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Designing Laplace Pressure Pattern for micro-Droplet Manipulation Lei Wu, Zhichao Dong, Fengyu Li, and Yanlin Song Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b03908 • Publication Date (Web): 27 Dec 2017 Downloaded from http://pubs.acs.org on December 29, 2017
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Designing Laplace Pressure Pattern for microDroplet Manipulation Lei Wu1, ‡, Zhichao Dong2, ‡, Fengyu Li1* and Yanlin Song1* 1
Key Laboratory of Green Printing, Institute of Chemistry, Chinese Academy of Sciences,
Zhongguancun North First Street 2, 100190 Beijing, PR China. 2
Laboratory of Bio-inspired Smart Interface Sciences, Technical Institute of Physics and
Chemistry, Chinese Academy of Sciences, Zhongguancun East Road, 29, 100190 Beijing, PR China. ‡ These authors contributed equally.
KEYWORDS. wettability boundary, conical pattern, superhydrophobic, Laplace pressure, droplet patterning
ABSTRACT. Manipulation of arrayed tiny droplets is important in liquid dispersion, liquid transportation, bioassays, nucleation, integrated electronics and various lab experiments that require delivering precise and minute volumes of droplets. Liquid dispensed from a small orifice or split from surface patterns are typical methods, but the acquired droplet diameters are similar to that of the nozzle and pattern. Here we demonstrate that tiny droplets with dimensions much
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smaller than the pattern can be arrayed advantageously through designing a Laplace pressure pattern based on conical morphology and wetting heterogeneity. The pattern could selectively resist liquid’s motion and drive the capillary bridge breaking of macro-drop into arrayed tiny droplets at wettability boundaries. Arrayed picoliter droplets can be acquired on a submillimeter-scaled pattern with a feature size of several hundred micrometers. Through regulating the conical morphologies and the wetting heterogeneity, the volume and number of tiny droplets can be accurately controlled. As a paradigm, adopting droplets of nanoparticle dispersion, various arrayed functional assemblies can be fabricated. This integration of conical morphology and wetting heterogeneity offers a powerful kit for patterned micro-droplets quantitative and locational manipulation, and opens a new avenue to achieve functional units in a facile and highthroughput way.
Arrayed tiny droplets is central to liquid dispersion,1-3 liquid transportation,4-7 bioassays,8-9 nucleation,10-12 integrated electronics13-14 and various lab experiments that require delivering precise and minute volumes of droplets.15-16 Generally, orifice-based and orifice-free methods are typical two ways to produce tiny droplets, examples including inkjet printing,17-19 microfluidics,20-21 and surface patterns,22-26 etc.. Despite the effectiveness of the orifice-based printing devices, confined geometry of the nozzle poses several challenges, such as satellite droplets, propensity to clog and orifice size depended droplet dimension. Orifice-free methods, such as capillary bridge breaking by patterned surface based on physical confinement27-28 or chemical heterogeneity based on closed-system or open system,29-31 could restrain satellites and exactly pattern liquids at predetermined regions. Wang et al. reported that droplet arrays even with size gradient can be elegantly produced in the closed system.32 However, similar to the orifice-based methods, the volumes of tiny droplets still depend largely on the dimensions of the
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surface patterns.33-34 As a hypothesis, if the liquid on pattern can dewet during the capillary bridge breaking process, the volumes of arrayed droplets could be effectively reduced.
In nature, Laplace effect is frequently harnessed by creatures to collect and transport liquid for survival. Cone is a typical gradient structure for generating Laplace pressure. For example, drought-tolerant cactus exploits conical structure along a single cactus spine, to produce a directional liquid transportation system for water collecting35 (Figure S1), whose Laplace pressure direction is along with the water moving direction. Here, we employ Laplace pressure to resist the motion of the macro-drop by designing a conical wettability pattern, through which forced dewetting while capillary bridge breaking process can be realized and tiny droplets can be acquired (Figure 1A-C). The Laplace pressure direction is against macro-drop moving and contributes to the capillary bridge breaking, which results in tiny droplets acquired at the pattern boundary with accurate quantitation and dimensions much smaller than the pattern. In addition, we identify three distinct wettability-related modes of macro-drop motion on the conical wettability patterns and explain through modeling the underlying mechanism. We further reveal how to manipulate micro-droplet dimensions through tuning the pattern parameters or droplet characteristics and extended this strategy to micro-assembly fabrication.
In order to achieve micro-droplets with a much smaller dimension than the wettability pattern, the substrate must satisfy three criteria: (1) appropriate liquid-solid adhesion on the conical pattern to help macro-drop adhering but dewetting on the pattern,36-37 (2) effective wettability boundaries as energy barriers for successively micro-droplets generated from macro-drop, and (3) proper pattern morphology to further reduce the micro-droplet dimension. As is well known, the pinning or sliding of the three phase contact line (TCL) of a liquid droplet is significantly
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influenced by surface properties especially wettability. Therefore, superhydrophobic surface,38 together with a series of manually introduced conical wettability patterns, i.e., superhydrophilic pattern, hydrophilic pattern and hydrophobic pattern, were prepared and compared.
RESULTS: Figure 1A shows the schematic diagram of the experimental set-up. A droplet holder with a diameter of 6.0 mm was employed and mounted above a programmable moving platform, whose moving direction is parallel to the axis of the conical wettability pattern. The distance between the substrate and the holder was adjusted as 5.0 mm. High-speed cameras recorded the liquidsolid dynamic interactions from top and side views. The pattern dimensions used in this experiment ranges from 50 µm to 3 mm. The conical wettability patterned superhydrophobic surface was prepared from UV-photolithography, metal-assisted etching and fluorination successively (Figure S2-S5). Here, a four corner star shape, whose width was 3.0 mm for easy monitoring, was selected as the model pattern. The morphology of a typical conically patterned superhydrophobic substrate is shown in Figure 1B, C. The detailed characterization of the silicon nanowire structure is shown in Figure 1D, E.
The dynamic macro-drop capillary bridge breaking processes were monitored in real time on a four corner star shaped pattern with interior angle of 30° and a moving velocity of 2.0 cm/s, and corresponding captures of droplet morphologies on different heterogeneities are illustrated in Figure 2A-C. For the superhydrophilic-superhydrophobic surface (Figure 2A), as the liquidsolid adhesion is high (Figure 2G) on the superhydrophilic pattern, water completely covers the whole pattern during the macro-drop moving process. Even though the receding contact angle (RCA) of the macro-drop kept decreasing (Figure 2D) during the sliding process, the advancing
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TCL and receding TCL were both pinned and a liquid film with similar shape of the superhydrophilic part (3 mm four corner star shape) is left after macro-drop capillary bridge breaking.39 In comparison, for the hydrophilic patterned superhydrophobic substrate (Figure 2B), liquid partially wetted the hydrophilic pattern since the advancing TCL cannot reach the apex of the cone due to the generated Laplace pressure. In addition, the receding TCL can dewet on the hydrophilic pattern forced by the continuously moving macro-drop (Figure 2E). In cooperation with the energy barrier introduced by the superhydrophobic boundary, a filament occurs due to the cooperation of the advancing and receding TCL, and then breakup due to the RayleighTaylor instability, which finally left a tiny droplet (554.1 ± 12.6 µm diameter) smaller than the wettability pattern. When macro-drop moved on a hydrophobic patterned superhydrophobic surface, as shown in Figure 2C, the deformation of the macro-drop TCL is much less obvious because of the large RCA of the hydrophobic region and little wetting difference between the hydrophobic pattern and the superhydrophobic region. The receding TCL kept retreating on the hydrophobic pattern when reaching the RCA (Figure 2F), accompanying with advancing TCL confined by the conical pattern, a much smaller droplet (96.3 ± 5.4 µm) was left on the apex of the hydrophobic conical pattern. Thus, only conical morphology is not enough to realize forced dewetting while capillary bridge breaking process (superhydrophilic-superhydrophobic conical pattern, Figure 2A). Through accompanying with appropriate wetting heterogeneity, the forced dewetting while capillary bridge breaking process can be realized and be observed on the conical hydrophilic-superhydrophobic and hydrophobic-superhydrophobic substrates.
Comparing with the superhydrophilic pattern, volume of tiny droplets can be reduced to 1/20 on the hydrophilic pattern, and to 1/160 on the hydrophobic pattern. The modes of macro-drop motion on the conical pattern is wettability related, therefore the volume of tiny droplet is
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wetting heterogeneity related. We also monitor the macro-drop interacting with the conical patterns with three wetting heterogeneities, with the increasing of wetting heterogeneity, the interacting time of macro-drop with the pattern decreases (Movie S1). In order to understand the wetting heterogeneity influenced interacting time and droplet volume variation, distance sequences of the dragging force during the liquid motion were preformed and shown in Figure 2G-I. The droplet bore different amount of force on the conical wettability pattern and the superhydrophobic region. Increasing the hydrophilicity of the pattern, a lager force was tolerated when macro-drop moving along the pattern (Figure S6), which results in a longer interacting time and larger droplet volume. Besides dragging force, the RCA was also influenced by the wettability of the pattern (Movie S2). Since macro-drop shows the same value of advancing contact angle on the superhydrophobic region, the RCA difference (∆θ, difference between advancing contact angle on superhydrophobic region and RCA on the pattern) was only determined by the pattern. With the increase of wetting heterogeneity, ∆θ increases (Figure S7) and its trend is in accordance with the force-distance data (Figure 2G-I). As a result, with the wetting property of the conical pattern regulated from superhydrophilicity to hydrophilicity and to hydrophobicity, the interacting time decreases and decreased dimensions of tiny droplets can be prepared on conical patterns with the same dimensions.
To fully understand the forced dewetting while capillary bridge breaking process, high speed videos is used to capture the droplet dragging process on a hydrophilic-superhydrophobic conical wettability pattern with angle of 30°. Droplet shape variation on the hydrophilicsuperhydrophobic conical pattern is illustrated in Figure 3B. As shown in Movie S3 and Figure 3B, the receding TCL (white dot line, Figure 3B) of the macro-drop keeps retreating along the moving direction while dragging due to unbalanced Laplace pressure originated from appropriate
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wetting heterogeneity and conical morphology of the pattern. In addition, the receding TCL experiences distortion, and the capillary bridge between the macro-drop and tiny droplet becomes thinner and thinner until breaking. After the capillary bridge breaking, the advancing TCL (yellow dot line, Figure 3B) of the tiny droplet generated and simultaneously retreat due to the tremendous distortion (unbalanced Laplace pressure) of the droplet, which leads to the generation of tiny droplet much smaller dimension than the pattern. Thus, the receding TCL retreats along the dragging direction (white dot line, Figure 3B) and the advancing TCL retreats against the dragging direction (yellow dot line, Figure 3B), the cooperation of which contributes to the smaller dimension of tiny droplet.
Besides the wetting properties of the conical pattern, the micro-droplet patterning process can also be regulated through the variation of conical pattern morphology. The interior angle of the conical pattern, which mainly influences the Laplace pressure, can also be utilized to regulate the size of the micro-droplet. Taking hydrophilic-superhydrophobic substrate as an example, patterns with nine different interior angles, ranging from 10º to 90º with 10 degrees’ intervals were prepared (Figure S8). The interacting time of macro-drop with the conical pattern (Figure S9) and the diameters of micro-droplets both increase with the increase of the conical angle (Figure 3C and Figure S10). Thus, the RCA of the conical pattern, which determined the dewetting behavior of TCL on pattern, in coordination with the conical structure for generated Laplace pressure, as well as the superhydrophobic region, which repelled wetting and confined the dewetting region, played critical roles on the macro-drop capillary bridge breaking process and the volume of the micro-droplet.
DISCUSSION:
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Having clarified that wetting heterogeneity and conical pattern morphology both influence the micro-droplet patterning process, force analyses are then carried out to interpret the mechanism of macro-drop capillary bridge breaking. Considering the motion of the drop, as shown in Figure 3A and Figure S11, three competitive forces dominate the formation process of the tiny droplet: one driving force and two resistance forces. The driving force is provided by the dragging force , which leads to droplet motion. By analyzing the interaction process, it is found that during the exertion of dragging force on the water droplet, an air film appeared and grew which finally leads to the rupture of the liquid filament. In other words, by integrating the force exerted on the liquid filament, the dragging force can be acquired and expressed as:40
= ∙ 2 = sin ∙ ∙ 2
(1)
where and are starting and stopping diameters of the liquid filament as shown in Figure 3A, I and III, respectively. is the liquid surface tension, and is the interior angle of the pattern.
Since the conical pattern shape and the hetero-wettability between the wettability pattern and the superhydrophobic surface, the resistance forces induced by the patterned surface operate to counteract and droplet deformation. In this hetero wetting state, the advancing contact angle on the superhydrophobic region and the RCA on the pattern work coordinately, which results in one of the resistance force ∆
!" .
In addition, droplet deformed along the pattern
because of the conical morphology. The Laplace pressure, ∆# , generated by the conical pattern on the macro-drop before capillary bridge breaking which impedes the wetting of the apex by the moving droplet, contributing to the capillary bridge breaking of macro-drop. Combining the act of surface wetting differences and Laplace pressure, the resistance forces are given by 41: $% %&' ($ = ∆
!"
+ ∆#
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2
(3% 45
6
= 2 (cos ." − cos . )1 + ( where ." and .
−
(3% 47 6
)∙8
(2)
are the advancing contact angle of the superhydrophobic region and the
receding contact angle of the hydrophilic part, respectively. 1 and 1 are the starting position and stopping position of TCL as shown in Figure 3A, I and III, respectively, which is in correspondence with the starting and stopping . 9 and 9 are the radius of the deformed droplet right before capillary bridge breaking (Figure 3A, II).
The volume of tiny droplets can be deduced by balancing the relative acting ingredients as equals to $% %&' ($. Thus the diameter : of the micro-droplet can be expressed as: : = 21 = 1 +
; (3% 45
