Directional Transport Behavior of Droplets on Wedge-Shaped

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Directional Transport Behavior of Droplets on Wedge-Shaped Functional Surfaces Ming Liu, Yin Yao, Yazheng Yang, Zhilong Peng, and Shaohua Chen J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b00641 • Publication Date (Web): 26 Apr 2019 Downloaded from http://pubs.acs.org on April 26, 2019

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The Journal of Physical Chemistry

Directional Transport Behavior of Droplets on Wedge-Shaped Functional Surfaces Ming Liu1, 2, Yin Yao1, 2, Yazheng Yang1, 2, Zhilong Peng1, 2, *, Shaohua Chen1, 2, ** 1

Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing, 100081,

China 2

Beijing Key Laboratory of Lightweight Multi-functional Composite Materials and Structures,

Beijing Institute of Technology, Beijing 100081, China

Abstract Functional surfaces attract considerable research interests due to many practical applications. Wedge-shaped functional surface is a typical example, which can be designed to achieve self-cleaning, water collection, heat dissipation or separation of mixed droplets, depending on the wettability of wedge-shaped areas inset in a hydrophobic substrate surface. In this work, a simple technology is proposed to achieve a wedge-shaped functional surface, which could realize directional transport of droplets. It is found that the transport behavior of droplets depends significantly on the wedge angle, the static contact angle of wedge-shaped hydrophilic region and the droplet volume. An approximate theoretical model is established, which can predict the most important parameter, i.e., the transport displacement. The theoretical prediction can be verified experimentally. Furthermore, an interesting phenomenon of multi-step acceleration is also observed in the transport process. With the aid of the present simple technology, several functional surfaces for directional transport of droplets can be well designed, including root-like patterned surfaces and non-linearly spiral or curve patterned surfaces. All the results should be helpful for flexible design 1

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of functional surfaces for droplet transport in micro-fluidics or lab-on-a-chip applications.

2


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1. Introduction Micro-fluid devices involve complex liquid-handling tasks, including liquid transport, pinning, separation, coalescence and micro-chemical reactors, all of which are related to the moving or spreading behavior of droplets from one place to another. The initial study of liquid transport was focused on theoretical research and the wettability gradient of surfaces was assumed to increase linearly along the direction of motion. The mechanism of a moving droplet on a wettability gradient surface was first identified by Greenspan 1. Motivated by cell spreading and based on the molecular kinetic theory, Greenspan 1 established a moving model of contact lines to analyze the motion of droplets. Brochard 2 restricted their discussion to the isothermal case and assumed that the droplet shape influenced by gravity was negligible. Subramanian et al.

3

achieved the driving force acting on a spherical-cap droplet

moving on a wettability gradient surface and predicted the moving velocity of droplets approximately. However, the spherical assumption is far from the truth and the linearly varying wettability gradient of substrate surface is difficult to achieve. In order to approximate the gradient wettability, multiple regions with different wettability were required

4-5,

which are actually difficult to precisely control in

practical engineering applications. Recently, solid wettability gradient surfaces can be well fabricated by chemical patterning 6-8, physical texturing 9-11, or a composite interface of both 12. To avoid the complex process of preparing surfaces with gradually varying wettability, Khoo and Tseng

13

presented a chemically patterned nanotextured surface with wedge-shaped 3



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gradient, which only contains two types of wettability on different regions. In order to study the moving velocity in experiments, they also assumed that the footprint of a droplet was a circle with a trailing edge and a second order nonlinear ordinary differential equation was derived by considering the interaction between the driving force (Fcapillary) and resistant forces (Fviscous+Fhsyteresis+Ffriction+Fsurface tension), in which a conclusion is that the spontaneous directional motion of droplets was controlled by both the surface tension gradient and nanowetting actuation. Afterwards, Alheshibri et al.

14

reported a technique to transport liquid on a planar, wedge-shaped hydrophilic

aluminum surface inset in a hydrophobic copper surface. Under the interaction of various forces, such as net surface tension force, contact angle hysteresis, pinning force, they found that droplets would spread on the aluminum surface area and move towards the end of the wedge. Ghosh et al. 7 successfully extended the wedge-shaped gradient surface from metal materials to other materials. The aqueous suspension of TiO2 nanoparticles and fluoroacrylic copolymer dispersion (PMC) was sprayed on different substrates, e.g., metals, polymers, paper, to form a superhydrophobic surface with microstructures, and the UV treatment of the superhydrophobic substrate through a patterned photo mask was used to form superhydrophilic regions. It was found that droplets could move along the wedge-shaped gradient surface with its tail pinned to the two straight hypotenuses, during which the morphology of the main part of the moving droplet is approximated as an ellipsoid and the whole thing is shaped like a tadpole. The lateral pinning contact lines and the tadpole shape result in a larger contact angle at the 4


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leading edge and a smaller contact angle at the trailing edge of the droplet. Therefore, the contact angle of the liquid bulge does not follow the Young’s equation. To evaluate the capillary force, a priori knowledge of the varying average contact angles along the axial displacement computed by Brinkmann 15 was critical. Morrissette et al 16

further studied the transport and mixing of self-driven liquids on an open surface

micro-fluidic platform with a similar preparing method to Ghosh et al. 7. So far, subsequent studies of liquid transport on wettability patterned surfaces 17-19 have shown that functional surfaces transporting liquids efficiently cannot be achieved without complex modifications, for example, microstructures on the base surface. On the other hand, in order to predict the transport displacement or velocity of droplets theoretically, most studies focused on various forces acting on droplets 3, 7, 14, 19,

especially the surface tension and capillary force. However, a rapid prediction of

transport displacement or velocity of droplets cannot be carried out without values of several parameters, such as the interfacial tension, friction coefficient, etc., even an empirically correction factor. A straightforward functional surface possessing spontaneously directional droplet transport features and a theoretical prediction of transport displacement and velocity without many measured parameters should be more favorable. Motivated by the aim mentioned above, the present work uses a simple, wettability-patterned method to produce an open, wedge-shaped functional surface without microstructures by patterning a hydrophilic region on a hydrophobic photopolymer substrate, which is a relatively simple technology and can induce 5



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droplets to spread from one place to anywhere requiring. Based on the principle of mass conservation, a theory model is developed. The theoretically predicted transport displacement of droplets is well compared with experimental measurements. An interesting multi-step acceleration phenomenon is also found experimentally. Several functional

surfaces

can

be

further

desingned

based

on

the

present

wettability-patterned technology. The present design of functional surfaces and results would be attractive for many practical applications involving rapid chip cooling

20,

biotechnology 21-23 or water management in fuel cells 24.

2. Experimental Section The SOMOS Imagine 8000 of photopolymer, as a base material, is adopted in the present experiment, which can be achieved by 3D printing technology. A square photopolymer plate is shown in Figure 1a with a width of 40 mm. Then, the photopolymer is cleaned several minutes by consecutive ultrasonication in absolute ethyl alcohol and dried in N2. Afterwards, to exhibit the hydrophilicity, one side of the photopolymer is exposed to downstream oxygen plasma for 10 s with about 10 mA current intensity and 4 to 6 Pa pressure, on which it has been found to be easier to form hydrophobic chemical groups after treated by fluoride

25-26.

After

exposing the hydrophilic surface to 1H, 1H, 2H, 2H-Perfluorodecyltrichlorosilane for 6h in vacuum, a perfluorinated coating surface is formed, which is hydrophobic and could reduce contact angle hysteresis 19, 26. For a flat surface of photopolymer without microstructures/nanostructures, it is found in our experiment that the silanized time is at least 6 h to achieve a maximum contact angle and a longer time does not change the 6


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contact angle and contact angle hysteresis any longer, but a shorter time would lead to a smaller contact angle and a larger contact angle hysteresis. Based on the treated hydrophobic surface, an open wedge-shaped functional surface can be produced with the aid of a photopolymer patterned mask prepared by 3D printing technology as shown in Figure 1b, which is made of several wedges with different wedge angles. Covering the photopolymer patterned mask on the treated hydrophobic surface and then exposing the whole surface to oxygen plasma for different durations but with the same current intensity 10 mA and pressure 4 to 6 Pa as before, the uncovered hydrophobic parts of substrate surfaces become wedge-shaped hydrophilic regions and the contact angle of hydrophilic regions depends on the exposure time. Based on such a simple technique, other functional surfaces can also be made using different patterned masks. The schematic of experimental setup for spontaneous droplet transport is shown in Figure 2, where a high speed video acquisition system, a water drop delivery system and a wedge-shaped functional surface, as major apparatuses, are involved. A water droplet is squeezed out from a syringe of the contact angle analyzer (OCA25, Data physics, German) at the ambient temperature, which is initially suspended from the needle. As the syringe goes down slowly, the droplet is deposited at the tip of the wedge-shaped hydrophilic area. Afterwards, the droplet will tend to leave the tip and spread towards the end of the wedge-shaped hydrophilic area due to the unbalanced force. The whole process is recorded by a high-speed camera (VW9000, Keyence, Japan) at 1000 frames per second, which is placed on a stand with the lens downward 7



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as shown in Figure 2.

3. Results and Discussion 3.1 Transport behavior of droplets on wedge-shaped functional surfaces. The wettability of the silanized surface is measured firstly. The contact angle is about 126.1o for a distilled water droplet as shown in Figure 3 (a), which demonstrates a hydrophobic feature. In the oxygen plasma treated region, the contact angle is about 30.5o as shown in Figure 3(b), which is hydrophilic. The present wedge-shaped functional surface is essentially made of hydrophobic silanized area inserted by wedge-shaped oxygen plasma treated regions. During the droplet transport experiment, the distilled water is dyed brown for more precise observation and analysis. It is verified that the dyed distilled water possesses almost the same contact angle as the pure one on the same surface (see Figure S1). Furthermore, both the advancing and receding contact angle depicting the dynamic feature of a moving droplet have also been measured experimentally. A 5μl deionized water droplet is injected into the 10μl pre-droplet on the surface with a velocity of 1 μl/s and then the droplet is sucked back with the same velocity. The advancing and receding contact angles are obtained by analyzing the dynamic contact angles. The contact angle hysteresis can be achieved from the difference between the advancing and receding contact angles. All results are given in Table S1 in Supporting Information, in which three kinds of surfaces with different wettability are involved, i.e., the original photopolymer, the silanized area and the oxygen plasma treated region. From Table S1 in Supporting Information, it can be found that the contact angle of photopolymer is 97.6o, representing 8


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hydrophobic. However, the contact angle hysteresis of photopolymer is about 25.6o, which is not conducive to the motion of droplets. Moreover, the larger the contact angle of the hydrophobic region, the larger the unbalanced capillary force would be for droplets on the wedge-shaped functional surface consisting of hydrophobic and hydrophilic zones 3, 14. Therefore, the surface of photopolymer needs to be modified to achieve a larger contact angle and a smaller contact angle hysteresis, both of which favor droplet transport. The present functional surface has a small contact angle hysteresis on the silanized hydrophobic area and an intermediate contact angle hysteresis on the hydrophilic area as shown in Table S1. As for the wettability of different regions of the functional surface changing with aging 27, the result is shown in Figure S2 in Supporting Information. It is found that the wettability stability of hydrophilic region is maintained for about 2 days and then the contact angle degrades from 30.5o to about 97.6o of the original photopolymer, instead of 126o of the silanized hydrophobic surface. It is because the ultraviolet light in oxygen plasma causes surface silanization to fail. However, if we expose the degraded surface to oxygen plasma for 100s again, which will immediately revert to hydrophilic as shown in the cycle curve in Figure S2a. The same thing happens for the contact angle hysteresis and the advancing/receding contact angle of the hydrophilic region as shown in Figures S2b and S2c, respectively. In general, two-day stability of the present sample seems adequate for some biological or micro-nano engineering applications, such as drugs delivery in clinical operations. We are also looking for ways to prepare surfaces with a longer stable time. Different from the two-day 9



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stability of hydrophilic region, the hydrophobic wettability of the silanized region remains stable for at least 5 days of measurement as shown in Figure S2 in Supporting Information. When a droplet is deposited at the hydrophilic wedge tip on the gradient functional surface, the droplet would be driven by the unbalanced capillary force 3, 14, 28-29, which drags the droplet to transport along the wedge-shaped hydrophilic orbit from the tip to the backend. Moreover, due to the low contact angle hysteresis of the hydrophobic region shown in Table S1, the part of droplets in the hydrophobic region would also be driven to the hydrophilic track without residual. Snapshots of a 15μl colored water droplet transporting on a wedge-shaped functional surface with a 10o hydrophilic wedge angle are shown in Figures 4(a)-4(f). A ruler is used to estimate the transport displacement and the transport time is also recorded for each snapshot. One should be noted that the tip of the syringe needle is not exactly at the zero position as shown in Figure 4(f), because the center of droplets hung on the syringe needle should coincide with the tip of hydrophilic wedge area. A previous study by Brinkmann and Lipowsky

15

studied the final behavior of a

static droplet on a rectangular superhydrophilic orbit inset in a superhydrophobic substrate surface. They found that the final shape of droplets depends on the ratio V/L3, where V denotes the liquid volume and L denotes the orbital width. For the case with a small value of V/L3, the static liquid was considered as a semi-cylindrical shape, which is different from the present configuration on a wedge-shaped orbit as shown in Figures 4(a)-4(f). It shows that, during the transport process, a rapidly advancing film 10


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leaves the hydrophilic wedge tip and moves towards its backend, while the main part of droplets stays at the initial location, forming a dumbbell shape. However, if the wedge angle of the hydrophilic area is relatively large, for example, 30o, the dumbbell shaped droplet during transport cannot be found as shown in Figure 5, which is due to a relatively large resultant dragging force induced by the large wedge angle. As a result, it leads to a rapid transport process and a rapid speed. Of course, the final configuration keeps a stable combined-shape of partial cone and partial sphere as shown in Figure 4(f) and Figure 5(f), no matter what the wedge angle is. Such a wedge-shape influenced phenomenon was actually mentioned by Alheshibri et al. 14, but without any practical example and explanation. From Figures 4 and 5, it is easy to find that the final transport displacement and the instant velocity should be significantly influenced by the wedge angle of the hydrophilic area, the phenomenon of which is analyzed in details in the following text. 3.2 The final transport displacement. The final displacement of droplets transporting on such a functional surface is an important concerned parameter. The final configuration of droplets can be approximated as a combination of partial cone and partial sphere as shown in Figure 4(f) and Figure 5(f). An approximate mathematical model for the final configuration of droplets on the wedge-shaped hydrophilic area is exhibited in Figure 6, where x denotes the transport direction, θ denotes the wedge angle, x1 denotes the length of partial cone, lAB (=2l) denotes the width of interface between the partial cone and the partial sphere, x2 (= l) denotes the 11



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bottom radius of spherical crown. The final transport displacement xf equals x1+x2. A circle of radius R is used to calibrate the contour of the interface between the partial cone and the partial sphere at x= x1 as shown in Figure 6(b). The geometrical relationship among the contact angle α on the hydrophilic region, the height of interface h, and the half-width of interface l can be easily found. In addition, the effect of droplet gravity on the contact angle is concerned experimentally as shown in Figure S3 in Supporting Information, where the contact angle of droplets of different volumes is measured on the hydrophilic area. It shows that gravity has little effect on the contact angle for droplets with volume from 10 μl to 35 μl, which is large enough in the present transport experiment. From Figure 6(b), we have

R

l , sin 

h  R  l cot  .

(1)

The cross sectional area of interface S between the partial cone and the partial sphere is calculated as

l2  l 2 cot  . S= 2 sin 

(2)

The volume of partial cone V1 between zero and x1 is V1 

1 3 1    x1 tan 2   2  cot    3 2  sin  

(3)

The relation between x1 and x2 can also be obtained as 1 x2  x1 tan θ. 2

(4)

Using Eq. (4) yields the volume of partial sphere

12


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1  V2 =   3R  h  h 2 2 3



2

1  2  1    tan   x13   cot     cot   .   6 2 sin sin   

(5)

3

Then, the total volume of droplets can be obtained

V  V1  V2 2 1 2 1   2    1   3 1   x  tan   2  cot     tan    cot    cot    . 2  sin  2  sin   6  sin     3 3 1

(6) Combining Eqs.(3), (5) and (6) yields the final displacement of droplets x f  x1  x2 

1

2 3 1  1   1  2     1   2 1 3  V tan  1  tan     2  cot    tan    cot     cot    . 2  2   3  sin  2  sin   6   sin   

(7) Compared with previous studies

1, 7, 19,

either the interfacial tension or friction

coefficient is not easy to obtain, so we give up the direct introduction of the two parameters in Eq.(7) when predicting the final transport displacement. From Eq.(7), one can see that the transport displacement depends only on the wedge angle θ, droplet volume V and contact angle α in the hydrophilic area. Based on the theoretical model, the final transport displacements are predicted as shown in Figure 7, where the results of experimental measurement are also given for comparison. In the experiments, the wedge-shaped functional surface is exposed under oxygen plasma for 30 s and 100 s, respectively. As a result the contact angle of the corresponding surface is α = π/3 and π/6, respectively. Therefore, in the theoretical model, we adopt the contact angle as α = π/3 and π/6 to predict the final transport 13



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displacement. Figure 7 shows a good consistence of the experimental and theoretical results for cases with droplets of different volumes on different wettability surfaces. Both the experimental measurements and the theoretical predictions exhibit that the final transport displacement decreases with an increasing wedge angle θ. For a fixed wedge angle, the larger the volume of droplets, the larger the final transport displacement would be. In practical applications, for example, droplets can be constantly supplied to cool down far away surfaces of micro-devices. Keeping the hydrophobic region unchanged with a contact angle 126.1o and using water droplets of the same volume 10μl, we conduct comparative experiment on functional surfaces with wedge-shaped hydrophilic regions of different wettability. Here, the wedge-shaped hydrophilic region with contact angles of 60o and 30.5o is adopted, respectively. Both the theoretical predictions and experimental results are given in Figure 8, where it shows that the final transport displacement increases with a decreasing contact angle of hydrophilic areas in the case with a fixed wedge angle. 3.3 The instant transport velocity. With a fixed volume of droplets and wettability of hydrophilic regions, the instant transport velocity of droplets moving on wedge-shaped functional surfaces with different wedge angles is measured experimentally as shown in Figure 9. It is found that there are two remarkable features for the instant transport velocity. The first one is that the instant transport velocity increases very sharply at the initial stage till a maximum value, which can be explained by the surface tension force acting on the three-phase contact line (TPCL) of droplets. The surface tension force can be expressed as γ[cosαs- cosα(t)] 3, where 14


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α(t) is the instantaneous contact angle as the droplet spreads, αs is the local equilibrium contact angle and γ is the liquid-gas interfacial tension assumed to be a constant. At the initial time, the spherical droplet hung on the needle of syringe approaches to the tip of wedge on the functional surface. At this time ( t  0 ), α(t) is about 180o and αs is a constant less than 90o. As the droplet spreads, α(t) will be close to αs, which causes the surface tension force to decrease from positive to zero. As a result, the instant transport velocity would increase first and decrease after achieving a maximum. However, during the period of velocity slowing down, another remarkable feature is oscillation, leading to a phenomenon of multiple-accelerating (PMA), which can be explained by the changing droplet shape during the transporting process as shown in Figure 4. At the initial stage, a large resultant driving force is produced due to the droplet edges contacting with surfaces of different wetting properties. The front contact line of the droplet moves quickly, inducing the first acceleration transport at the initial stage. But the main part of the droplet stays at the initial location because the flowing velocity inside the droplet is much lower than that of the front contact line, leading to the phenomenon of droplet coarsening coalescence of droplets

5, 30-33.

14.

A meniscus appears during the

In order to achieve balance, the liquid inside the

droplet would flow into the front part through the meniscus. As the front part of the droplet moves forward, the resultant driving force gradually decreases and even becomes resistance due to the variation of the three-phase contact lines located on different wettability surfaces, leading to the first valley in the velocity curve. At the meantime, the liquid inside the droplet catches up with the front part gradually and the 15



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volume of the front part gradually increases. A positive resultant driving force is produced again due to the varying contact angle and the pressure difference, which drives the front contact line to accelerate movement, leading the second acceleration transport. As the droplet continues to move forward, multi-step acceleration transport is produced. The net force decreases gradually at each time till it disappears at the final equilibrium state. (see SI-movie 1 in Supporting Information, which only contains the initial process of a transporting droplet). The interval between each acceleration decreases as the wedge angle of hydrophilic tracks increases as shown in Figure 9. It is because a larger wedge angle would induce a wider meniscus, which would accelerate the flowing velocity of liquid inside the droplet 5. As a result, the final equilibrium state of the droplet can be obtained in a short time on the functional surface with a large wedge angle hydrophilic track. In addition, the maximum instant transport velocity is influenced significantly by the wedge angle. The larger the wedge angle, the larger the maximum instant transport velocity is, which is due to the dragging force at the initial stage depending on the length of the front contact line 14, 34. The effect of wettability of the wedge-shaped hydrophilic region on the instant transport velocity is also studied experimentally as shown in Figure 10. From Table S1, it is found that the contact angle hysteresis increases with the increase of the contact angle in the hydrophilic region, which leads to a resistance to a droplet movement. Moreover, a smaller contact angle in the hydrophilic region would induce a larger unbalanced capillary force 3, 14. Therefore, it can be concluded that in the case 16


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with a fixed wedge angle and a determined volume of droplet, the transport velocity would increase as the contact angle of the wedge-shaped hydrophilic region decreases. From Figure 10a, it is interesting to find that a multiple-accelerating phenomenon is very obvious in the case with a relatively small wedge angle, while it is relatively inconspicuous in the case with a relatively large wedge angle. In a word, in order to achieve a high instant transport velocity, a large wedge angle or a small contact angle of wedge-shaped hydrophilic regions is required in the present experiment. In previous studies, the transport velocity is also an important parameter that is focused on. Daniel and Chaudhury

35

proposed a method to obtain

the transport velocity 5-10 mm/s for droplets resting on a wettability surface. Khoo and Tseng

13

got a quite large speed of 500 mm/s for a 2 μl droplet on chemically

patterned nanotextured surfaces. In contrast, there is no prefabricated microstructure on the present wedge-shaped functional surfaces and only inevitable small roughness exists, whose SEM photos are provided in Figure S4 in Supporting Information. A much large transport velocity 201.06 mm/s can be achieved for a 15 μl droplet on the functional surface with a 30o wedge angle combining with a 30.5o contact angle. 3.4 Droplet transport on different-shaped functional surfaces. Although the above mentioned wedge-shaped functional surface can transport droplets from one place to another, a single track is not enough to finish prescribed tasks in practice efficiently. For example, cells or drugs need to be transported to multichannel positions or regions. Based on the present wettability-patterned technology, different kinds of 17



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functional surfaces with multi-step shaped patterns can be well fabricated as long as the mask is different, for example, two kinds of masks shown in Figures 11(a)-11(b). Using the present technology, the final multi-step shaped functional surfaces would possess different shaped hydrophilic regions, for example, hierarchical ones shown in Figures 11(c)-11(d) based on masks in Figures 11(a)-11(b). A water droplet can be transported on the multi-step functional surfaces as shown in Figure 12. As a water droplet is deposited on the tip of any secondary orbit, it will be transported along the secondary orbit until the secondary orbit is full covered, and then the droplet will be further transported and gathered on the main track. Subsequently, the droplet will be transferred to the other secondary orbits connected to the main track. Moreover, with different supply rates and liquid volumes, the droplet would be transported with different velocities. Indeed, it can be demonstrated that a multi-step functional surface has a flexible characteristic of transport droplet from any “branch” to the other “branches”, whether the angle β is an acute or obtuse angle. Inspired by the above linear wedge-shaped functional surface, more nonlinear functional surfaces based on the same wettability-patterned technique can also be designed as shown in Figure 13, for examples. The hydrophilic track can be designed as a curve, which can generate more flexible transport behaviors needed in practical engineering. Figures 13(a1)-13(a5) and Figures 13(b1)-13(b5) exhibit obviously the droplet transport on irregular curved tracks and spiral tracks, respectively. Even a hydrophilic track with a 90o or 150o turning angle can be realized to achieve droplet 18


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transport as shown in Figures 13(c1)-13(c6) and Figures 13(d1)-13(d6). Applying such a concept, we can design curved or spiral paths to avoid the influence of existing surface defects on droplet transport in practical applications. All these transport tracks would play a significant role in lab-on-a-chip.

4. Conclusion A simple wettability-patterned technology is proposed to fabricate functional surfaces without surface microstructures, on which directional transport of droplets can be realized. The flat photopolymer achieved by 3D printing technology is exposed to oxygen plasma to obtain a hydrophilic surface, which is then silanized to form a hydrophobic one. Next with a mask, a wedge-shaped functional surface can be achieved by exposing a wedge-shaped region on the hydrophobic surface to oxygen plasma selectively again. The wedge-shaped region is hydrophilic, around which it is hydrophobic. It is found that droplets deposited at the tip of the wedge-shaped hydrophilic region could transport spontaneously towards the end. The transport behaviors, including the final transport displacement and the instant transport velocity, are significantly influenced by the wedge angle, the contact angle of the wedge-shaped region as well as the volume of droplets. In order to predict the transport displacement, a simple theoretical model is further proposed, the predicted result by which agrees with the experimental measurements. On such a simple prepared functional surface, the transport velocity can achieve about 200 mm/s, which is comparable with, even larger than that on some complexly obtained functional surfaces. Furthermore, based on such a simple wettability-patterned technology, many 19



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kinds of functional surfaces for spontaneous droplet transport can be realized, for example, curve-tracked or spiral-patterned ones, even hierarchical ones. The present technology and the results should be helpful for the design of multi-functional transport in lab-on-a-chip, biological research, MEMS or NEMS applications.

ASSOCIATED CONTENT Supporting Information. Figure S1 shows the contact angle of dyeing droplet; Figure S2 shows the changes in wettability with aging; Figure S3 shows the effect of gravity on contact angle; Figure S4 shows the SEM photos of functional surfaces; Table S1 shows the wettability properties of different surfaces; Movie 1 shows the phenomenon of multi-step acceleration (AVI).

AUTHOR INFORMATION Corresponding Author * Email: [email protected] (Z. P); **Email: [email protected] or [email protected] (S. C) Notes The authors declare no competing financial interest.

Acknowledgements This work was supported by National Natural Science Foundation of China (Grant No. 11532013, 11872114, 11672302, 11772333); and Graduate Technological Innovation Project of Beijing Institute of Technology (Grant No. 2017CX10037).

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TOC Graphic

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Figure 1. (a) A square photopolymer base material (white color) with a side-length 40 mm. (b) A photopolymer patterned mask made of several wedges with different wedge angles (white color). 205x82mm (300 x 300 DPI)


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Figure 2. A schematic of the experimental device. 191x149mm (300 x 300 DPI)



Figure 3. A 10 μl droplet of distilled water on different regions of a wedge-shaped functional surface. (a) On the silanized region showing a hydrophobic behavior. (b) On the oxygen plasma treated region showing a hydrophilic feature. 191x61mm (300 x 300 DPI)


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Figure 4. Snapshots of a 15 μl distilled water transporting on a wedge-shaped functional surface with a 10° wedge angle. The transport displacement at each picture can be estimated through the ruler and the transport time is also recorded for each picture. 175x163mm (300 x 300 DPI)



Figure 5. Snapshots of a 15 μl distilled droplet moving on a wedge-shaped functional surface with a 30° wedge angle. 175x165mm (300 x 300 DPI)


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Figure 6. A mathematical model for the final configuration of droplets staying on the wedge-shaped hydrophilic area. (a) Vertical view. (b) Side view. 253x71mm (300 x 300 DPI)



Figure7. Comparison of the final transport displacement predicted theoretically and experimentally as a function of the wedge angle θ and the volume of droplets V. (a) On the wedge-shaped functional surface fabricated under 30 s of oxygen plasma exposure with the contact angle α=π/3. (b) On the wedge-shaped functional surface fabricated under 100 s of oxygen plasma exposure with the contact angle α= π/6. 251x97mm (300 x 300 DPI)


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Figure 8. Displacement as a function of the wedge angle on wedge-shaped functional surfaces with hydrophilic areas of different wettability, i.e., different contact angles. 137x104mm (300 x 300 DPI)



Figure 9. Instant transport velocity varying with time on wedge-shaped functional surfaces with different wedge angles. 138x103mm (300 x 300 DPI)


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Figure 10. The instant transport velocity as a function of moving time on wedge-shaped functional surfaces with different wettability of hydrophilic regions. (a) The wedge angle is θ = 10° and the volume of droplets is V = 10 μl. (b) The wedge angle is θ = 30° and the volume of droplets is V = 15 μl. 255x99mm (300 x 300 DPI)



Figure 11. (a-b) Two kinds of photopolymer masks. (c-d) Two kinds of multi-step shaped functional surfaces. The dotted lines denote the main track, secondary tracks and their angular bisectors. 253x190mm (300 x 300 DPI)


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Figure 12. Droplet transport on photopolymer plate substrates with multi-step patterns. 259x181mm (300 x 300 DPI)



Figure 13. Droplet transport (a1)-(a5) on a curved track, (b1-b5) on a spiral track, (c1-c6) on a track with a 90° turning angle and (d1-d6) on a track with a 150° turning angle. 259x179mm (300 x 300 DPI)


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TOC Graphic 85x47mm (300 x 300 DPI)


Directional Transport Behavior of Droplets on Wedge-Shaped

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