move, store, and mix microdroplets with low adhesion. In addition, by using periodic microstructured surfaces to create these superhydrophobic surfaces, to create superhydrophobic surfaces, the different wetting states, i.e., Wenzel or Cassie-Baxter state18,19 , can be used to achieve three-dimensional manipulation. For example, the bottom surface can be functionalized, and upon wetting and dewetting of the droplet, a reaction can occur with the droplet and surface, which can be subsequently followed by mixing and droplet transport. While the Cassie to Wenzel transition by applying external fields and forces has been of particular fundamental interest to researchers20,21 , the possibility of controlling wetting regimes with magnetic fields has not been demonstrated and offers new possibilities for the rapid development of microfluidic devices22–24 . In this work, we induce Cassie to Wenzel wetting transitions of ferrofluid droplets on superhydrophobic microstructured surfaces using planar electromagnets. The wetting transition occurs by taking advantage of droplet resonance where an oscillating magnetic field is 3
applied, and subsequently reduces the energy required to achieve the wetting transition. The demonstration of droplet wetting transition is an important component towards realizing a magnetic-based microfluidic platform in the future.
II.
EXPERIMENTAL SETUP
Figure 1 shows a schematic of the experimental setup used to manipulate and capture images of the ferrofluid droplet. The ferrofluid (EMG705, Ferrotec) used in the experiments, consists of magnetic particles with diameters of approximately 30 nm suspended in water, where the physical properties are reported in Table 1. The ferrofluid droplets ranging in volume from 1 μl to 10 μl were placed on the superhydrophobic microstructured surface (see Section II.A) by pipette. The apparent contact angle, measured by a custom goniometer, ranged from 130◦ - 140◦ on the surfaces, which is slightly lower than water due to the presence of surfactants in the ferrofluid. The electromagnetic actuation stage was placed directly underneath the superhydrophobic surface, which utilizes copper micro-coils printed on double-sided copper-plated printed circuit boards (PCBs). DC and AC currents were supplied through the copper coils to vary the magnetic field strength to change the wetting states of the droplet, respectively. Each of the experiments was recorded by a high-speed camera (Phantom v7.1, Vision Research) with backlight illumination to enhance the contrast of the droplet.
A.
Superhydrophobic surface
The superhydrophobic surfaces consist of periodic pillar arrays with diameters of d = 2 μm, height 8 μm and spacings of δ = 5 μm or δ = 7 μm. They were fabricated in 4
FIG. 1. Schematic of the experimental setup showing the sample placed on top of the electromagnetic actuation stage. Visualizations were obtained from the side using a high speed camera with backlit illumination. TABLE I. Physical properties of the ferrofluids Ferrotec EMG705Elborai 25 . Property
value
density, ρ
1194 kg/m3
viscosity, η
2.48 mPa · s
surface tension, σ
42.1 mN · m
magnetic susceptibility, χm
1.89
saturation magnetization
206.6 G
silicon using contact lithography and deep reactive ion etching (DRIE). To make the surfaces superhydrophobic, they were subsequently silanized by trichlorosilane using chemical vapor deposition (CVD). A SEM picture is given in Fig. 2.
B.
Micro-coil Electromagnets
The planar micro-coil electromagnets were designed and fabricated, similar to ones developed by Beyzavi and NguyenBeyzavi and Nguyen 26 . Planar rectangular coils were chosen for simplicity26,27 . The copper wires were defined using standard lithography and chemically 5
FIG. 2. SEM picture of a superhydrophobic surface used in the experiments; spacings of δ = 5 μm.
etched in ferric chloride solution. The copper wires are 35 μm thick and 100 μm wide. Planar coils consist of a series of n current-carrying wires with finite length. To compute the magnetic field generated by a single coil, or by any geometrical arrangement of coils, the magnetic fields created by each wire is determined. The superposition of the magnetic fields of all those segments results in the total magnetic field. Applying the Biot-Savart’s law to a segment of wire carrying current I, parallel to the x − z plane, the magnetic field is
Hx = 0 zI Hy = − 4π
x2
dl 3 (x − l)2 + (y − a)2 + z 2
x1
(y − a)I Hz = − 4π
x2
x1
(1)
dl 3 2 2 2 (x − l) + (y − a) + z
where x1 and x2 are the coordinates of the two ends of the segment and a is the distance of the wire from the plane x − z; x, y, z are the coordinates of the point where the magnetic field is computed. Following a coordinate transformation procedure, the magnetic field of a segment oriented at any direction can be obtained following the same equations. 6
The total magnetic field of a micro-coil consisting of n pieces can be computed by superimposing the magnetic fields from Eq. (1) Hcoil =
n
Hi .
(2)
i=i
The magnetic flux B is subsequently determined as Bcoil = μ0 Hcoil (1 + χm )
(3)
where χm is the susceptibility of the medium where the magnetic field is computed and μ0 is the permeability of the free space, μ0 = 4π · 10−7 .
C.
Experimental procedure
The micro-coil geometry used for the wetting transition studies is shown in Fig. 3.
FIG. 3. Schematic of fabricated copper micro-coils on the PCB with 96 windings for wetting transition experiments. The black micro-coil is used for actuation, while the two red micro-coils is used to create a virtual channel.
The two coils on the top side of the PCB were connected to a constant current source to create a virtual channel that traps the droplet in place. The micro-coil on the bottom side was connected to a signal generator that generates electric current at a prescribed frequency. 7
As the ferrofluid droplet was excited by an oscillating electromagnetic field in both horizontal and vertical components, the droplet deformed with surface waves that extended over the meridian stripe parallel to the vibration direction (Fig. 3). To examine the influence of the excitation frequency, the following procedure was used: 1. A droplet of volume V was gently deposited on the surface by handheld pipette; 2. The excitation frequency ω was set; 3. The current was increased step by step from 0 to 0.5 A. Note, we could not increase the magnetic field amplitude indefinitely since the current through the coils is limited by Joule heating; 4. If transition occurred (the apparent contact angle changed from 130◦ -140◦ to 80◦ -90◦ ), we recorded the minimum current value, otherwise we proceeded to a new frequency value.
III.
WETTING TRANSITION
Figure 4(a) shows time-lapse images with a droplet undergoing wetting transition at a frequency 44 Hz. In contrast, Fig. 4(b) shows a droplet undergoing magnetic induced oscillations at a frequency 5 Hz, different from resonant condition experiencing strong deformations but, no wetting transition. The wetting transitions occurred at frequencies associated with resonant conditions, as predicted by the following analysis. The resonant frequencies for various droplet sizes can be determined by using the dispersion relation ωj2
=
σ 3 gqj + qj tanh(qj H) ρ 8
(4)
(a)
(b)
FIG. 4. Time-lapse images of the wetting transition for a 1 μl droplet. (a) Images showing transition at a frequency of 44 Hz; current I = 169 mA. (b) Images showing no transition at a frequency of 5 Hz; current I = 500 mA.
Here, qj is the wave vector that corresponds to the selected mode j and H is the mean depth of the droplet, H=
V . π(R sin θ)2
(5)
Noblin et al.Noblin, Buguin, and Brochard-Wyart 28 observed that the modes with fixed contact line correspond to j = 2, 3, . . . while those with moving contact line are described by j = 1, 3/2, 5/2, . . . The wetting transition occurred when the effective pressure pex inside the droplet is larger 9
400
300
200
100
0
10
20
30
40
50
60
70
80
90
100
frequency (Hz)
500
400
300
200
100
0
0
10
20
30
40
600
500
400
300
200
100
0
10
20
30
40
50
60
70
80
90
100
600
500
400
300
200
100
0
0
10
20
30
40
60
70
frequency (Hz)
80
90
100
500
400
300
200
100
0
10
20
30
40
50
60
70
frequency (Hz)
(d)
60
70
80
90
100
80
90
100
(c)
600
0
50
frequency (Hz)
(b) current (mA), ratio pex /pcrit (–)
current (mA), ratio pex /pcrit (–)
(a)
0
50
frequency (Hz)
80
90
100
current (mA), ratio pex /pcrit (–)
0
600
current (mA), ratio pex /pcrit (–)
500
current (mA), ratio pex /pcrit (–)
current (mA), ratio pex /pcrit (–)
600
600
500
400
300
200
100
0
0
(e)
10
20
30
40
50
60
70
frequency (Hz)
(f)
FIG. 5. Droplet response to current changes as a function of frequency for different droplet volumes. ◦: current, pressure ratio; for clarity the plotted frequency step is 5 Hz, while experiments were carried out at 1 Hz step. ◦: current input; : ratio pex /pcrit . The micro-coil is made up by 96 pieces. (a): Results for a 1 μl droplet. The micro-engineered surface is characterized by d = 2 μm and δ = 7 μm. (b) Results for a 5 μl droplet. The micro-engineered surface is characterized by d = 2 μm and δ = 7 μm. (c ): Results for a 10 μl droplet. The micro-structured surface with d = 2 μm and δ = 7 μm. (d): Results for a 1 μl droplet. The micro-engineered surface is characterized by d = 2 μm and δ = 5 μm. (e): Results for a 5 μl droplet. The micro-engineered d surface is characterized by d = 2 μm and δ = 5 μm. (f): Results for a 10 μl droplet. The micro-engineered surface is characterized by d = 2 μm and δ = 5 μm.
than the critical pressure pcrit transition29,30
pex > pcrit . 10
(6)
TABLE II. Comparison between the resonant frequency ωj predicted by Eq. 4 and the frequency at which wetting transition occurred, ωtr . The data refer to a micro-coil consisting of 96 pieces and a micro-engineered surface characterized by d = 2 μm and δ = 7 μm; N T indicates that no transition occurred at that particular frequency. 1 μl
5 μl
10 μl
mode j
ωj (Hz)
ωtr (Hz)
ωj
ωtr (Hz)
ωj
ωtr (Hz)
1
18
16
12
11
10
10
1.5
47
44
28
24
23
22
2
94
NT
50
NT
40
NT
2.5
157
149
79
72
61
56
3
157
NT
79
NT
61
NT
The external pressure is associated with the inertial forces while the internal pressure is associated with the anti-wetting Laplace pressure. The critical pressure is pcrit = −
σf cos θ , (1 − f )ψ
(7)
where ψ is the ratio between the pillar perimeter and its area and f is the ratio between the pillar area and the pillar apparent area; σ is the surface tension and θ is the apparent wetting angle. The excess pressure over atmospheric pressure inside the droplet is the sum of the inertia pressure pi – whose contribution can be related mainly to the vertical oscillation – to the Laplace contribution pL and to the hydrostatic pressure pex = pi +
2σ + ρgH + pm R(θ)
(8)
where ρ is the droplet density. The amplitude of the additional pressure due to the inertial 11
forces related to the vertical vibration of the droplet is ρV Aω 2 pi = . πR(θ)2 sin2 θ
(9)
where V is the droplet volume, A and ω are the amplitude and the frequency of the oscillation. The deviation z of the droplet from the equilibrium can be expressed as 2πx . λ
(10)
8π 2 Aσ λ
(11)
z = A sin Therefore, the maximum Laplace pressure is pmax = L
where λ is twice the mean distance between the wave nodes. The term pm stems from the additional magnetic body force. Such term can be estimated as pm =
π 3 d MB 6 A πR(θ)2 sin2
θ
(12)
where B is the magnetic field at the center of the droplet and the gradient of the magnetic field is estimated as ∇B ≈
B . A
This term ranges between 5% to 30% of the inertial pressure
pi , according to the operational conditions; note, however that this term is very likely overestimated by Eq. 12 due to an overestimation of the gradient of the magnetic field. It is also worth to point out that the magnitude of this term is not enough, however, to induce wetting transition: by the application of a steady magnetic field has never been able to induce wetting transition. Since the order of magnitude estimation shows that the contribution of pm can not be responsible of the wetting transition and since its computation is rough, we decided to note include its contribution in the computation. In Fig. 5 we plot the ratio between the excess pressure from Eq. 8, and the critical pressure, Eq. 7, and the input current provided to the coils; as expected, when transition 12
occurs this ratio is larger than unity. This ratio is larger than unity only at (or close to) resonance (as indicated in Table II). In this case, the Laplace pressure is maximal and gives rise to the transition. Far from resonance, the main role in Eq. 8 is played by the inertia, which is proportional to the amplitude and to the squared frequency of the oscillations, see Eq. 9; however, since the magnetic field used in the experiments is relatively low, we can not induce transition based on inertia forces. The importance of magnetic force, relative to gravitational and surface tension can be shown by computing the Bond number (Bo) and the magnetic Bond number (Bom ). The Bond number is defined as the ratio between gravity and surface tension forces Bo = ρgd2 /4σ. The magnetic Bond number is computed as Bo = dBM/2σ, where M is the magnetization density31 . Since, magnetization density M is not available for out fluid we used the magnetization density of the EMG-707, as done by Zhang et al12. For droplets of d=1,5, 10 μl, as used in Fig. 5, and for a input current of I=0.5 A, the resulting Bond numbers are, respectively, Bo ≈ 0, 03, 0.08, 0.12 and Bom ≈ 0.07, 0.13, 0.17; as can be noted Bo ≈ Bom , i.e. the magnitude of the gravity and of the magnetic body forces are, in our experiment, comparable.
We speculate that the wetting transition occurs when the triple line is de-pinned, corresponding to the so-called Type-II regime (mobile contact line)28 for smooth surfaces; this observation is also supported by the fact that the computed frequency corresponds to the ones describing waves with un-pinned contact line, see Table II. The vibrating interface contains not only convex parts, but also concave ones where the Laplace pressure is negative. It seems reasonable to suggest that the transition occurs when the crest of a wave is near the triple line that gives rise to the local increase in the Laplace pressure, leading to the triple-line displacement and subsequent wetting transition. 13
IV.
CONCLUSIONS
In this paper we investigated an electromagnetic force to transition ferrofluid droplets on planar superhydrophobic surfaces. We showed that, even though the magnetic force is small at small liquid volumes, the superhydrophobic surface, characterized by low adhesion, provides the possibility to manipulate wetting transitions of droplets. We also showed that at the resonance, for the un-pinned contact line case, the deformation is so large that the Laplace pressure becomes large enough to induce wetting transition. On the contrary, inertia forces, even at resonant conditions, are not strong enough to cause the droplets to change wetting states. The possibility to induce wetting transition at lower power input promises new opportunities for discrete droplet manipulation for various microfluidic technologies.
ACKNOWLEDGMENTS
We wish to acknowledge R. Xiao for preparing the superhydrophobic surfaces and prof. M. Zahn and S. Khushrushahi for fruitful discussions and suggestions. Work done under the UniBSMIT-MechE faculty exchange Program co-sponsored by the CARIPLO Foundation, Italy under Grant No. 2008-2290.
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Z. Long, A. Shetty, M. Solomon, and R. Larson, “Fundamental of magnet-actuated droplet on a open hydrophobic surface,” Lab Chip 9, 1567 (2009).
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Z.-G. Guo, F. Zhou, J.-C. Hao, Y.-M. Liang, W.-M. Liu, and W. Huck, “Stick and slide ferrofluidic droplets on superhydrophobic surfaces,” App. Phys. Lett. 89, 081911 (2006).
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N. Pamme, “Magnetism and microfluidics,” Lab Chip 6, 24 (2005).
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N. Nguyen, “Micro-magnetofluidics: interactions between magnetism and fluid flow on the microscale,” Microfluid Nanofluid 12, 1 (2012).
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R. Wenzel, “Resistance of solid surfaces to wetting by water,” Ind. Engin. Chem 28, 988 (1936).
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E. Bormashenko, R. Pogreb, G. Whyman, and M. Erlich, “Cassie-Wenzel wetting transition in vibrating drops deposited on rough surfaces. Is the dynamic Cassie-Wenzel wetting transition a 2d or 1d affair?” Langmuir 23, 6501 (2007).
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17
Highlights -
S0894-1777(14)00043-0 http://dx.doi.org/10.1016/j.expthermflusci.2014.02.012 ETF 8160
To appear in:
Experimental Thermal and Fluid Science
Received Date: Revised Date: Accepted Date:
29 December 2013 7 February 2014 7 February 2014
Please cite this article as: P. Poesio, E.N. Wang, Resonance induced wetting state transition of a ferrofluid droplet on superhydrophobic surfaces, Experimental Thermal and Fluid Science (2014), doi: http://dx.doi.org/10.1016/ j.expthermflusci.2014.02.012
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
AIP/123-QED
Resonance induced wetting state transition of a ferrofluid droplet on superhydrophobic surfaces P. Poesio1, a) and E.N. Wang2 1)
Universit` a degli Studi di Brescia, via Branze 38, 25123 Brescia,
Italy 2)
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307
(Dated: 9 June 2014)
We investigated manipulating wetting transitions of ferrofluid droplets on planar superhydrophobic surfaces by electromagnetic stimulation. We showed that even if magnetic forces are small at small liquid volumes (1 to 10 μl) , they can be effectively used to induce Cassie to Wenzel transition when the exciting frequency is close to the resonant frequency. We related the wetting transition to the increase of the Laplace pressure as a consequence of the large deformation that occurs close to the resonant frequency; on the contrary, inertia forces were not able to induce such a transition. This study promises a new approach to manipulate ferrofluid droplets for various microfluidic and lab-on-chip technologies. Keywords: Wetting transition; superhydrophobic surface; ferrofluid
a)
Electronic mail: [email protected]
1
I.
INTRODUCTION
Many microfluidic applications utilize continuous-flow silicon, polymer, or glass-based microchannels equipped with valves, mixers, pumps, and sensors to perform rapid reactions, detection, and analyses1–3 . While these devices have demonstrated significant promise, the integration of various components is often challenging and a bottleneck in lab-on-a-chip technologies. In addition, the adaptability of these devices to new applications or to the addition of new components is limited; typically, the devices have to be redesigned and newly fabricated, which can have significant lead times. More recently, discrete dropletbased approaches where a liquid plug is suspended in an inert carrier fluid have received interestFair 4 owing to the ability to control individual droplets independently and to perform complex tasks in nano- to pico-liter volumesNiu et al. 5 , Rastogi and Velev 6 . However, challenges due to contamination of isolated plugs by diffusion through the carrier fluid can occur and accurate volume conservation is difficult to achieve. In contrast to closed channel microfluidic architectures, recent interests in controlling discrete liquid droplets on surfaces have emerged to help eliminate the need for microchannels. Mechanisms for droplet manipulation include electrowetting4,7–9 , dielectrophoresisGascoyne et al. 10 , thermocapillarity11 , surface acoustic waves12,13 , magnetic forces in combination with superparamagnetic particles14,15 . In particular, magnetic actuation has demonstrated several unique advantagesPamme 16 . An updated review on micro magnetofluidics can be found in Nguyen17 . For example, superparamagnetic particles can be remotely manipulated by permanent magnets or electromagnets located off-chip, which provides the possibility to decouple the substrate in contact with the droplets from the actuation stage. In such a case, the surface can be low cost and disposable which eliminates cross-contamination, 2
while the actuation stage (more expensive and complex) can be repeatedly used since it is not in direct contact with the fluid sample. In addition, the magnetic interaction is weakly dependent on pH, ionic strength, and temperaturePamme 16 , which promises a more robust platform. Furthermore, magnetic actuation is particularly suitable for biological and biomedical applications since low frequency magnetic fields do not harm biological tissuesPamme 16 . However, in contrast to the other actuation mechanisms mentioned above, the magnetic force is a body force, i.e., the magnetic moment is proportional to the volume. As droplets decrease to microscale sizes, the actuation mechanism is less effective. For example, in the case of a droplet sliding on a surface, the smaller the droplet, the larger the frictional force is compared to the driving body force. Combining the use of superhydrophobic surfaces with magnetic actuation, however, promise a platform to move, store, and mix microdroplets with low adhesion. In addition, by using periodic microstructured surfaces to create these superhydrophobic surfaces, to create superhydrophobic surfaces, the different wetting states, i.e., Wenzel or Cassie-Baxter state18,19 , can be used to achieve three-dimensional manipulation. For example, the bottom surface can be functionalized, and upon wetting and dewetting of the droplet, a reaction can occur with the droplet and surface, which can be subsequently followed by mixing and droplet transport. While the Cassie to Wenzel transition by applying external fields and forces has been of particular fundamental interest to researchers20,21 , the possibility of controlling wetting regimes with magnetic fields has not been demonstrated and offers new possibilities for the rapid development of microfluidic devices22–24 . In this work, we induce Cassie to Wenzel wetting transitions of ferrofluid droplets on superhydrophobic microstructured surfaces using planar electromagnets. The wetting transition occurs by taking advantage of droplet resonance where an oscillating magnetic field is 3
applied, and subsequently reduces the energy required to achieve the wetting transition. The demonstration of droplet wetting transition is an important component towards realizing a magnetic-based microfluidic platform in the future.
II.
EXPERIMENTAL SETUP
Figure 1 shows a schematic of the experimental setup used to manipulate and capture images of the ferrofluid droplet. The ferrofluid (EMG705, Ferrotec) used in the experiments, consists of magnetic particles with diameters of approximately 30 nm suspended in water, where the physical properties are reported in Table 1. The ferrofluid droplets ranging in volume from 1 μl to 10 μl were placed on the superhydrophobic microstructured surface (see Section II.A) by pipette. The apparent contact angle, measured by a custom goniometer, ranged from 130◦ - 140◦ on the surfaces, which is slightly lower than water due to the presence of surfactants in the ferrofluid. The electromagnetic actuation stage was placed directly underneath the superhydrophobic surface, which utilizes copper micro-coils printed on double-sided copper-plated printed circuit boards (PCBs). DC and AC currents were supplied through the copper coils to vary the magnetic field strength to change the wetting states of the droplet, respectively. Each of the experiments was recorded by a high-speed camera (Phantom v7.1, Vision Research) with backlight illumination to enhance the contrast of the droplet.
A.
Superhydrophobic surface
The superhydrophobic surfaces consist of periodic pillar arrays with diameters of d = 2 μm, height 8 μm and spacings of δ = 5 μm or δ = 7 μm. They were fabricated in 4
FIG. 1. Schematic of the experimental setup showing the sample placed on top of the electromagnetic actuation stage. Visualizations were obtained from the side using a high speed camera with backlit illumination. TABLE I. Physical properties of the ferrofluids Ferrotec EMG705Elborai 25 . Property
value
density, ρ
1194 kg/m3
viscosity, η
2.48 mPa · s
surface tension, σ
42.1 mN · m
magnetic susceptibility, χm
1.89
saturation magnetization
206.6 G
silicon using contact lithography and deep reactive ion etching (DRIE). To make the surfaces superhydrophobic, they were subsequently silanized by trichlorosilane using chemical vapor deposition (CVD). A SEM picture is given in Fig. 2.
B.
Micro-coil Electromagnets
The planar micro-coil electromagnets were designed and fabricated, similar to ones developed by Beyzavi and NguyenBeyzavi and Nguyen 26 . Planar rectangular coils were chosen for simplicity26,27 . The copper wires were defined using standard lithography and chemically 5
FIG. 2. SEM picture of a superhydrophobic surface used in the experiments; spacings of δ = 5 μm.
etched in ferric chloride solution. The copper wires are 35 μm thick and 100 μm wide. Planar coils consist of a series of n current-carrying wires with finite length. To compute the magnetic field generated by a single coil, or by any geometrical arrangement of coils, the magnetic fields created by each wire is determined. The superposition of the magnetic fields of all those segments results in the total magnetic field. Applying the Biot-Savart’s law to a segment of wire carrying current I, parallel to the x − z plane, the magnetic field is
Hx = 0 zI Hy = − 4π
x2
dl 3 (x − l)2 + (y − a)2 + z 2
x1
(y − a)I Hz = − 4π
x2
x1
(1)
dl 3 2 2 2 (x − l) + (y − a) + z
where x1 and x2 are the coordinates of the two ends of the segment and a is the distance of the wire from the plane x − z; x, y, z are the coordinates of the point where the magnetic field is computed. Following a coordinate transformation procedure, the magnetic field of a segment oriented at any direction can be obtained following the same equations. 6
The total magnetic field of a micro-coil consisting of n pieces can be computed by superimposing the magnetic fields from Eq. (1) Hcoil =
n
Hi .
(2)
i=i
The magnetic flux B is subsequently determined as Bcoil = μ0 Hcoil (1 + χm )
(3)
where χm is the susceptibility of the medium where the magnetic field is computed and μ0 is the permeability of the free space, μ0 = 4π · 10−7 .
C.
Experimental procedure
The micro-coil geometry used for the wetting transition studies is shown in Fig. 3.
FIG. 3. Schematic of fabricated copper micro-coils on the PCB with 96 windings for wetting transition experiments. The black micro-coil is used for actuation, while the two red micro-coils is used to create a virtual channel.
The two coils on the top side of the PCB were connected to a constant current source to create a virtual channel that traps the droplet in place. The micro-coil on the bottom side was connected to a signal generator that generates electric current at a prescribed frequency. 7
As the ferrofluid droplet was excited by an oscillating electromagnetic field in both horizontal and vertical components, the droplet deformed with surface waves that extended over the meridian stripe parallel to the vibration direction (Fig. 3). To examine the influence of the excitation frequency, the following procedure was used: 1. A droplet of volume V was gently deposited on the surface by handheld pipette; 2. The excitation frequency ω was set; 3. The current was increased step by step from 0 to 0.5 A. Note, we could not increase the magnetic field amplitude indefinitely since the current through the coils is limited by Joule heating; 4. If transition occurred (the apparent contact angle changed from 130◦ -140◦ to 80◦ -90◦ ), we recorded the minimum current value, otherwise we proceeded to a new frequency value.
III.
WETTING TRANSITION
Figure 4(a) shows time-lapse images with a droplet undergoing wetting transition at a frequency 44 Hz. In contrast, Fig. 4(b) shows a droplet undergoing magnetic induced oscillations at a frequency 5 Hz, different from resonant condition experiencing strong deformations but, no wetting transition. The wetting transitions occurred at frequencies associated with resonant conditions, as predicted by the following analysis. The resonant frequencies for various droplet sizes can be determined by using the dispersion relation ωj2
=
σ 3 gqj + qj tanh(qj H) ρ 8
(4)
(a)
(b)
FIG. 4. Time-lapse images of the wetting transition for a 1 μl droplet. (a) Images showing transition at a frequency of 44 Hz; current I = 169 mA. (b) Images showing no transition at a frequency of 5 Hz; current I = 500 mA.
Here, qj is the wave vector that corresponds to the selected mode j and H is the mean depth of the droplet, H=
V . π(R sin θ)2
(5)
Noblin et al.Noblin, Buguin, and Brochard-Wyart 28 observed that the modes with fixed contact line correspond to j = 2, 3, . . . while those with moving contact line are described by j = 1, 3/2, 5/2, . . . The wetting transition occurred when the effective pressure pex inside the droplet is larger 9
400
300
200
100
0
10
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40
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70
80
90
100
frequency (Hz)
500
400
300
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100
0
0
10
20
30
40
600
500
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100
0
10
20
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100
600
500
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0
0
10
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70
frequency (Hz)
80
90
100
500
400
300
200
100
0
10
20
30
40
50
60
70
frequency (Hz)
(d)
60
70
80
90
100
80
90
100
(c)
600
0
50
frequency (Hz)
(b) current (mA), ratio pex /pcrit (–)
current (mA), ratio pex /pcrit (–)
(a)
0
50
frequency (Hz)
80
90
100
current (mA), ratio pex /pcrit (–)
0
600
current (mA), ratio pex /pcrit (–)
500
current (mA), ratio pex /pcrit (–)
current (mA), ratio pex /pcrit (–)
600
600
500
400
300
200
100
0
0
(e)
10
20
30
40
50
60
70
frequency (Hz)
(f)
FIG. 5. Droplet response to current changes as a function of frequency for different droplet volumes. ◦: current, pressure ratio; for clarity the plotted frequency step is 5 Hz, while experiments were carried out at 1 Hz step. ◦: current input; : ratio pex /pcrit . The micro-coil is made up by 96 pieces. (a): Results for a 1 μl droplet. The micro-engineered surface is characterized by d = 2 μm and δ = 7 μm. (b) Results for a 5 μl droplet. The micro-engineered surface is characterized by d = 2 μm and δ = 7 μm. (c ): Results for a 10 μl droplet. The micro-structured surface with d = 2 μm and δ = 7 μm. (d): Results for a 1 μl droplet. The micro-engineered surface is characterized by d = 2 μm and δ = 5 μm. (e): Results for a 5 μl droplet. The micro-engineered d surface is characterized by d = 2 μm and δ = 5 μm. (f): Results for a 10 μl droplet. The micro-engineered surface is characterized by d = 2 μm and δ = 5 μm.
than the critical pressure pcrit transition29,30
pex > pcrit . 10
(6)
TABLE II. Comparison between the resonant frequency ωj predicted by Eq. 4 and the frequency at which wetting transition occurred, ωtr . The data refer to a micro-coil consisting of 96 pieces and a micro-engineered surface characterized by d = 2 μm and δ = 7 μm; N T indicates that no transition occurred at that particular frequency. 1 μl
5 μl
10 μl
mode j
ωj (Hz)
ωtr (Hz)
ωj
ωtr (Hz)
ωj
ωtr (Hz)
1
18
16
12
11
10
10
1.5
47
44
28
24
23
22
2
94
NT
50
NT
40
NT
2.5
157
149
79
72
61
56
3
157
NT
79
NT
61
NT
The external pressure is associated with the inertial forces while the internal pressure is associated with the anti-wetting Laplace pressure. The critical pressure is pcrit = −
σf cos θ , (1 − f )ψ
(7)
where ψ is the ratio between the pillar perimeter and its area and f is the ratio between the pillar area and the pillar apparent area; σ is the surface tension and θ is the apparent wetting angle. The excess pressure over atmospheric pressure inside the droplet is the sum of the inertia pressure pi – whose contribution can be related mainly to the vertical oscillation – to the Laplace contribution pL and to the hydrostatic pressure pex = pi +
2σ + ρgH + pm R(θ)
(8)
where ρ is the droplet density. The amplitude of the additional pressure due to the inertial 11
forces related to the vertical vibration of the droplet is ρV Aω 2 pi = . πR(θ)2 sin2 θ
(9)
where V is the droplet volume, A and ω are the amplitude and the frequency of the oscillation. The deviation z of the droplet from the equilibrium can be expressed as 2πx . λ
(10)
8π 2 Aσ λ
(11)
z = A sin Therefore, the maximum Laplace pressure is pmax = L
where λ is twice the mean distance between the wave nodes. The term pm stems from the additional magnetic body force. Such term can be estimated as pm =
π 3 d MB 6 A πR(θ)2 sin2
θ
(12)
where B is the magnetic field at the center of the droplet and the gradient of the magnetic field is estimated as ∇B ≈
B . A
This term ranges between 5% to 30% of the inertial pressure
pi , according to the operational conditions; note, however that this term is very likely overestimated by Eq. 12 due to an overestimation of the gradient of the magnetic field. It is also worth to point out that the magnitude of this term is not enough, however, to induce wetting transition: by the application of a steady magnetic field has never been able to induce wetting transition. Since the order of magnitude estimation shows that the contribution of pm can not be responsible of the wetting transition and since its computation is rough, we decided to note include its contribution in the computation. In Fig. 5 we plot the ratio between the excess pressure from Eq. 8, and the critical pressure, Eq. 7, and the input current provided to the coils; as expected, when transition 12
occurs this ratio is larger than unity. This ratio is larger than unity only at (or close to) resonance (as indicated in Table II). In this case, the Laplace pressure is maximal and gives rise to the transition. Far from resonance, the main role in Eq. 8 is played by the inertia, which is proportional to the amplitude and to the squared frequency of the oscillations, see Eq. 9; however, since the magnetic field used in the experiments is relatively low, we can not induce transition based on inertia forces. The importance of magnetic force, relative to gravitational and surface tension can be shown by computing the Bond number (Bo) and the magnetic Bond number (Bom ). The Bond number is defined as the ratio between gravity and surface tension forces Bo = ρgd2 /4σ. The magnetic Bond number is computed as Bo = dBM/2σ, where M is the magnetization density31 . Since, magnetization density M is not available for out fluid we used the magnetization density of the EMG-707, as done by Zhang et al12. For droplets of d=1,5, 10 μl, as used in Fig. 5, and for a input current of I=0.5 A, the resulting Bond numbers are, respectively, Bo ≈ 0, 03, 0.08, 0.12 and Bom ≈ 0.07, 0.13, 0.17; as can be noted Bo ≈ Bom , i.e. the magnitude of the gravity and of the magnetic body forces are, in our experiment, comparable.
We speculate that the wetting transition occurs when the triple line is de-pinned, corresponding to the so-called Type-II regime (mobile contact line)28 for smooth surfaces; this observation is also supported by the fact that the computed frequency corresponds to the ones describing waves with un-pinned contact line, see Table II. The vibrating interface contains not only convex parts, but also concave ones where the Laplace pressure is negative. It seems reasonable to suggest that the transition occurs when the crest of a wave is near the triple line that gives rise to the local increase in the Laplace pressure, leading to the triple-line displacement and subsequent wetting transition. 13
IV.
CONCLUSIONS
In this paper we investigated an electromagnetic force to transition ferrofluid droplets on planar superhydrophobic surfaces. We showed that, even though the magnetic force is small at small liquid volumes, the superhydrophobic surface, characterized by low adhesion, provides the possibility to manipulate wetting transitions of droplets. We also showed that at the resonance, for the un-pinned contact line case, the deformation is so large that the Laplace pressure becomes large enough to induce wetting transition. On the contrary, inertia forces, even at resonant conditions, are not strong enough to cause the droplets to change wetting states. The possibility to induce wetting transition at lower power input promises new opportunities for discrete droplet manipulation for various microfluidic technologies.
ACKNOWLEDGMENTS
We wish to acknowledge R. Xiao for preparing the superhydrophobic surfaces and prof. M. Zahn and S. Khushrushahi for fruitful discussions and suggestions. Work done under the UniBSMIT-MechE faculty exchange Program co-sponsored by the CARIPLO Foundation, Italy under Grant No. 2008-2290.
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Highlights -