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No-loss transportation of water droplets by patterning a desired hydrophobic path on a superhydrophobic surface Haibao Hu, Sixiao Yu, and Dong Song Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b01654 • Publication Date (Web): 30 Jun 2016 Downloaded from http://pubs.acs.org on July 5, 2016
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NoNo-loss Transportation of Water Droplets by Patterning a Desired esired Hydrophobic Path on a Superhydrophobic Surface Haibao Hu*, Sixiao Yu and Dong Song* School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, People’s Republic of China Supporting Information
ABSTRACT：The directional transportation of droplet on solid surfaces is essential in a wide range of engineering applications. It is convenient to guide liquid droplets in a given direction utilizing the gradient of wettability, by which the binding forces can be produced. Compared with the mass-loss transportation of a droplet moving along hydrophilic paths on the horizontal superhydrophobic surface, we present no-loss transportation by fabricating a hydrophobic path on the same surface under the tangential wind. Through experimental exploration and theoretical analysis, the conditions of no-loss transportation of a droplet are mainly considered. We demonstrate that the lower (or upper) critical wind velocity, under which the droplet will start up on the path (or derail from the path) is determined by the width of the path, the length of the contact area in the direction parallel to the path, the drift angle between the path and wind direction as well as surface wettability of the pattern. Meanwhile, the no-loss transportation of water droplets along the desired path zigzagging on a superhydrophobic surface can be achieved steadily under an appropriate condition. We anticipate that such robust no-loss transportation will find an extensive range of applications.
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1. INTRODUCTION Droplet movement on solid surfaces is very prevalent in daily life and has been paid extensively attentions for their important scientific value and numerous industrial applications in many fields, such as self-cleaning1-2, anti-icing3-5, microfluidics6-7, and droplet manipulation8-9. A varied range of experiments have confirmed that the droplets moving on solid walls can originate variant behaviors including vibration, slipping, creeping and rolling, depending on both the droplet itself and physiochemical properties of the external fields. In essence, the movement and deformation of droplets are predominated by the pinning location, viscous and inertial stresses, interfacial tensions, and gravity, etc, which are always in a state of approximate balancing10-20. In particular, the study on the manipulation of droplets in a designed direction becomes particularly enriched owing to its immense importance in micro electromechanical systems, lab-on-a-chip architectures, water management systems, etc. The popular methods of controlling droplet are to exert manipulative forces on the droplet by manipulating the external forces such as magnetic fields, electric fields, heat gradients and vibration21-27. Nguyen et al.24 successfully manipulated the ferrofluid droplet in the magnetic field fulfilled by two pairs of planar coil. Roux et al.27 controlled a conducting droplet in the three-dimensional space by the effect of electrostatic actuation. On another research line, many researchers found that micro and nano structures with non-uniform chemical composition on a solid surface would create unique wetting anisotropy phenomena, including contact angle hysteresis and other intriguing dynamics scenarios of droplets28-33. And some fantastic progress of droplet manipulation using wetting anisotropy has been reported, such as controlling the impinging droplet to rebound and splash8, spreading a droplet to form an intended film10, cutting a droplet in a precise proportion34. Meanwhile，a potential method of transporting droplets35, 36 is provided due to the binding force produced by the gradient of wettability. Recent reports have described that the transportation of liquid droplets in a given direction is feasible through utilizing wetting anisotropy. Suzuki et al.37 revealed that the droplets can be selected according to the volume differences by setting the surface rotating
in-plane
on
the
sloping
fluoroalkylsilane
(FAS17)
surface
periodically
line-patterned
with
octadecyltrimethoxysilane (ODS). Xu et al.38 and Yang et al.39 demonstrated that a water droplet could be directed
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exactly along a hydrophilic line on the superhydrophobic surface on an inclined surface. To guide droplets, Seo et al.40 converted superhydrophobic
Si nanowire
arrays
to
hydrophilic
patterns
using a
UV-enhanced
method
photodecomposition of the dodecyltrichlorosilane (DTS), and such method is reproducible on the same surface. Similar guidance behavior was attained by fixing a line-patterned groove on a hydrophobic surface by Sommers et al.41 Compared with the methods mentioned in the first paragraph, droplet transporting on solid surfaces by wetting anisotropy is without an additional controlling equipment, and is of potential importance in many industrial applications such as water drainage in the proton exchange membrane fuel cells (PEMFCs)42-44. Despite significant progress on the fabrication of wetting anisotropy and the validation of control, it remains elusive that how and to what extent the wetting anisotropy can modulate the transporting behavior of droplets. In this work, we performed a series of droplet-transportation experiments on superhydrophobic surfaces with hydrophobic and hydrophilic paths in a wind tunnel, and presented a no-loss transportation regime. To explore such transportation quantitatively, the wind velocity range, driving droplets to accomplish the no-loss transportation along the paths, was characterized by the lower (or upper) critical wind velocity for the droplet to start to move along or derail off the path. The critical velocity is correlated to the width of the path, the length of the contact area in the direction parallel to the path as well as the drift angle between the path and the wind direction, which was analyzed theoretically. Meanwhile, the theoretical analyses concerned with the transporting behaviors of droplets has been deduced to explain the intricate interplay between W, L, α and wetting anisotropy. The predictions are in accordance with the experimental results.
2. EXPERIMENTAL SECTION: SECTION: Fabrication and Characterization of the Tested Substrates. We prepared three types of paths with different wettability on glass slides of 25 mm wide, 75 mm long and 1 mm thick. The first path is a pure hydrophilic glass slide without any treatment except being cleaned by absolute ethyl alcohol, with the advancing and receding contact angle being 82° and 20°, respectively. The second one was made by a clean commercial Polyethyleneterephthalate (PET) foil with the advancing and receding contact angle being 94° and 32°, separately. The third path was fabricated by
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polydimethylsiloxane (PDMS, Sylgard 184, Dow Corning) with the advancing and receding contact angle being 110° and 64°, separately. To make a PDMS surface, the pre-polymer PDMS with curing agent (10:1weight ratio) was de-aired in vacuum for 15 minutes, and cast onto a glass slide to form a film with thickness ~1mm. the liquid PDMS was then cured at 60℃ for 2 hours. Fabrication of the hydrophobic hydrophobic / hydrophilic paths on the superhydrophobic coat. In order to introduce
hydrophobic (or hydrophilic) paths with gradient wettability on the samples, a commercial superhydrophobic coating, Ultra-Ever Dry (from Ultra Tech International), was sprayed on these substrates, using shadow mask method, which has been described detailedly in our previous publication45. Firstly, the shadow mask with patterns was pressed tightly on the substrate. Then, the superhydrophobic coating was sprayed on the substrate. After the solidification of 30 minutes, the shadow mask was peeled off, and the hydrophobic (or hydrophilic) paths were finally introduced on the superhydrophobic coat with the thickness of ~20 µm. The roughnesses of the paths are less than 5nm, and that of the superhydrophobic region outside the path is 2.6 µm, with random micro and nano structures on it. The images of the sample on the PDMS substrate under a scanning electron microscope (SEM) are shown in figure 1.
Figure 1 The images of (a) the superhydrophobic region and (b) a tested path made of PDMS as well as (c) a boundary of the path under a SEM. The tested PDMS substrates have a low roughness less than 5 nm, which is as similar as other substrates, whereas the roughness of the superhydrophobic area is 2.6 µm. The height of the superhydrophobic coat is ~20 µm.
Test of Transportation Transportation of Water Droplets. The movements of water droplets along these as-prepared paths were
measured in a wind tunnel, with velocity in the range of 1.83 m/s and 18.27 m/s. The two statuses when the droplet started to move and derail off the path were recorded by a high speed camera (MotionXtra NX-4, IDT Corporation) with 600×600 pixels at 500 fps. Deionized water droplets were used in the experiment, with the density, surface tension, and viscosity being 996 kg/m3, 0.073 N/m, and 0.001 Pa·s, respectively.
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Langmuir 3. RESULTS AND DISCUSSION Figure 2 shows the movements of droplets transported on three horizontal paths with different wettability under tangential wind captured by the high speed camera. The width of the path is 0.4 mm, and the corresponding wind velocities (Vwind) from figure 2a to figure 2c are 5.96 m/s, 3.82 m/s and 2.78 m/s, respectively. We name the movements in figure 2a-b as mass-loss transportation, because wherever it goes, some water stain remains on the path. In figure 2a, the tail is connective and very thin. However, on the hydrophilic path shown in figure 2b, the tail is split into several fragments and the loss of fluid is reduced compared with the one in the figure 2a. Different from the first two pictures, the motion in figure 2c is perfect no-loss transportation without leaving any fluid behind, when a droplet is guided by the PDMS path. This no-loss transportation regime is of relevance to many emerging applications such as lab-on-a-chip architectures, anti-icing, etc.
Figure 2 Droplet transportation on paths with different wettability. (a) and (b) are the mass-loss transportation directed by the hydrophilic path (glass and PET, respectively). (c) is the no-loss transport directed by the hydrophobic path (PDMS). All the droplets are 20µL. All the paths are 0.4mm. The wind velocities are 5.96 m/s, 3.82 m/s, 2.78m/s, respectively. Scale bar is 2.0 mm.
The mass-loss transportation regime is able to be converted to the no-loss transportation by increasing the hydrophobicity of the path region. However, the velocity of the wind driving the droplet will decrease with increasing the hydrophobicity of the path, which means the resistance applied on the droplet by the path will decrease simultaneously. The restraint in the perpendicular direction of path exerted by the reduction of wettability gradient at the boundary of path, suggests that the droplet transport along the intended hydrophobic path is more difficult than that along a hydrophilic one. Thus, no-loss transportation of water droplets by patterning a designed hydrophobic path on a superhydrophobic surface may be hard to accomplish.
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The stable stable nono-loss transportation. transportation. The experimental phenomena are extremely different from the conventional assumptions. We found that under proper conditions, a droplet moving on the path exhibits a stable directing transportation with no water left behind. Figure 3a shows certain snapshots of a 30 µL droplet moving along the sinusoidal PDMS path (width W = 0.3mm) under wind velocity = 2.72 m/s (Supporting Information, Movie 1). The droplet would not move until was over 2.00 m/s. When the wind velocity increased to = 2.72 m/s, the droplet began to move sluggishly, and constantly adjusted its velocity to accommodate the ever-changing path with a maximum velocity of 0.012 m/s at ~15.5 s. In particular, the droplet would always approach to the downwind side of the path during the whole process as shown in figure 3a. It should be noted that the transportation could accomplished only within a special wind velocity range. When the wind velocity increased to 7.2 m/s as shown in figure 3b, the droplet would be blown off the path during the transportation because the constraint of the path on it was not strong enough (Supporting Information, Movie 2). The derail position of the droplet in figure 3 located at the point with maximum drift angle at the time of 4.25 s.
Figure 3 Single droplet moves along the sinusoidal PDMS path with different wind speeds. The stable no-loss transportation (a) and the transportation with derailment (b) of the droplet are fulfilled on the hydrophobic path (PDMS) on the superhydrophobic coat. The time of every snapshot is listed out. The wind velocities in (a) and (b) are 2.72 m/s and 7.64 m/s, separately. The volume of the droplet is 30µl. The droplet has been dyed in red for visualization. The two pictures are mosaic merging individual photos selected from the droplet-transportation video (Supporting Information, Movie 1 and Movie 2). Scale bar is 5 mm.
The upper upper (or lower) lower) critical wind velocity. velocity. In order to explore the ability of droplet transportation via hydrophobic path, the critical wind velocity under which the droplet start to move (named the lower critical wind velocity,
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) and the other critical wind velocity over which the droplet derails off the path (named the upper critical wind
velocity,
) were measured in the wind tunnel. A series of droplet transportations on straight paths with different width (W) and drift angles (α, the included angle between the path and the wind direction) were conducted. Different droplets with volume of 15 µL, 30 µL and 50 µL were tested on the PDMS paths with four different width (W = 0.38 mm, 0.72 mm, 1.06 mm and 1.36 mm) and five drift angles (α = 30°, 40°, 50°, 70°, 80°). Each measurement was repeated at least 10 times.
(a) Figure 4
(b)
The lower and upper critical wind velocities under (a)different widths of paths with a fixed angle of 50°and (b) different
drift angles α with a fixed width of 0.72 mm. The solid symbols () represent the lower critical wind velocity ( ), and the hollow symbols () represent the upper critical wind velocity (
). Each point is the average of at least 10 tests.
Figure 4a plots the variation of upper and lower critical wind velocities as a function of path width (W) under a fixed drift angle α = 50°. As shown by the solid symbols in figure 4a, increases with path width (W), as larger resistance is applied on the droplet on a wider path. However, the wider the path is, the stronger the constraint on the droplet will be, resulting in a larger driving force having to be appiled on the droplet and
increasing at the same time as shown by the hollow symbols in figure 4a. For example, the of a 30 µL droplet on the path with W = 0.38 mm and 1.36 mm are 4.39 m/s and 6.67 m/s, respectively, while
under the same condition are 7.22 m/s and 12.34 m/s, respectively. And the velocity range ( ~
) decreases when the width of the path becomes narrow, which indicates that the droplet cannot be transported if the width is too slender under such fixed angle. Meanwhile, a bigger droplet requires a smaller lower critical wind velocity, indicating that the larger droplet is easier to be directed, but it is
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also vulnerable to derail off the path. Figure 4b shows the upper and lower critical wind velocity changes as a function of the drift angle α with a fixed path width W = 0.72 mm. As α increases, increases more and more rapidly while the upper critical wind velocity (
) decreases inconspicuously, which indicates a larger drift angle makes a droplet harder to start up but easier to be blown off the path. Meanwhile, the wind velocity range ( ~
) of no-loss transportation is extended when the droplet becomes smaller. It is noteworthy that even the drift angle reaching as high as 80°, the 15 µL droplet could still be transported successfully. Theoretical analysis. analysis. A mechanical analysis has been conducted to elucidate the mechanism of the droplet
transportation. Figure 5 is the simplified diagram of a droplet moving along the hydrophobic path surrounded by the superhydrophobic surface. As shown in figure 5a, the droplet is constraint within the path area and there should be no contact between the droplets and superhydrophobic surface. The driving force, , is exerted by the tangential wind, and the droplet is hindered by the surface tensions of the three-phase contact line at the hydrophobic path area ( and in the tangential direction of the path, and in the normal direction of the path). In this analysis, the velocity of the droplet moving forward and the viscous resistance within the droplet are neglected as the droplet moving velocity is much smaller than the wind velocity according to our experiments. For example, the maximum velocity of the droplet in figure 3b is 0.038 m/s, while the corresponding wind velocity is 7.64 m/s. When the droplet starts to move along the hydrophobic path, its contact angle at the head area reaches the advancing contact angle ( ) while the one at the tail area reaching the receding contact angle ( ). Here, and are the contact angle on a plain surface made by the same material of the path. The hindering force can be estimated as − = γWcos − cos , where γ and W are the air-water surface tension and the width of the path, separately. The component of the driving force along the path direction is ∙ cos . To drive the droplet to move forward, it should satisfy cos ≥ !cos − cos
(1)
Here, approximates to ~#$ according to the previous research 46, 47，where R, µ and are the droplet
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radius, water dynamic viscosity coefficient and wind velocity, separately. Thus, the is explained as
= % ∙ &' ( ∙
)&' *+ ,&' *- .
(2)
Here, k is the proportionality coefficient. It should be noted that equation (1) and (2) are not applicable to the one on the hydrophilic path, because the three-phase contact line at the tail sticks to the surface without moving forward with the droplet as shown in figure 2a-b.
Figure 5 Droplet on the hydrophobic path. (a) is the front view of a droplet on the hydrophobic path. (b) is the schematic diagram of the forces on the droplet moving along the hydrophobic path. In (b), the gray area represents the superhydrophobic region and the narrow stripe between the shadow areas is the hydrophobic path region; the red area in the path is the contact area of the droplet on the path and the circle area represents the droplet. is the resultant driving force generated by the tangential wind; and are the surface tension generated by the three-phase contact line at the path area. and correspond to the surface tension generated by the three-phase contact line at the superhydrophobic area in the direction perpendicular to the path, which constraints the droplet within the path as moving forward. α is the drift angle between the direction of the wind and the path.
The droplet will be blown off the path if the wind velocity is too high. Considering the critical state of the droplet running off the path, the equilibrium relationship should be = / 012 and = / 012 ∗ , where ∗ is the same as the advancing contact angle on the superhydrophobic surface; L is the length of the contact area in the direction parallel to the path as shown in figure 5. So the maximum of the constraint force vertical to the path is expressed as − 4 5 = / cos − 012 ∗ . Because the component of the driving force in the normal direction of the path is ∙ sin ~#$ sin ,
can be calculated as
= % ∙ '89 ( ∙
∗ )&' *+ ,&' *-
.
(3)
Figure 6a-b respectively plots the relationship between and W, and cos , to demonstrate the validity of equation (2). Figure 6a shows the lower critical wind velocity ( ) is proportional to the width of the path (W) for each droplet which is in good agreement of equation (2) ( ~ W). It is the hindering force of the droplet ( − )
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generated by the three-phase contact line, which is proportional to the width of the path, that results in increasing linearly with increasing path width. Meanwhile, decreases with increasing the droplet volume, which can also be indicated from equation (2) ( ~ 1/R). So a larger droplet is much easier to be driven by the wind. As shown in Figure 6b, decreases with cos in an inversely proportional trend ( ~ cos ), which is in good agreement with equation (2) according to the fitted line. The component of the driving force in the path direction ( ∙ cos ) decreases with α increasing, so the droplet is harder to move. To demonstrate the validity of equation (3), figure 6c-d respectively plots the relationship between
and L,
and sin α. In figure 6c, the length of L was obtained from the side view of the moving droplet. Because L was not able to be changed directly, it was altered via adjusting the width of the path by keeping the droplet volume constraint. It shows proportional relationship between
and L on the path, which is in good agreement of equation (3) (
~ L). For the same droplet, the value of L increases accordingly with the increase of W, resulting in the hinder force − 4 5 = / cos − 012 ∗ being much stronger, so the droplet is much harder to run off the path. Similarly,
decreases with increasing the droplet volume, which is also inferred from equation (3) (
~ 1/R). So a larger droplet is easier to be blown off by the wind. In figure 6d, the relationship between the upper critical wind velocity (
) and the drift angle (α) follow the scaling law
~ 1/sin α, which is consistent with equation (3). For the same droplet, as the drifting angle α increases, the component of the driving force normal to the path ( ∙ sin ) grows accordingly, thus the droplet is easier to be blown off the path. It can be seen from equation (2) and (3) that,
and are also determined by the advancing and the receding contact angles of the hydrophobic path. In order to reduce and make the droplet easier to be driven forward, the contact angle hysteresis at the path area should be as small as possible. On the other hand, the advancing angle at the superhydrophobic surface should be much bigger than the receding angle at the path area to enlarge
as much as possible, making the droplet harder to be blown off the path. Nevertheless, the wettability of the path achieving the transportation without mass loss still needs more study due to the complexity of the wettability and the boundary conditions on the anisotropic surfaces.
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(a)
(b)
(c)
(d)
Figure 6 The critical wind velocities changes with W, L and α. (a) is changing with path width (W) where the solid lines fitted the data linearly. (b) is changing with cos where the solid lines are fitted using equation: ~ 1/cos . (c) is ;
