Excellent Liquid Unidirectional Transport Inner Tilted‐Sector Arrayed Tubes

Liquid unidirectional transport exhibits critical applications from water harvesting to microfluidics. Despite extensive progress, implementation of liquid unidirectional transport that is not subjected to the liquid surface tension and injecting velocity also remains a great challenge. Here, a tilted‐sector arrayed tube for excellent liquid unidirectional transport is proposed that applies to a vast width domain of liquid surface tension and injecting velocity. In addition, the transport direction is abnormally against the tilted direction of structure, in stark contrast to the traditional understanding that is along tilted direction. This excellent and unique liquid unidirectional transport is caused by synergistic effects of tilted sectors and tube structures, which induce a unique 3D liquid propagation mode as well as a large Laplace pressure asymmetry between the front and rear sides of the liquid. Moreover, the antigravity climbing, circuit isolating, and chemical reaction controlling can be achieved based on the excellent liquid unidirectional transport. It is envisioned that the design can be extensively applied in microfluidics, lab‐on‐a‐chip devices, and biochemistry microreactors.


Introduction
Liquids' unidirectional transport without external energy input has attracted extensive attention due to their great promising in many fields, such as microfluidics, [1][2][3] chemical reactions, [4] water harvesting, [5][6][7] lubrication, [8,9] DNA microarrays, [10] and biomedical analysis. Recently, multifarious liquid transport strategies have been proposed that rely on the asymmetry of physical structures and surface energy, which generate a directional driving force via breaking the symmetricity of contact line. Typical of them are inspired by living organisms DOI: 10.1002/admi.202300239 including butterfly wings, [11,12] spider silk, [4,[13][14][15][16] cactus, [17][18][19] Nepenthes, [20][21][22][23] Araucaria, [24] or engineering-based design of gradients in topography [25][26][27][28][29][30] and wettability. [31][32][33][34][35] Chen et al. [20] reported a continuous and directional water transport on the rim of the pitcher based on the asymmetric multiscale structure. Ju et al. [17] found that cactus can achieve droplet-directed transport induced by a combination structures of conical spines and trichomes. Li et al. [36] designed a liquid diode to realize the long-range directional transport of liquid via breaking the contact line pinning at the advancing edge while simultaneously arresting the reverse motion at the rear side. Despite notable progresses, the liquid unidirectional transport is always unstable with smaller surface tension ( ) as well as contact angle ( ) or larger injecting velocity (V i ) of liquid. For example, Chu et al. [37] designed an asymmetric nanostructured surface to achieve unidirectional liquid spreading, while which could not work with liquid surface tension as well as contact angle smaller or larger than specific values. Feng et al. [24] demonstrated that unidirectional transport of liquids could transfer to bidirectional transport via increasing injecting velocity. Therefore, it is a great challenge to implement liquid unidirectional transport that is not subjected to the liquid surface tension and injecting velocity.
Here, we fabricated a tilted-sector arrayed tube (TSAT) by a simple 3D printing, which manifests an excellent liquid unidirectional transport that applies to a vast width domain of liquid surface tension and injecting velocity. Interestingly, we find that the transport direction of liquid inner TSAT is always against the tilted direction of structure, in stark contrast to the traditional understanding that is along tilted direction. This excellent and unique liquid unidirectional transport is caused by synergistic effects of tilted sectors and tube structures, which induced a unique 3D liquid propagation mode as well as a large Laplace pressure asymmetry between the front and rear sides of the liquid. In addition, an antigravity climbing, circuit isolating, and chemical reaction controlling could be achieved. Our designed excellent liquid unidirectional transport strategy could show great potential in various applications including chemical reactions, drug transportation, and so on.

Fabrication of the TSAT
We implemented a digital light processing (DLP) 3D printing technology to fabricate the tilted-sector arrayed tube (schematic shown in Figure 1a). First, the printing resin between the bottom of the tank and the printing platform was cured by UV light (≈405 nm) according to the shape of the 2D slice of the designed 3D model. Then, repeated processes were carried out layer-bylayer to form the target sample. Figure 1b,c clearly exhibits the global and local structures of designed TSAT from top view and side view, respectively. The TSAT consists of a hollow tube (emerald green) and tilted-sector structure arrays (green) inlayed inside the inner wall along the axial direction. The morphology can be accurately expressed by the following parameters including the inner diameter (D) of the tube, the diameter (d) of the central pore, the tilting angle ( ), the transverse pitch (P), and thickness (T), which are 4000 μm, 1700 μm, 45°, 1000 μm, and 200 μm, respectively. Noted here is that the apparent and designed sizes of TSAT might be slightly different due to the limitation of printing accuracy. For example, the rectangular tip in the design model will appear rounded ( Figure S1, Supporting Information).
We simulated the transport of liquid with different surface tensions' inner TSAT by using COMSOL software (Figure 1d and Figure S2 (Supporting Information)). For pure water ( = 72 mN m −1 ) with of ≈72.2°, the liquid manifests a unidirectional transport against the tilted direction of structures, which is markedly distinct from conventional research findings ( Figure 1d). In addition, the simulated results are consistent on samples with rectangular and rounded tips, eliminating the effect of printing accuracy on our experiments ( Figure 1d and Figure S2a (Supporting Information)). Moreover, for lower surface tension liquids with of ≈30°( Figure S2b, Supporting Information), unidirectional transport performance still exists, demonstrating the effectiveness of a wide surface tension domain. Here, the contact angle is measured on a flat surface with the same material as TSAT. We envision that the simulated results could provide a general guidance for the following liquid transport experiments.
Variation in the transport distance s with contact angle and injecting velocities V i , where s was measured after infusing the liquid for 20 s. The volume of liquid injected is 100 μL. With ranging from 18.4°to 72.2°and V i ranging from 0 to 100 μL s −1 , unidirectional transport of liquid along the +x-direction is also achieved. f) The comparison of and V i range for liquid unidirectional transport of our designed TSAT and the previous studies.

Unidirectional Transport of Liquid on TSAT
We investigated the transport behavior of liquids' inner TSAT with series of surface tension and injecting velocities V i ( Figure  2 and Movie S1 (Supporting Information)). The liquid surface tension is controlled by mixing ethanol into water with different mass fraction c which can be descript as c = m e /(m e + m w ). Here, m e and m w are the mass of ethanol and water, respectively. The relationship between as well as and c are shown in Figure S3 (Supporting Information), which show a negative correlation. When c changes from 0% to 100%, decreases from ≈73 to 22 mN m −1 and decreases from 72.2°to 18.4°, respectively. Figure 2a,b and Movie S1 (Supporting Information) display the transport of liquid with c = 0% ( = 72.2°) and 35% ( = 42.7°) inner TSAT at an injecting velocity V i = 5 μL s −1 , respectively. With continuously infusing of liquid, both liquids transport against the tilted direction of sector structures, reaching 14 and 9 mm in 20 s, respectively. Here the sector-tilting direction is defined as the +x-direction. Figure 2c shows the image sequences of liquid with c = 0% ( = 72.2°) spreading in the TSAT at an injecting velocity V i of 100 μL s −1 . Even though the V i is 20 times higher than that in Figure 2a, a unidirectional transport of liquid along the +x-direction is also achieved, manifesting an excellent stability.
We further investigated the relationship between contact angle , injecting velocity V i , and liquid transport distance s inner TSAT. Here, the total injecting volume of liquid is 100 μL. For ranging from 18.4°to 72.2°(22 mN m −1 < < 73 mN m −1 ) at V i of 5 and 100 μL s −1 , the liquid always transports along the +x-direction (Figure 2d). In addition, even for liquid with contact angle = 3.2°or surface tension = 18.4 mN m −1 , the unidirectional transport also occurs ( Figure S4, Supporting Information). Here, the evaporation of liquid could be ignored in transport process even for easily evaporated ethanol ( Figure S5, Supporting Information). The time-dependent variation of transport distance s is plotted in Figure S6a (Supporting Information), manifesting a positive correlation between and s. Similarly, a unidirectional transport of liquid along the +x-direction always exists with V i ranging from 0 to 100 μL s −1 (Figure 2e and Figure S6b (Supporting Information)). Noted here is that the transport distance s is positive correlation to contact angle and injecting velocity V i , which is because that increasing the contact angle and injecting velocity V i can lead to the increase in the volume of the locked gas in the root of the tilted-sector structure during transport process. Taken together, our designed TSAT possesses an excellent liquid unidrectional transport that applies to a vast width domain of liquid surface tension and injecting velocity, which is quite distinct from previous studies (Figure 2f).

Mechanism of Unidirectional Liquid Transport Inner TSAT
To understand the mechanism responsible for excellent liquid unidirectional transport inner TSAT, we examined the interfacial configuration of liquids with = 72.2°and = 42.7°at the front and rear sides with injecting velocity of 5 μL s −1 (Figure  3a,b and Movie S2 (Supporting Information)). Since the liquid   Figure S9 and Movie S2 (Supporting Information)). We also conducted additional experiments to exclude the influence of injecting needle to liquid transport behavior ( Figure S10, Supporting Information).
We then performed a force analysis to explore the mechanism of liquid unidirectional transport inner TSAT. At the scenario that liquid is confined by structure pinning, curved configurations are generated at the front and rear sides, which induced two Laplace pressures, P f and P r , expressed as P f = 2 /R f = −4 cos( + )/d and P r = 2 /R r = 4 cos( − )/d, respectively (Figure 3e,f). Here, R f and R r are the radii of curvatures at the front and rear sides of liquid, respectively. Combining the two, we obtain the Laplace pressure difference, described as ∆P = 4 [cos( − ) + cos( + )]/d = 8 cos cos /d. Noted here is that our mode is only applied to liquid with smaller than 90°that allows liquid to spread on target surface. We can clearly obtain that ∆P for all the liquid with smaller than 90°transporting inner designed tube with different ( < 90°) and d is always larger than 0, meaning a unidirectional transport in the +x-direction that is consistent with our experimental observations in Figure 2d and Figure S11 (Supporting Information).
In addition, a convex shape of liquid with P f < 0 when > 45°a nd a concave one with P f > 0 when < 45°at the front side (Figure 3e,f) can be accurately predicted by our model, which are also consistent with data in Figure 3a,b.

Multiscenario Applications of the TSAT
Liquid unidirectional transport can be applied in multiscenario practical applications. Figure 4a and Figure S12 (Supporting Information) illustrate the antigravity transport of liquid inner TSAT placed under a tilt angle (from 0°to 90°). For the TSAT with smaller , liquid displays a unidirectional transport along the +x-direction (s > 0). With the increase of , a bidirectional transport of liquid occurs when the driving force is not enough to overcome gravity. For injecting liquid with V i of 5 μL s −1 in 20 s, the conversion of the two modes for liquid with = 72.2°a nd 42.7°occurs at = 30°and 40°, respectively (Figure 4b,c). In addition, further investigation shows that the larger the surface tension is, the smaller the critical tilt angle is ( Figure S13, Supporting Information).
This result indicates that our designed TSAT can endow liquid a certain ability for antigravity transport, which underpins liquid to easily cross a curved TSAT with a height of ≈6 mm (Figure 4d and Movie S3 (Supporting Information)). In addition, the liquid unidirectional transport inner TSAT can be applied to open an isolated circuit and light up a light-emitting diode, which provides a simple route for constructing a fluid gate (Figure 4e and Movie S4 (Supporting Information)). Moreover, the TSAT can be used as a microreactor to achieve site-directed fusion and chemical reaction between two kinds of liquid (Figure 4f and Movie S5 (Supporting Information)). Taken together, the multiscenario applications of the TSAT could by widely used in various microfluidic systems.

Conclusion
In summary, we have implemented a 3D printing technology to fabricate a TSAT consisting of a hollow tube and tilted-sector structure arrays inlayed inside. Underpinning by the uniquestructure-induced 3D liquid propagation mode as well as a large Laplace pressure asymmetry, an excellent liquid unidirectional transport that applies to a vast width domain of liquid surface tension and injecting velocity is achieved. Based on this excellent performance, our designed surface manifests multiscenario applications, including antigravity climbing, microcircuit and microreactor systems, which will further strengthen the engineering significance of liquid unidirectional transport.

Experimental Section
Materials: Acrylic photosensitive resin, called "HTL", used for 3D printing was purchased from BMF Nano Materials Technology Co., Ltd. (Shenzhen, China). Ethanol was obtained from Tianjin Kaili Metallurgical Research Institute (Tianjin, China). Deionized water with a resistance of 18.2 MΩ was acquired from a laboratory ultrapure water system (Summer-S2-20H, Sichuan Delishi Technology Co., Ltd., Sichuan, China).
Fabrication of TSAT: The TSAT was fabricated by using DLP 3D printing technology (M-Jewelry U30 from Ningbo Smart Digital Technology Co., Ltd.). First, a TSAT model was constructed by using SolidWorks 2018 Software. Then, the designed model was sliced into layers for a printable command sequence, and further imported into the printer for 3D printing. The print light wavelength, energy density, bottom exposure time, top exposure time, exposure resolution, layer thickness, platform lift distance, and platform lift stop time during the printing process were 405 nm, 29 mW cm −2 , 13 s, 7 s, 33 μm, 20 μm, 5 mm, and 3 s, respectively. After printing, the printed parts were treated by simple rinsing with 100% ethanol and ultrasonic cleaning for 3 min. Finally, the printed TSATs were placed in a vacuum drying oven for drying and in a UV light box for 3 min for secondary curing before the use in experiments.
Liquid Transport on the TSAT: The liquid transport experiment was conducted at room temperature. In the experimental process, liquids with different surface tensions were injected into the sample through a stainless needle (with an outer diameter of 0.5 mm and an inner diameter of 0.25 mm) at injecting velocity ranging from 5 to 100 μL s −1 , by using a syringe pump (Baoding LongerPump Co., LTD., Baoding, China). Here, the liquids with different surface tensions were obtained by mixing ethanol and water with a series of mass fractions c ranging from 0% to 40%. A highspeed camera (NAC MEMRECAM ACS-3 M16-color, NAC Image Technology, Inc., Tokyo, Japan) was employed to record the macroscopic and microscopic dynamics of liquid transport at a frame rate of 500 fps. The experimental setup diagram of unidirectional liquid transport is shown in Figure S14 (Supporting Information).
Characterization: The structure of TSAT was obtained by using a stereomicroscope (VHX-900F, Keyence Co., LTD., Osaka, Japan). Surface tensions of mixed water-ethanol solutions and static contact angle of liquid droplet (5 μL) on a flat surface with the same material of TSAT were measured by using an OCA25 Standard Contact Angle Goniometer (Dat-aPhysics GmbH Co., LTD., Filderstadt, Germany). The values of the above parameters were investigated by an average of five measurements.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.