Self-comparison measurement for slippage on superhydrophobic surfaces based on the wetting transition This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2010 J. Micromech. Microeng. 20 115022 (http://iopscience.iop.org/0960-1317/20/11/115022) Download details: IP Address: 128.42.202.150 The article was downloaded on 07/10/2012 at 12:23 Please note that terms and conditions apply. View the table of contents for this issue, or go to the journal homepage for more Home Search Collections Journals About Contact us My IOPscience
Transcript
Self-comparison measurement for slippage on superhydrophobic surfaces based on the
wetting transition
This article has been downloaded from IOPscience. Please scroll down to see the full text article.
Received 7 July 2010, in final form 7 September 2010Published 15 October 2010Online at stacks.iop.org/JMM/20/115022
AbstractThis paper describes a self-comparison measuring method for the slip length of fluid flow oversuperhydrophobic surfaces consisting of a pillar array based on the wetting transition. Thewetting transition of the liquid resting on a superhydrophobic surface in the measuring coursemay lead to the disappearance of the slippage effect, which can be used to measure the sliplength before the wetting transition. Based on this feature, the slip length formula for thismeasuring method is deduced. Then, to verify this method, a rheological experiment for70wt% glycerin solution flow over a superhydrophobic surface with carbon nanotube (CNT)forest was carried out on a commercial rheological system with plate-and-plate configuration.Results show that even on the CNT-coated surface that can induce little slip length, theexperimental slip length is still on the same scale as the theoretical one. This measuringmethod can be used to measure the slip length of liquid flow over the superhydrophobicsurface consisting of a pillar array with good flexibility.
(Some figures in this article are in colour only in the electronic version)
1. Introduction
Due to their broad potential application, microfluidic devicesas well as their design have attracted wide attention [1–3].Downsizing such devices raises numerous problems, one beingthe huge increase in fluid resistance. To solve this problem,employing superhydrophobic surfaces as the inner wall ofthese devices has been thought of as an effective way due tothe larger slippage effect of fluid flow over such surfaces [4, 5].Such a slippage effect has been estimated by both theoreticalanalysis and numerical simulation; however, to date, there arestill very few experimental works on this phenomenon due tothe lack of an experimental method.
To characterize the fluid slippage effect on superhydro-phobic surfaces, several methods, such as the pressure dropmeasuring method [6, 7], droplet rolling velocity measuringmethod [8, 9], μ-PIV method [10] and rheological method[11, 12], have been proposed. However, in these methods,
1 Author to whom any correspondence should be addressed.
there are still more or less shortages that hamper theexperiment or influence the experimental result. In thepressure drop measuring method [6, 7], it is necessary toconstruct an ever-tiny channel for an observable dragreduction, making it hard to carry out this method. In thedroplet rolling velocity method [8, 9], the rolling velocityof a droplet depends not only on the slippage effect at theinterface, but also on the dynamics of the three-phase contactline, making this method unable to quantitatively characterizethe slippage effect simply. In the μ-PIV method also [10], it isdifficult to construct the ever-tiny flow channel. Moreover,this method is limited by the resolution and the speedof the camera and by the scale of the surface character.In this context, Choi and Kim [11, 12] proposed arheological measuring method for the slippage effect onsuperhydrophobic surfaces. Although such a method can beused widely for superhydrophobic surfaces with structureranging from nanometer scale to even hundreds of micrometerscale, it has been criticized due to the liquid edge effector end effect [13, 14]. This effect is schematized in
J. Micromech. Microeng. 20 (2010) 115022 J Li et al
(a) (b)
Figure 1. The edge or end effect of liquid on a superhydrophobic surface in the rheological system. (a) and (b) the cases of liquid resting inthe gap between the clamp and a hydrophobic surface and that between the clamp and a superhydrophobic surface, respectively.
figure 1. Generally, when the test liquid rests on a smoothhydrophobic surface, as shown in figure 1(a), its borderwould take the shape of a drum. While the smoothhydrophobic surface is represented by a superhydrophobicsurface, as shown in figure 1(b), the larger contact angleof the liquid on the superhydrophobic surface will lead toa decrease in the apparent contact area between the liquidand the superhydrophobic surface. Such a decrease in theapparent contact area will induce a reduction in driving torque,making the experimental slip length larger than the actual one[13].
Here, we propose a measuring method for the slippageeffect of fluid flow over superhydrophobic surfaces coveredwith a micro pillar array based on the wetting transition ina single measuring course. In this measuring course, thewetting transition of the liquid resting on superhydrophobicsurfaces occurs from the Cassie state to the Wenzel state,leading to the disappearance of the slippage effect as wellas the increase in driving force. The calculation formula forthis method is deduced. Then the validity of this method isverified by a rheological measurement for the slip length of70 wt% glycerin solution flow over a carbon nanotube forest(CNT)-coated superhydrophobic surface.
2. Measurement methodology
In the literature [15–17], the slippage effect is usuallyquantified by a slip length, which is defined as the distanceinside the surface at which the extrapolated fluid velocitywould equal the velocity of the surface. According to thisdefinition, the slip length reads
b = vs
dv/dz, (1)
where b is the slip length, vs is the slip velocity and dv/dz
is the shear rate experienced by the fluid. On the rheologicalsystem with a plate-and-plate configuration, the shear rate isdefined as
dv/dz = ωR/D, (2)
Figure 2. Schematic diagram for the definition of the equivalentradius.
where R is the radius of the clamp, D is the gap between thetest surface and the clamp and ω is the angular velocity of theclamp, and the shear stress is expressed as
τ = 2M/(πR3), (3)
where τ is the shear stress and M is the driving torque. Notethat this shear stress definition implies an assumption that thetest liquid in the gap has a drum-shaped border. However,such an assumption cannot be satisfied in a situation where thetest surface is a superhydrophobic one, as shown in figure 2.Therefore, to describe such a situation, it is necessary to definea suitable shear stress. Here, we first define an equivalentradius to represent the clamp radius in (3) and then construct aformula similar to (3) for the shear stress. For the Newtonianfluid, such an equivalent radius R′′ satisfies the relation R′′ =(2DMnb/(πRμω))1/3, where μ is the liquid viscosity and Mnb
is the driving torque acting on the clamp when the shear rateis ωR/D and no slip occurs on the superhydrophobic surface.The updated formula for (3) is
τ = 2M/(πR′′3). (4)
Employing the definition of the equivalent radius, onecan consider easily the situation where certain fluid slipoccurs on the superhydrophobic surfaces. Generally, on a
2
J. Micromech. Microeng. 20 (2010) 115022 J Li et al
superhydrophobic surface with the slip length of b, the drivingtorque can be written as
M = πR′′3 · Rμ(ω − ω′)/(2D), (5)
where ω′ is the slip angular velocity of the liquid onsuperhydrophobic surfaces when the clamp rotates at theangular velocity of ω. According to (1), the slip angularvelocity satisfies the following relation:
ω′ = b(ω − ω′)/D. (6)
Combining (5) and (6), the formula of the slip length is asfollows:
b = πR′′3μD/(2M) · (ωR/D) − D. (7)
In this method, the equivalent radius is determined ina situation after the wetting transition of the liquid on thesuperhydrophobic surface from the Cassie state to the Wenzelstate due to the little change in the liquid border in thiscase compared to that in the Cassie state (before the wettingtransition). While it is easy to measure the fluid slip lengthon the superhydrophobic surface in the Wenzel state, theequivalent radius can be calculated by
R′′3 = 2MW(bW + D)/(πμD(dv/dz)W ), (8)
where MW is the driving torque in the Wenzel state, bW isthe fluid slip length on the test surface in the Wenzel state and(dv/dz)W is the shear rate. Finally, substituting this equivalentradius into (7), we obtain the slip length in the Cassie state asfollows:
b = (D + bW)(MW/(dv/dz)W )/(MC/(dv/dz)C) − D, (9)
where MC is the driving torque in the Cassie state at the shearrate of (dv/dz)C . In particular, for a surface with bW ≈ 0,this slip length in the Cassie state reads b = ((μaW/μaC)–1)D,where μaW and μaC are, respectively, the apparent viscositiesin the Wenzel and Cassie states.
3. Experimental section
3.1. Preparation of sample
The CNT forest on the surface was prepared by the chemicalvapor deposition (CVD) method. The Si 〈1 0 0〉 substrate witha square area of 22 × 22 mm was first rinsed using distilledwater and ethanol. The growth procedure for CNT forestwas as follows. (i) An ultra-thin ferrocene film (∼20 nm),which was used as a catalyzer for CNT growth, was sputtercoated on the substrate by using JGP560C VI. In this process,the pressure of the vacuum condition was 9.0 × 10−5 Pa, theflux of Ar was 40 sccm and the power was 100 W. Then thesubstrate was introduced into a furnace (CVD(Z)-06/60/3,Risine, Hefei, China), and N2 was introduced into the furnaceto drive the air away. (ii) The substrate was heated up underthis condition at 10 ◦C min−1 until the temperature reached600 ◦C. (iii) The metal film was deoxidized by H2 whose fluxwas 100 sccm, and at the same time the substrate was heatedto 850 ◦C. (iv) CVD growth was performed by introducingacetylene vapor. The key point was that the catalyst wasnever exposed to air during atmospheric heating and nanotubegrowth processes.
Figure 3. SEM image for CNT forest.
3.2. Characterization of the surface morphology
The morphology of the surface was investigated by JXA-840A scanning electron microscopy (SEM) (JEOL Ltd, Tokyo,Japan), at an operating voltage of 20 kV. The apparent contactangle of a distilled water droplet on the CNT-coated surfacewas measured by using a 1 μL water droplet on a ContactAngle System (OCAH 200, Dataphysics Co., Germany).
3.3. Rheological experiment
The rheological experiment was carried out on a commercialrheological system (AR-G2, TA Instruments, USA) witha plate-and-plate configuration. The clamp used in theexperiment was a flat clamp with a diameter of 20 mm.The experimental process contained two steps: one stepwas the preparation of the system and another step was themeasurement of the driving torque and the angular velocity.In the preparation, the zero point of the clamp relative to thetest surface was determined first, and then the phase of theclamp was mapped three times in the precise mapping mode.In the measuring process, the 70 wt% glycerin solution wasinjected into the gap between the clamp and the test surfaceby an injector to make sure that the gap was about 700 μm,and then a series of driving torques were acted on the clampto obtain the given angular velocities of the clamp. In all ofthese processes, the temperature was kept at 20 ± 0.1 ◦C bya Peltier plate. All these measuring results were recorded bythe controlling computer.
4. Results and discussion
Figure 3 presents the morphology of the CNT-coated surfaceand the image of a water droplet resting on such a surface. It isclear that the diameter of a single CNT is tens of nanometers,and several CNTs are gathered together to form clusters withtypical scale of 1 μm. The contact angle of a water droplet onsuch a surface is 160 ± 2◦. According to the Cassie–Baxterrelation and the intrinsic contact angle of 84◦, the fractionof the CNTs to the whole apparent surface area is only 0.05.Theoretically, on such a surface, the fluid slip length is about1 μm [16, 17], which has also been verified by the μ-PIVmeasurement [10].
3
J. Micromech. Microeng. 20 (2010) 115022 J Li et al
50 60 70 80 90 10020
22
24
26
28
30
32
CNTs coated surface
smooth surfaceap
pa
ren
t vis
co
sity (
mP
a·s
)
shear rate (s-1)
50 60 70 80 90 1001.2
1.5
1.8
2.1
2.4
2.7
3.0 CNTs covered surface
smooth surface
appare
nt shea
r str
ess (
Pa)
shear rate (s-1)
(a) (b)
Figure 4. The apparent shear stresses and viscosities measured on the CNT-coated surface and a smooth surface. (a) The apparent shearstresses and (b) the apparent viscosities of the liquid.
50 60 70 80 90 100
-2
0
2
4
6
8
slip
len
gth
(µ
m)
shear rate (s-1)
Figure 5. The slip length calculated by the current method.
As mentioned above, the CNT-coated surface has largercontact angle for a water droplet, leading to the liquid edgeeffect or end effect in the rheological experiment [13]. Asstated, such an edge effect might induce a smaller apparentshear stress as well as apparent viscosity compared to thenormal case. We also observed such differences in the apparentshear stresses and the apparent viscosities measured on a CNT-coated superhydrophobic surface and a smooth hydrophobicsurface, as shown in figure 4. If all these differences are causedby the slippage effect on the superhydrophobic surface, thecalculated slip length would be much larger than the theoreticalone (∼1 μm), and reach to 100 μm.
Using this method, we calculated the experimental sliplength from the measured data in figure 4, as shown infigure 5. In the calculation, due to the wetting transition at
(a) (b)
Figure 6. The images of a test liquid droplet on the CNT-coated surface after the liquids experience the shear rates of (a) 10 s−1 and(b) 100 s−1.
a higher shear rate, the slip length in this stage was taken tobe zero [10]. Then the slip length in the Cassie state (at alower shear rate) is ∼6 μm, which is at the same scale as thetheoretical one. Therefore, the current method is suitable tomeasure the slip length on superhydrophobic surfaces similarto the CNT-coated surface.
The remaining issue is whether the wetting transitionoccurs in the experiment. To elucidate this issue, weinvestigate the contact state of the test liquid resting on thesuperhydrophobic surface after both rheological experimentsat a lower shear rate (10 s−1) and at a higher shear rate(100 s−1). The pictures as well as the side profiles of theliquid droplet in these both cases are shown in figure 6. Notethat both these liquid droplets are captured after they contractfrom a spreading state in the gap between the test surfaceand the clamp to a new steady state, i.e. the contact angles ofthe droplets in both panels are the receding contact angle. Itis clear that the contact angles of the liquid droplets on thesuperhydrophobic surface in different cases are different fromeach other, which indicates that a wetting transition occursfrom the Cassie state to the Wenzel state due to the larger shearrate. Such a wetting transition might be induced by the bendof CNTs when these CNTs are sheared by the test liquid, asshown in figure 7. It is widely known that most of the wettingtransitions of liquid on structured surfaces are due to the liquidinterface between structures advancing into these structures[18, 19]. In this experiment, the contact angle between eachCNT and the liquid interface will increase from θn to θs dueto the shear force from the liquid. Once θs is greater than theadvancing contact angle of the liquid on the smooth carbon
4
J. Micromech. Microeng. 20 (2010) 115022 J Li et al
(a) (b) (c)
Figure 7. The mechanism of the contact state transition of the test liquid on the CNT-coated surface. (a) The case where the liquid rests onthe surface steadily, (b) the case where the liquid flows, and (c) the case after the wetting transition.
material, the liquid will fill into the space between CNTs, i.e.the wetting transition occurs, as shown in figure 7(c).
To carry out this measurement, the wetting transitionphenomenon is a key process. In fact, such measurement canalso be used for other superhydrophobic surfaces on whichthe wetting state of the liquid is easily controlled by the waysproposed recently [20, 21].
5. Conclusion
In conclusion, a measuring method for the fluid slip lengthon superhydrophobic surfaces was proposed based on thewetting transition in the measuring course when the shearrate increases. It was verified by the experimental resultfor 70 wt% glycerin solution flow over CNT-coated surface.The remaining drawback of this method is that the wettingtransition is necessary, which can be realized by the methodsdescribed in the literature [20, 21].
Acknowledgments
This work was supported by the Key Research Foundation ofthe National Nature Science Foundation of China (grant no.50435030), a Foundation for the Author of National ExcellentDoctoral Dissertation of PR China. We would like to thank DrChunxia Wu for her helpful discussion.
References
[1] Chen D, Du W, Liu Y, Liu W, Kuznetsov A, Mendez F E,Philipson L H and Ismagilov R F 2008 The chemistrode: adroplet-based microfluidic device for stimulation andrecording with high temporal, spatial, and chemicalresolution Proc. Natl Acad. Sci. USA 105 16843–8
[2] Bouzigues C I, Tabeling P and Bocquet L 2008 Nanofluidics inthe Debye layer at hydrophilic and hydrophobic surfacesPhys. Rev. Lett. 101 114503
[3] Choi S and Chae J 2010 Methods of reducing non-specificadsorption in microfluidic biosensors J. Micromech.Microeng. 20 075015
[4] Watanabe K, Udagawa Y and Udagawa H 1999 Dragreduction of Newtonian fluid in a circular pipe with a highlywater-repellent wall J. Fluid Mech. 381 225–38
[5] Choi C-H, Ulmanella U, Kim J, Ho C-M and Kim C-J 2006Effective slip and friction reduction in nanogratedsuperhydrophobic microchannels Phys. Fluids 18 087105
[6] Ou J, Perot B and Rothstein J P 2004 Laminar drag reductionin microchannels using ultra-hydrophobic surfaces Phys.Fluids 16 4635–43
[7] Ou J and Rothstein J P 2005 Direct velocity measurements ofthe flow past drag-reducing ultra-hydrophobic surfacesPhys. Fluids 17 103606
[8] Gogte S, Vorobieff P, Truesdell R, Mammoli A, van Swol F,Shah P and Brinker C J 2005 Effective slip on texturedsuperhydrophobic surfaces Phys. Fluids 17 051701
[9] Byun D, Saputra and Park H C 2006 Drag reduction onmicro-structured superhydrophobic surface 2006IEEE Int.Conf. Robotics and Biomimetics pp 818–23
[10] Joseph P, Cottin-Bizonne C, Benoıt J-M, Ybert C, Journet C,Tabeling P and Bocquet L 2006 Slippage of water pastsuperhydrophobic carbon nanotube forests inmicrochannels Phys. Rev. Lett. 97 156104
[11] Choi C-H and Kim C-J 2006 Large slip of aqueous liquid flowover a nanoengineered super-hydrophobic surface Phys.Rev. Lett. 96 066001
[12] Lee C, Choi C-H and Kim C-J 2008 Structured surfaces for agiant liquid slip Phys. Rev. Lett. 101 064501
[13] Bocquet L, Tabeling P and Manneville S 2006 Comment on‘large slip of aqueous liquid flow over a nanoengineeredsuperhydrophobic surface’ Phys. Rev. Lett. 97 109601
[14] Choi C H and Kim C J 2006 Choi and Kim reply Phys. Rev.Lett. 97 109602
[15] Navier C L M H 1823 Memoire sur les lois du mouvement desfluides Mem. Acad. Roy. Sci. 6 389–440
[16] Philip J R 1972 Integral properties of flows satisfying mixedno-slip and no-shear conditions J. Appl. Math. Phys.23 960–8
[17] Lauga E and Stone H A 2003 Effective slip in pressure-drivenStokes flow J. Fluid Mech. 489 55–77
[18] Yu Y, Zhao Z H and Zheng Q S 2007 Mechanical andsuperhydrophobic stabilities of two-scale surfacial structureof lotus leaves Langmuir 23 8212–6
[19] Liu B and Lange F F 2006 Pressure induced transitionbetween superhydrophobic states: configuration diagramsand effect of surface feature size J. Colloid Interface Sci.298 899–909
[20] Dorrer C and Ruhe J 2007 Condensation and wettingtransitions on microstructured ultrahydrophobic surfacesLangmuir 23 3820–4
[21] Krupenkin T N, Taylor J A, Wang E N, Kolodner P, Hodes Mand Salamon T R 2007 Reversible wetting–dewettingtransitions on electrically tunable superhydrophobicnanostructured surfaces Langmuir 23 9128–33
