A wicking Nylon 6 polymer material was produced through surface structuring by a direct femtosecond laser nano/microstructuring approach. The produced wicking structure is an array of parallel microgrooves, the surface of which is textured with irregular nanostructures and fine microstructures. High-speed imaging of water spreading vertically uphill against the gravity discloses a series of capillary flow regimes with h ∝ t, h ∝ t1/2, and h ∝ t1/3 scaling laws, where h is the height of capillary rise and t is the time. In the initial stage, the capillary flow occurs with a single front, from which at a certain time a precursor front forms and advances ahead of the main one. Our study shows that the onset of the precursor front occurs in h ∝ t flow regime. The created material exhibits excellent wicking properties and may find applications in various technologically important areas.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
At the present time, there is a significant demand for high-performance polymer capillary materials in such technologically important areas as microfluidics [1,2], optofluidics [3,4], lab-on-chip [5,6], energy-harvesting [4,7], and Maisotsenko cycle (M-cycle) air-conditioning [8–12]. In particular, the M-cycle air-conditioning field currently needs more advanced polymer capillary materials for improving cooling efficiency. The M-cycle coolers are novel indirect evaporative cooling (IEC) systems capable of cooling the air down to the dew-point temperature, while the lowest cooling temperature of the traditional IEC systems is limited by the wet bulb temperature. These novel air-conditioning systems are by a factor of 3-4 more efficient than the traditional mechanical vapor-compression systems. Theoretically, the efficiency of M-cycle cooling systems can be higher by a factor of 8-10 compared with the compressor ones [8,10,11,13]. However, a microfiber cellulose material with a bulk capillarity that is widely used as a heat/mass exchanging medium in commercially produced M-cycle coolers does not allow achieving a higher efficiency. To further improve the cooling efficiency and performance of M-cycle air-conditioners, there is a need in wicking materials with surface capillarity instead of the bulk one, which have a better heat exchange performance due to a significantly smaller thickness of the water layer on the wet side of a wall separating wet and dry channels in the M-cycle heat/mass exchanger. A hint for producing materials with surface capillarity can be found in nature. For example, the surface capillarity of Pitcher plant stems from parallel microchannels on its peristome surface . In this work, we create a polymer (Nylon 6) material, the surface capillary of which results from parallel microgrooves similar to the Pitcher plant microchannels. Nylon 6 (polyamide) is a widely used polymer in a large variety of applications due to its excellent mechanical, thermal, chemical, and other properties. To produce microgrooves on Nylon 6, we use a femtosecond laser nano/microstructuring technology [15–18] based on direct laser ablation [19–21]. Using this approach, various capillary surface structures have been previously produced on metals [22–24], semiconductors [25–27], and glasses [28,29]. Here, using the direct femtosecond laser nano/microstructuring approach, we produce a 1D array of parallel microgrooves on the Nylon 6 substrate surface, rendering it extremely wicking. The produced surface structure is hierarchical and includes both nano- and microscale structural features. High-speed imaging of water rise vertically uphill against the gravity allowed us to identify a series of capillary flow regimes with h ∝ t, h ∝ t1/2, and h ∝ t1/3 dynamics and to track the onset and evolution of the precursor front. For the first time, we found an initial h ∝ t capillary flow regime in the multiscale hierarchical polymeric structure. Furthermore, our new finding is that the onset of the precursor front occurs in the h ∝ t regime. In contrast to the well-studied both classical Washburn h ∝ t1/2 regime and capillary flow regimes after it, the initial h ∝ t stage preceding to Washburn’s law was not in a focus of research activities in the past and its understanding is very limited. However, the importance of understanding capillary flow regimes prior to Washburn’s stage has become recently a critical issue due to the current trend in miniaturization of microfluidic devices, where the length of capillary channels is small (few millimeters). Our new findings contribute to this important field in microfluidics. Our study of capillary flow dynamics shows fast water spreading on the laser-structured surface, indicating a high potential of the created material for application in M-cycle [8–12] and other technologies [1–7].
2. Experimental setup
Nylon 6 plates were purchased from Goodfellow. The received plates were cleaned with alcohol and then processed using a laser setup similar to described elsewhere . The femtosecond laser (Astrella, Coherent Inc.) that we use for processing the samples generates 83-fs pulses with energy about 7 mJ/pulse at a maximum repetition rate of 1 kHz with a central wavelength of 800 nm. The laser beam is focused onto a sample by a lens with a focal distance of 150 mm. A half-wave plate and polarizing beamsplitter cube are used to vary laser power. We produce a 1D array of parallel microgrooves on the Nylon 6 sample by raster scanning the sample across the laser beam using a computer-controlled X-Y translation stage. Laser processing parameters for producing an efficient wicking structure were found by varying laser fluence, focal laser spot diameter, pulse repetition rate, step between scanning lines, and scanning speed. Laser processing of the sample is performed in atmospheric air. Here, to produce wicking surface structure, we use laser fluence of F = 2.9 J/cm2, focused laser spot size of d = 120 µm, pulse repetition rate of p = 1000 Hz, step between scanning lines of S = 100 µm, and scanning speed of V = 2.5 mm/s. Effects of different exposure modes on stationary water contact angle θ are shown in Table 1. The contact angle was measured with an OSA 200 system (Ningbo NB Scientific Instruments) using video recording mode at a speed of 30 fps, allowing to measure the contact angle as a function of time after drop deposition on the laser-treated surface. The data in Table 1 show both stationary contact angle θ and time tCA when stationary water contact angle is achieved. A surface structure that exhibits both θ ≈ 0° and the smallest tCA is selected. The dimensions of the laser-structured area are 25 mm × 40 mm. The laser processed samples are characterized by both optical microscopy (3D laser scanning microscope VK-X1100 from Keyence) and scanning electron microscopy (SEM) (Zeiss Sigma 300).
The capillary rise dynamics of a liquid is studied on a vertically-positioned sample using the experimental setup shown in Fig. 1. A high-speed VEO 710L Phantom camera at a speed of 1000 frames per second is used to capture liquid spreading. The spatial resolution of video recording is about 100 µm. The studied liquid is de-ionized water. To accurately identify the moment (t = 0) when the liquid touches the sample, we use a glass reservoir filled with water slightly above the reservoir edge for sharp capturing the moment when the sample touches a convex water surface. The water-sample contact is realized by slow translating the water container vertically towards the sample using a computer-controlled translation stage. This makes a gentle and reproducible contact of water with the sample edge. All experiments were performed at the ambient temperature of 23°C.
3. Results and discussion
Figure 2(a) shows a photograph of the laser-structured Nylon 6 sample. Structural features of the treated surface are shown in Figs. 2(b)–2(e). The period and depth of the microgrooves are about 100 and 75 µm, respectively. SEM images in Figs. 2(d) and 2(e) demonstrate that the surface of microgrooves is extensively textured with random nano- and fine micro-structures of various shapes and sizes in a range between 30 nm and 10 µm, similar to previously laser-produced microgrooves on metals , semiconductors , and glasses . A water drop placed on horizontal laser-treated surface quickly spreads and forms a thin film with a contact angle close to zero, indicating that the treated surface is superhydrophilic . For comparison, the contact angle of a water drop deposited on an untreated surface is measured to be 63°.
Figure 3 shows a typical snapshot of water rise on the surface of a vertically-positioned sample at t = 382 ms. The Visualization 1 demonstrates a video of water spreading, where one can directly see how quickly water runs uphill on the surface of the laser-structured polymer. Figure 4(a) shows the plot of capillary rise height on the vertically-oriented surface as a function of time obtained from processing of the video shown in the Visualization 1. When the edge of the microgroove array touches the water surface, water quickly penetrates into the microgrooves and undergoes several flow stages during its spreading vertically uphill. In the initial stage, the water spreading has a single front but at a certain time a thin precursor film forms ahead of this initial main front, resulting in a capillary flow with two distinguishable fronts as shown both in the snapshot in Fig. 3 and in Fig. 4(a), where h(t) plots for both fronts are demonstrated. To understand the capillary rise in the initial stage, we plotted the water front spreading velocity as a function of time in Fig. 4(b). At t = 1 ms the spreading velocity is found to be about 12 cm/s (h ≈ 100 µm) and then it decreases to about 1.2 cm/s in a time domain between 1 ms and 39 ms. In this time domain, the velocity value undergoes significant fluctuations that can be explained by the pinning effect induced by the roughness of the microgroove surface . These fluctuations hinder the identification of the capillary flow scaling law at t < 39 ms in our experiment. In a time domain 39 < t < 100 ms, the capillary rise velocity is observed to be constant, indicating h ∝ t scaling law of capillary spreading, referred to as the inertial regime . This linear capillary flow stage is marked in Fig. 4(a) and is shown in detail in Fig. 4(c). Figures 4(b) and 4(c) clearly show that double front spreading begins at t ≈ 95-100 ms in h ∝ t stage. As seen in Figs. 4(b) and 4(c), after the formation of the precursor front, the main front continues to move at the same constant speed as before, and the h ∝ t regime ends at t ≈ 124 ms when the capillary rise of the main front is about 2 mm. Thus, the time domain of the linear spreading is between 39 and 124 ms. Although the linear regime has been previously studied in a few capillary systems [32–38], its understanding is currently to a large extent insufficient. The h ∝ t stage precedes the classical Washburn h ∝ t1/2 dynamics. The Washburn capillary flow regime is marked in Fig. 4(a) for both main and precursor fronts. Figure 4(a) shows that Washburn’s regime does not begin immediately after the linear regime but there is a transitional time span between these regimes. As seen in Fig. 4(a), Washburn’s regime takes place between 200 and 2100 ms for the precursor front, while it lasts between 400 and 2200 ms for the main front. Figure 4(d) shows the plots of h as a function of t1/2 for these time intervals, where it is seen that this dependence is linear, indicating the Washburn t1/2 dynamics. In the Washburn flow regime, the capillary pressure is balanced by viscous drag; and the classical equation derived by Washburn for the flow in a capillary tube  reads33,39–42], closed microchannels , nanochannels [44–46], open microgrooves [47–50], arrays of micropillars [51–53], porous materials , and others . For V-microgrooves, the Washburn capillary flow is given by h2 = K(α,θ)[γd0/µ]t, where d0 is the groove depth and K(α,θ) is the geometry term with α being the groove angle . Our study shows that the Washburn dynamics is also observed in the microgrooves with extensively structured walls, providing an additional evidence of the universal nature of Washburn’s law.
The data in Fig. 4(a) show h ∝ t1/3 dynamics of the capillary flow after the Washburn stage for both precursor and main fronts. Detailed plots of the h ∝ t1/3 regime are shown in Fig. 4(e), where h as a function of t1/3 is shown, demonstrating a linear dependence. It is seen that the t1/3 flow stage in our structure begins at 2200 and 2700 ms for the precursor and main fronts, respectively. Previously, the h ∝ t1/3 dynamics has been observed in corners , microgrooves , and micropillar array . In particular, Deng et al.  have observed the t1/3 flow regime for acetone and ethanol in an array of V-microgrooves produced on a copper surface and found that it is given by50], where the h ∝ t1/2 regime quickly changes to h ∝ t1/3 one, the capillary rise in our structure exhibits a rather long transition from h ∝ t1/2 to h ∝ t1/3 that lasts 100 and 500 ms for the precursor and main fronts, respectively [see Fig 4(a)]. The t1/3 imbibition dynamics results from a hybrid balance of the capillary drive and both viscous and gravitational drags . Due to increasing gravitational drag, the h ∝ t1/3 regime comes to an end at a certain time. In our capillary structure, the h ∝ t1/3 regime ends at 2800 and 4900 ms for the precursor and main fronts, respectively. The water front height at the end of the h ∝ t1/3 regime reaches 36.8 and 30.3 mm for the precursor and main fronts, respectively, as seen in Fig. 4(a). In the study by Deng et al. , the h ∝ t1/3 flow regime in their V-microgroove structure changes to an exponential behavior that is the final stage of capillary flow. In our study, after the t1/3 stage the capillary flow continues with decreasing velocity, and the main front rises to a height of 38.5 mm at 6600 ms, actually, reaching the top edge of the laser-treated area (40 mm) as marked in Fig. 4(a). The precursor front rises to a height of 39.8 mm at 3500 ms, indicating excellent capillary properties of the created wicking polymer material in terms of the speed and distance of the transported liquid. This capillary flow features are important in solving critically important problem of eliminating dry-out spots in evaporative heat and mass exchangers.
In this study, using the direct femtosecond laser nano/microstructuring method, we created the wicking polymer material with excellent surface capillarity that makes water run vertically uphill against the gravity over a long distance at a high speed. The surface structure of the created wicking material is an array of parallel microgrooves, the surface of which is extensively textured with a combination of random nanostructures and fine microstructures. We find that water spreading in this surface structure of high morphological complexity undergoes a series of capillary flow regimes, including h ∝ t, h ∝ t1/2, and h ∝ t1/3 flow dynamics. Initially, water spreading occurs with a single (main) front, from which at a certain time a precursor front forms and advances ahead of the main one. Our new finding is the fact of existing an initial h ∝ t capillary flow regime in a multiscale hierarchical polymeric structure. Another new finding is that the formation of the precursor front occurs in h ∝ t flow regime. These findings are important for understanding the initial capillary flow stages preceding Washburn’s regime, which have recently attracted the research interest due to the miniaturization trend in microfluidic devices. The flow regimes identified in our study do not immediately change from one to other but are separated with the transitions of a rather long duration. The excellent capillary properties of the created polymer material may find applications in M-cycle air-conditioning, microfluidics, chemical and biological sensors, optofluidics, microreactors, lab-on-a-chip technologies, and micro total analysis systems (µTAS).
National Development and Reform Commission (D61012018002); Chongqing Basic and Frontier Research Project (cstc2018jcyjAX0209).
1. G. M. Whitesides, “The origins and the future of microfluidics,” Nature 442(7101), 368–373 (2006). [CrossRef]
2. P. N. Nge, C. I. Rogers, and A. T. Woolley, “Advances in microfluidic materials, functions, integration and applications,” Chem. Rev. 113(4), 2550–2583 (2013). [CrossRef]
3. C. Monat, P. Domachuk, and B. J. Eggleton, “Integrated optofluidics: a new river of light,” Nat. Photonics 1(2), 106–114 (2007). [CrossRef]
4. D. Erickson, D. Sinton, and D. Psaltis, “Optofluidics for energy applications,” Nat. Photonics 5(10), 583–590 (2011). [CrossRef]
5. P. Abgrall and A. M. Gue, “Lab-on-chip technologies: making a microfluidic network and coupling it into a complete microsystem – a review,” J. Micromech. Microeng. 17(5), R15–R49 (2007). [CrossRef]
6. S. Nagrath, L. V. Sequist, S. Maheswaran, D. W. Bell, D. Irimia, L. Ulkus, M. R. Smith, E. L. Kwak, S. Digumarthy, A. Muzikansky, P. Ryan, U. J. Bails, R. G. Tompkins, D. A. Haber, and M. Toner, “Isolation of rare circulating tumour cells in cancer patients by microchip technology,” Nature 450(7173), 1235–1239 (2007). [CrossRef]
7. G. Xue, Y. Xu, T. Ding, J. Li, J. Yin, W. Fei, Y. Cao, J. Yu, L. Yuan, L. Gong, J. Chen, S. Deng, J. Zhou, and W. Guo, “Water-evaporation-induced electricity with nanostructured carbon materials,” Nat. Nanotechnol. 12(4), 317–321 (2017). [CrossRef]
8. Z. Duan, C. Zhan, X. Zhang, M. Mustafa, X. Zhao, B. Alimohammadisagvand, and A. Hasan, “Indirect evaporative cooling: past, present and future potentials,” Renewable Sustainable Energy Rev. 16(9), 6823–6850 (2012). [CrossRef]
9. M. H. Mahmood, M. Sultan, T. Miyazaki, S. Koyama, and V. S. Maisotsenko, “Overview of the Maisotsenko cycle – A way towards dew point evaporative cooling,” Renewable Sustainable Energy Rev. 66, 537–555 (2016). [CrossRef]
10. H. Caliskan, A. Hepbasli, I. Dincer, and V. Maisotsenko, “Thermodynamic performance assessment of a novel air cooling cycle: Maisotsenko cycle,” Int. J. Refrig. 34(4), 980–990 (2011). [CrossRef]
11. S. Anisimov and D. Pandelidis, “Numerical study of the Maisotsenko cycle heat and mass exchanger,” Int. J. Heat Mass Transfer 75, 75–96 (2014). [CrossRef]
12. P. Xu, X. Ma, X. Zhao, Y. Xiong, and Y. Sun, “Feasibility analysis for a novel dew point air cooler applied in warm and humid climate: a case study in Beijing,” Energy Procedia 158, 2126–2131 (2019). [CrossRef]
13. W. Z. Gao, Y. P. Cheng, A. G. Jiang, T. Liu, and K. Anderson, “Experimental investigation on integrated liquid desiccant – Indirect evaporative air cooling system utilizing the Maisotesenko-Cycle,” Appl. Therm. Eng. 88, 288–296 (2015). [CrossRef]
14. H. Chen, P. Zhang, L. Zhang, H. Liu, Y. Jiang, D. Zhang, Z. Han, and L. Jiang, “Continuous directional water transport on the peristome surface of Nepenthes alata,” Nature 532(7597), 85–89 (2016). [CrossRef]
15. A. Y. Vorobyev and C. Guo, “Direct femtosecond laser surface nano/microstructuring and its applications,” Laser Photonics Rev. 7(3), 385–407 (2013). [CrossRef]
16. J. Cheng, C. Liu, S. Shang, D. Liu, W. Perrie, G. Dearden, and K. Watkins, “A review of ultrafast laser materials micromachining,” Opt. Laser Technol. 46, 88–102 (2013). [CrossRef]
17. K. M. T. Ahmmed, C. Grambow, and A. M. Kietzig, “Fabrication of micro/nano structures on metals by femtosecond laser micromachining,” Micromachines 5(4), 1219–1253 (2014). [CrossRef]
18. H. Pazokian, A. Selimis, J. Barzin, S. Jelvani, M. Mollabashi, C. Fotakis, and E. Stratakis, “Tailoring the wetting properties of polymers from highly hydrophilic to superhydrophobic using UV laser pulses,” J. Micromech. Microeng. 22(3), 035001 (2012). [CrossRef]
19. M. V. Shugaev, C. Wu, O. Armbruster, A. Naghilou, N. Brouwer, D. S. Ivanov, T. J. Y. Derrien, N. M. Bulgakova, W. Kautek, B. Rethfeld, and L. V. Zhigilei, “Fundamentals of ultrafast laser-material interaction,” MRS Bull. 41(12), 960–968 (2016). [CrossRef]
20. E. G. Gamaly, Femtosecond Laser-Matter Interaction: Theory, Experiments and Applications (Pan Stanford Publishing, 2011).
21. M. E. Povarnitsyn, V. B. Fokin, P. R. Levashov, and T. E. Itina, “Molecular dynamics simulation of subpicosecond double-pulse laser ablation of metals,” Phys. Rev. B 92(17), 174104 (2015). [CrossRef]
22. A. Y. Vorobyev and C. Guo, “Metal pumps liquid uphill,” Appl. Phys. Lett. 94(22), 224102 (2009). [CrossRef]
23. Z. Zhu, G. Li, J. Li, H. Xie, Y. Hu, J. Chu, and W. Huang, “Self-driven flow in surface grooves fabricated by femtosecond laser,” Surf. Coat. Technol. 242, 246–250 (2014). [CrossRef]
24. U. Hermens, S. Kirner, C. Emonts, P. Comanns, E. Skoulas, A. Mimidis, H. Mescheder, K. Winands, J. Krüger, E. Stratakis, and J. Bonse, “Mimicking lizard-like surface structures upon ultrashort laser pulse irradiation of inorganic materials,” Appl. Surf. Sci. 418, 499–507 (2017). [CrossRef]
25. A. Y. Vorobyev and C. Guo, “Laser turns silicon superwicking,” Opt. Express 18(7), 6455–6460 (2010). [CrossRef]
26. T. Wang, L. Jiang, X. Li, J. Hu, Q. Wang, S. Ye, H. Zhang, and Y. Lu, “Controllable anisotropic wetting characteristics on silicon patterned by slit-based spatial focusing of femtosecond laser,” Opt. Express 24(22), 25732–25741 (2016). [CrossRef]
27. S. A. Romashevskiy and A. V. Ovchinnikov, “Functional surfaces with enhanced heat transfer for spray cooling technology,” High Temp. 56(2), 255–262 (2018). [CrossRef]
28. A. Y. Vorobyev and C. Guo, “Water sprints uphill on glass,” J. Appl. Phys. 108(12), 123512 (2010). [CrossRef]
29. K. Yin, J. Duan, X. Sun, C. Wang, and Z. Luo, “Formation of superwetting surface with line-patterned nanostructure on sapphire induced by femtosecond laser,” Appl. Phys. A 119(1), 69–74 (2015). [CrossRef]
30. J. Drelich and E. Chibowski, “Superhydrophilic and superwetting surfaces: definition and mechanisms of control,” Langmuir 26(24), 18621–18623 (2010). [CrossRef]
31. R. K. Lade, E. J. Hippchen, C. W. Macosko, and L. F. Francis, “Dynamics of capillary-driven flow in 3D printed open microchannels,” Langmuir 33(12), 2949–2964 (2017). [CrossRef]
32. D. Quere, “Inertial capillarity,” Europhys. Lett. 39(5), 533–538 (1997). [CrossRef]
33. M. Stange, M. E. Dreyer, and H. J. Rath, “Capillary driven flow in circular cylindrical tubes,” Phys. Fluids 15(9), 2587–2601 (2003). [CrossRef]
34. A. Siebold, M. Nardin, J. Schultz, A. Walliser, and M. Oppliger, “Effect of dynamic contact angle on capillary rise phenomena,” Colloids Surf., A 161(1), 81–87 (2000). [CrossRef]
35. W. Huang, Q. Liu, and Y. Li, “Capillary filling flows inside patterned-surface microchannels,” Chem. Eng. Technol. 29(6), 716–723 (2006). [CrossRef]
36. T. Andrukh, D. Monaenkova, B. Rubin, W. K. Lee, and K. G. Kornev, “Meniscus formation in a capillary and the role of contact line friction,” Soft Matter 10(4), 609–615 (2014). [CrossRef]
37. S. Das, P. R. Waghmare, and S. K. Mitra, “Early regimes of capillary filling,” Phys. Rev. E 86(6), 067301 (2012). [CrossRef]
38. M. M. Weislogel and S. Lichter, “Capillary flow in an interior corner,” J. Fluid Mech. 373, 349–378 (1998). [CrossRef]
39. E. W. Washburn, “The dynamics of capillary flow,” Phys. Rev. 17(3), 273–283 (1921). [CrossRef]
40. M. O’Loughlin, K. Wilk, C. Priest, J. Ralston, and M. N. Popescu, “Capillary rise dynamics of aqueous glycerol solutions in glass capillaries: a critical examination of the Washburn equation,” J. Colloid Interface Sci. 411, 257–264 (2013). [CrossRef]
41. D. I. Dimitrov, A. Milchev, and K. Binder, “Capillary rise in nanopores: molecular dynamics evidence for the Lucas-Washburn equation,” Phys. Rev. Lett. 99(5), 054501 (2007). [CrossRef]
42. L. R. Fisher and P. D. Lark, “An experimental study of the washburn equation for liquid flow in very fine capillaries,” J. Colloid Interface Sci. 69(3), 486–492 (1979). [CrossRef]
43. J. Berthier, D. Gosselin, N. Villard, C. Pudda, F. Boizot, G. Costa, and G. Delapierre, “The dynamics of spontaneous capillary flow in confined and open microchannels,” Sens. Transducers 183(12), 123–128 (2014).
44. M. Yang, B. Cao, W. Wang, H. Yun, and B. Chen, “Experimental study on capillary filling in nanochannels,” Chem. Phys. Lett. 662, 137–140 (2016). [CrossRef]
45. J. Haneveld, N. R. Tas, N. Brunets, H. V. Jansen, and M. C. Elwenspoek, “Capillary filling of sub-10 nm nanochannels,” J. Appl. Phys. 104(1), 014309 (2008). [CrossRef]
46. N. R. Tas, J. Haneveld, H. V. Jansen, M. C. Elwenspoek, and A. van den Berg, “Capillary filling speed of water in nanochannels,” Appl. Phys. Lett. 85(15), 3274–3276 (2004). [CrossRef]
47. L. A. Romero and F. G. Yost, “Flow in an open channel capillary,” J. Fluid Mech. 322(1), 109–129 (1996). [CrossRef]
48. R. R. Rye, J. A. Mann, and F. G. Yost, “The flow of liquids in surface grooves,” Langmuir 12(2), 555–565 (1996). [CrossRef]
49. J. Tian, D. Kannangara, X. Li, and W. Shen, “Capillary driven low-cost V-groove microfluidic device with high sample transport efficiency,” Lab Chip 10(17), 2258–2264 (2010). [CrossRef]
50. D. Deng, Y. Tang, J. Zeng, S. Yang, and H. Shao, “Characterization of capillary rise dynamics in parallel micro V-grooves,” Int. J. Heat Mass Transfer 77, 311–320 (2014). [CrossRef]
51. L. Courbin, E. Denieul, E. Dressaire, M. Roper, A. Ajdari, and H. A. Stone, “Imbibition by polygonal spreading on microdecorated surfaces,” Nat. Mater. 6(9), 661–664 (2007). [CrossRef]
52. J. Bico, C. Tordeux, and D. Quere, “Rough wetting,” Europhys. Lett. 55(2), 214–220 (2001). [CrossRef]
53. S. J. Kim, M. W. Moon, K. R. Lee, D. Y. Lee, Y. S. Chang, and H. Y. Kim, “Liquid spreading on superhydrophilic micropillar arrays,” J. Fluid Mech. 680, 477–487 (2011). [CrossRef]
54. J. I. Siddique, D. M. Anderson, and A. Bondarev, “Capillary rise of a liquid into a deformable porous material,” Phys. Fluids 21(1), 013106 (2009). [CrossRef]
55. A. D. Dussaud, P. M. Adler, and A. Lips, “Liquid transport in the networked microchannels of the skin surface,” Langmuir 19(18), 7341–7345 (2003). [CrossRef]
56. A. Ponomarenko, D. Quere, and C. Clanet, “A universal law for capillary rise in corners,” J. Fluid Mech. 666, 146–154 (2011). [CrossRef]
57. N. Obara and K. Okumura, “Imbibition of a textured surface decorated by short pillars with rounded edges,” Phys. Rev. E 86(2), 020601 (2012). [CrossRef]