# Capillary Wicking on Heliamphora minor-Mimicking Mesoscopic Trichomes Array

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Biological Characterization and the Fabrication of Biomimetic Samples

^{−1}spread radially on the pubescent wall and filled the interval at the same time. Therefore, the film thickness increases as the height becomes higher. Finally, the film covers the trichomes and serves as the lubrication layer. Mimicking the pubescent zone, a polymerization-based 3D printer (Mini 8K, Phrozen Tech., Taiwan, China) using an ultraviolet liquid crystal display to initiate the photo reaction of the monomer methyl methacrylate—TiO

_{2}–SiO

_{2}mixture was used (Figure 1k), and the layer resolution and pixel resolution were 20 μm and 18 μm, respectively. After preparation, the mimetic samples were ultrasonically washed in commercial cleaning solutions (Go Print Co., Ningbo, China) for 5 min, dried by N

_{2}flow and post-cured under UV light for 3 min. Oxygen plasma treatment (DT-03, OPS Plasma Technology Co., Shenzhen, China) at an RF power of 300 W for 10 min was performed to adjust surface superhydrophilicity. SEM images of the printed mimetic samples sputtered with a thin layer of platinum (EM ACE, Leica, Wetzlar, Germany) at 10 kV were obtained (Figure 1l). The particles of TiO

_{2}and SiO

_{2}increase surface roughness and enable chemical modification (Figure 1m for energy-dispersive spectrometer).

#### 2.2. Capillary Wicking, High-Flux Siphon Application, and Mass Transportation

_{4}, FeCl

_{3}, and glucose, respectively, into water and repeated the wicking process. After long enough time for evaporation, the solute crystallization from the solution process was recorded using a Nikon D750, which reveals the mass transportation inside the wicking film.

## 3. Results and Discussion

#### 3.1. Capillary Wicking Height and Film Thickness

_{m}, of our fabricated material was determined to be 2200 µm, above which no obvious capillary wicking and interval filling were observed. This limitation is attributed to an insufficient driven pressure in the first interval, while the maximum pitch of two closet trichomes satisfies the condition where the pressure at the advancing meniscus in the first interval, P

_{M}, is balanced by the hydrostatic pressure, P

_{h}, such that

_{M}= P

_{air}− σL/p

_{m}

^{2}= P

_{h}= P

_{air}− ρgp

_{m}

_{m}= (Ll

_{c})

^{1/3}, where l

_{c}is (σ/ρg)

^{1/2}and called the capillary length. For the L = 2 mm used in our experiments, Equation (1) predicted a pitch limitation of 2.4 mm which is consistent with our results.

#### 3.2. Microscopic Capillary Wicking Dynamics

_{c}, along the perimeter of trichomes (Figure 3b), water gradually fills the interval and eventually covers almost the whole surface. The competition between the extension of the advancing meniscus on the substrate and the water spreading on the surface of trichomes contributes to the oscillation of film thickness in single interval that delays the spreading process.

_{c}= σπd

_{n}, where π is the circular constant and d

_{n}is the contact diameter of the trichomes in the nth row, decrease as the water spreads towards the tip of the trichomes due to their smaller d

_{n}. Additionally, the film thickness in the nth interval, e

_{n}, is non-uniform and decreases as the row number, n, increases (Figure 2c). Consequently, the capillary force along the perimeter of the trichomes varies with n and deforms the liquid–air interface in each interval to different extent during the filling process. Because e

_{n}is obviously influenced by the trichome length, L, as longer trichomes support a thicker film, the ratio between e

_{n}and L, denoted as α

_{n}, is utilized as a dimensionless quantity to describe the profile of the film. In the case of trichome lengths of 1 mm, 2 mm, and 3 mm, the variation of α

_{n}with n shows a similar tendency, suggesting a self-similarity of the film profile.

_{n}[φ(z + ∆z) − φ(z)]

_{n}~e

_{n}p is the cross-sectional area perpendicular to the z axis. Considering an infinitely small step as ∆z approaches 0, and dividing Equations (2) and (3) by ∆z, their differential forms are given as

_{n}dφ/dz

_{n}. Substituting T into Equation (5) as well as the path, φ, by the profile function, f(z), obtains an equation describing the f(z):

^{2}= K

_{n}(1 + (f′)

^{2})

^{1/2}

_{n}= ρgS

_{n}/F is a constant related to the film thickness, e

_{n}. The boundary conditions are rigorously adjusted by the curvature at the contact points A and B to satisfy the Laplace pressure balance of the hydrostatic pressure.

_{n}/(K

_{n}z + C)

^{2}

_{n}modified to K

_{n}

_{+1}.

#### 3.3. Macroscopic Capillary Wicking Dynamics

^{1/10}; and the regime between the two stages is called the inertia–viscosity transition, which is described by the Lucas–Washburn equation as H~t

^{1/2}. However, mesoscopic structures enhance surface energy release and reduce the velocity gradient, which determine the viscous drag. The Reynolds number, Re = ρue

_{n}/μ, is O(10

^{2}), indicating that inertia dominates over viscosity, where u is the wicking velocity and μ is the viscosity of the liquid. The Bond number, Bo = ρgHe

_{n}/σ, is O(10

^{−2}), implying that the influence of gravity is negligible. Therefore, the governing equation for the mesoscopic wicking dynamics of a single interval column takes the following form:

_{n}, where k is a geometric factor and u = H′ is the first derivative of H. Considering that the thickness relates to the wicking height as e

_{n}~βH (Figure 3c), m is expressed as k′ρH

^{2}p, where k′ = kβ and a different scaling law can be obtained from Equation (8) (see Appendix A for detail):

_{c}, with respect to normalized time, σt/μ, was used to assess deviations from the expected tendency of different liquids (Figure 4d). The results indicate that all liquids follow the scaling law at the beginning, but deviate from their expected tendencies in the late stage because the viscosity-negligible condition that Re is large does not hold for thin films of viscous liquids such as silicone oil and ethylene glycol in our experiments.

#### 3.4. High-Flux Open Siphon Applications and Mass Transportation

_{out}− h

_{in}, where h

_{in}is the height difference from the inlet tank’s bottom to irs ridge top and h

_{out}is the height difference from the outlet tank’s bottom to its ridge top, influences the siphon flux [43] (Figure 5c).

_{in}, which determines the driving pressure difference across the free surface. The flux of our trichomes array achieved an open siphon, which is also strongly influenced by the h

_{in}, which the maximum flux reduces to half when the h

_{in}increases from 1.00 cm to 1.25 cm. Except for the maximum flux, flux under small two-sided height differences is enhanced by capillarity if the h

_{in}is small, which is attributed to a larger Laplace pressure difference across the meniscus for a small h

_{in}. Siphon applications that require high flux such as irrigation systems and drainage systems can be enhanced by adding a trichomes array with an optimized height difference on their surface.

## 4. Conclusions

^{2/3}, which is distinct from the H~t

^{1/2}observed in traditional capillary rising or wicking on surfaces modified with microscopic structures. Because the thickness and wicking dynamics are independent, high flux and fast speed can be achieved at the same time, which can improve the flow efficiency and has potential in applications such as high-flux siphons. Finally, we examined the mass transportation inside the film and observed thin-film evaporation, resulting in solute crystallization at higher levels first, which indicates a method utilized by the plant to transport nutrients in the digestive fluid from the pitcher to the upper pubescent zone, assisting in the attraction of insects. This work, exploring the capillary wicking phenomena on mesoscopic structures, advances our understanding of high-flux wetting behaviors and improves the design of efficient liquid transfer devices.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

- Let w(z) = f′(z), and the equation transforms into$$-\frac{dw}{{w}^{2}\sqrt{1+{w}^{2}}}={K}_{n}d\mathrm{z}$$$$\frac{1+{w}^{2}}{w}={K}_{n}\mathrm{z}+C$$
_{n}z + c as$$\left|w\right|=1/\sqrt{{v}^{2}-1}$$ - The solution of w from Equation (A3) can be obtained by substituting w(z) = f′(z) = K
_{n}f′(v):$$|w|\text{}=\text{}|{K}_{n}f\prime (v\left)\right|\text{}=1/\sqrt{{v}^{2}-1}$$$$f(v)=C\prime +\left\{\begin{array}{c}\frac{\mathrm{ln}\left|v\text{}+\text{}\sqrt{{v}^{2}\text{}+\text{}1}\right|}{{K}_{n}}\hspace{1em}v1\\ \frac{\mathrm{ln}\left|v\text{}-\text{}\sqrt{{v}^{2}\text{}-\text{}1}\right|}{{K}_{n}}\hspace{1em}v-1\end{array}\right.$$ - From Equation (A5), the curvature of meniscus κ, which is defined as$$\kappa =\frac{\left|f\u2033\right|}{{\left(1+{f\prime}^{2}\right)}^{\frac{3}{2}}}$$
_{n}/(K_{n}z + C)^{2}.

- Take m = k′ρH
^{2}p and u = H′ into consideration; eliminating p obtainsH^{2}H″ + 2H(H′)^{2}= σ*/pk′ - Let Φ(H) = H′; Equation (A7) can be transformed intoH
_{2}ΦΦ′ + 2HΦ^{2}= σ*/pk′Φ^{2}= 2σ*/3pHk′ + C_{1}/H^{4}_{1}is an integral constant. - Replace Φ with H′, and the solution to Equation (A9) can be acquired as2H
^{3}σ*/3pk′ + C_{1}= (tσ*/pk′ + C_{2})^{2}_{1}= C_{2}^{2}. If the initial velocity is considered infinitely small or zero, the simplest form of the scaling law is Equation (9), that is C_{1}= C_{2}= 0.

## Appendix B

Symbols | Definition | Unit |
---|---|---|

σ | Surface tension | N/m |

ρ | Density of liquids | kg/m^{3} |

μ | Viscosity of liquids | Pa·s |

g | Gravitational acceleration constant | kg·m/s^{2} |

l_{c} | Capillary length | m |

L | Length of trichomes | m |

p | Center-to-center pitch of trichome’s base | m |

d | Diameter of trichome’s base | m |

H | Capillary wicking height | m |

u | Capillary wicking velocity | m/s |

T | Tension force on meniscus profile | N |

θ | Deflection angle of profile tangent with respect to the z direction | ° |

F | Constant lateral force representing Tsinθ | N |

f | Function describing the meniscus profile | \ |

φ | Path length from point B to P | m |

e_{n} | Thickness in the nth interval | m |

α_{n} | Ratio of thickness to trichome length | \ |

S_{n} | Area of cross-section perpendicular to z axis | m^{2} |

K_{n} | Coefficient equals ρgS_{n}/F | m^{−1} |

κ | Curvature of meniscus | m^{−1} |

## References

- Bico, J.; Tordeux, C.; Quéré, D. Rough wetting. Europhys. Lett.
**2001**, 55, 214–220. [Google Scholar] [CrossRef] - Bico, J.; Thiele, U.; Quéré, D. Wetting of textured surfaces. Colloids Surf. A Physicochem. Eng. Asp.
**2002**, 206, 41–46. [Google Scholar] [CrossRef] - Ishino, C.; Reyssat, M.; Reyssat, E.; Okumura, K.; Quéré, D. Wicking within forests of micropillars. Europhys. Lett.
**2007**, 79, 56005. [Google Scholar] [CrossRef] - Kim, J.; Moon, M.-W.; Kim, H.-Y. Dynamics of hemiwicking. J. Fluid Mech.
**2016**, 800, 57–71. [Google Scholar] [CrossRef] - Chen, X.; Chen, J.; Ouyang, X.; Song, Y.; Xu, R.; Jiang, P. Water Droplet Spreading and Wicking on Nanostructured Surfaces. Langmuir
**2017**, 33, 6701–6707. [Google Scholar] [CrossRef] [PubMed] - Lee, J.; Suh, Y.; Dubey, P.P.; Barako, M.T.; Won, Y. Capillary Wicking in Hierarchically Textured Copper Nanowire Arrays. ACS Appl. Mater. Interfaces
**2019**, 11, 1546–1554. [Google Scholar] [CrossRef] [PubMed] - Lee, J.H.; Jung, B.; Park, G.-S.; Kim, H.-Y. Condensation and wicking of water on solid nanopatterns. Phys. Rev. Fluid
**2022**, 7, 024202. [Google Scholar] [CrossRef] - Courbin, L.; Denieul, E.; Dressaire, E.; Roper, M.; Ajdari, A.; Stone, H.A. Imbibition by polygonal spreading on microdecorated surfaces. Nat. Mater.
**2007**, 6, 661–664. [Google Scholar] [CrossRef] [PubMed] - McHale, G. Surface wetting: Liquids shape up nicely. Nat. Mater.
**2007**, 6, 627–628. [Google Scholar] [CrossRef] [PubMed] - Li, J.; Song, Y.; Zheng, H.; Feng, S.; Xu, W.; Wang, Z. Designing biomimetic liquid diodes. Soft Matter
**2019**, 15, 1902–1915. [Google Scholar] [CrossRef] - Gelebart, A.H.; Mc Bride, M.; Schenning, A.P.H.J.; Bowman, C.N.; Broer, D.J. Photoresponsive Fiber Array: Toward Mimicking the Collective Motion of Cilia for Transport Applications. Adv. Funct. Mater.
**2016**, 26, 5322–5327. [Google Scholar] [CrossRef] - Zhang, S.; Huang, J.; Chen, Z.; Yang, S.; Lai, Y. Liquid mobility on superwettable surfaces for applications in energy and the environment. J. Mater. Chem. A
**2019**, 7, 38–63. [Google Scholar] [CrossRef] - Dittrich, P.S.; Manz, A. Lab-on-a-chip: Microfluidics in drug discovery. Nat. Rev. Drug Discov.
**2006**, 5, 210–218. [Google Scholar] [CrossRef] [PubMed] - Si, Y.; Wang, T.; Li, C.; Yu, C.; Li, N.; Gao, C.; Dong, Z.; Jiang, L. Liquids Unidirectional Transport on Dual-Scale Arrays. ACS Nano
**2018**, 12, 9214–9222. [Google Scholar] [CrossRef] [PubMed] - van Erp, R.; Soleimanzadeh, R.; Nela, L.; Kampitsis, G.; Matioli, E. Co-designing electronics with microfluidics for more sustainable cooling. Nature
**2020**, 585, 211–216. [Google Scholar] [CrossRef] [PubMed] - Quéré, D. Wetting and Roughness. Annu. Rev. Mater. Res.
**2008**, 38, 71–99. [Google Scholar] [CrossRef] - Kim, S.J.; Moon, M.-W.; Lee, K.-R.; Lee, D.-Y.; Chang, Y.S.; Kim, H.-Y. Liquid spreading on superhydrophilic micropillar arrays. J. Fluid Mech.
**2011**, 680, 477–487. [Google Scholar] [CrossRef] - Hancock, M.J.; Sekeroglu, K.; Demirel, M.C. Bioinspired Directional Surfaces for Adhesion, Wetting and Transport. Adv. Funct. Mater.
**2012**, 22, 2223–2234. [Google Scholar] [CrossRef] - Chen, H.; Zhang, P.; Zhang, L.; Liu, H.; Jiang, Y.; Zhang, D.; Han, Z.; Jiang, L. Continuous directional water transport on the peristome surface of Nepenthes alata. Nature
**2016**, 532, 85–89. [Google Scholar] [CrossRef] - Krishnan, S.R.; Bal, J.; Putnam, S.A. A simple analytic model for predicting the wicking velocity in micropillar arrays. Sci. Rep.
**2019**, 9, 20074. [Google Scholar] [CrossRef] - Feng, S.; Zhu, P.; Zheng, H.; Zhan, H.; Chen, C.; Li, J.; Wang, L.; Yao, X.; Liu, Y.; Wang, Z. Three-dimensional capillary ratchet-induced liquid directional steering. Science
**2021**, 373, 1344–1348. [Google Scholar] [CrossRef] - Lecointre, P.; Laney, S.; Michalska, M.; Li, T.; Tanguy, A.; Papakonstantinou, I.; Quéré, D. Unique and universal dew-repellency of nanocones. Nat. Commun.
**2021**, 12, 3458. [Google Scholar] [CrossRef] [PubMed] - Zhu, Q.; Li, B.; Li, S.; Luo, G.; Zheng, B.; Zhang, J. Superamphiphobic Cu/CuO Micropillar Arrays with High Repellency towards Liquids of Extremely High Viscosity and Low Surface Tension. Sci. Rep.
**2019**, 9, 702. [Google Scholar] [CrossRef] [PubMed] - de Gennes, P.-G.; Brochard-Wyart, F.; Quéré, D.; Reisinger, A.; Widom, B. Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves; Springer: New York, NY, USA, 2004. [Google Scholar]
- Delannoy, J.; Lafon, S.; Koga, Y.; Reyssat, É.; Quéré, D. The dual role of viscosity in capillary rise. Soft Matter
**2019**, 15, 2757–2761. [Google Scholar] [CrossRef] [PubMed] - Yuan, Q.; Zhao, Y.-P. Multiscale dynamic wetting of a droplet on a lyophilic pillar-arrayed surface. J. Fluid Mech.
**2013**, 716, 171–188. [Google Scholar] [CrossRef] - Washburn, E.W. The Dynamics of Capillary Flow. Phys. Rev.
**1921**, 17, 273–283. [Google Scholar] [CrossRef] - Quéré, D. Inertial capillarity. Europhys. Lett.
**1997**, 39, 533. [Google Scholar] [CrossRef] - Kim, J.; Moon, M.-W.; Kim, H.-Y. Capillary rise in superhydrophilic rough channels. Phys. Fluids
**2020**, 32, 032105. [Google Scholar] [CrossRef] - Jaffe, K.; Michelangeli, F.; Gonzalez, J.M.; Miras, B.; Christine Ruiz, M. Carnivory in pitcher plants of the genus Heliamphora (Sarraceniaceae). New Phytol.
**1992**, 122, 733–744. [Google Scholar] [CrossRef] - Bauer, U.; Scharmann, M.; Skepper, J.; Federle, W. ‘Insect aquaplaning’ on a superhydrophilic hairy surface: How Heliamphora nutans Benth. pitcher plants capture prey. Proc. R. Soc. Lond. B Biol. Sci.
**2013**, 280, 20122569. [Google Scholar] [CrossRef] - Wang, X.; Shen, C.; Meng, P.; Tan, G.; Lv, L. Analysis and review of trichomes in plants. BMC Plant Biol.
**2021**, 21, 70. [Google Scholar] [CrossRef] - Vogler, E.A. Structure and reactivity of water at biomaterial surfaces. Adv. Colloid Interface Sci.
**1998**, 74, 69–117. [Google Scholar] [CrossRef] - Jurin, J., II. An account of some experiments shown before the Royal Society; with an enquiry into the cause of the ascent and suspension of water in capillary tubes. Philos. Trans. R. Soc. Lond.
**1718**, 30, 739–747. [Google Scholar] [CrossRef] - Weislogel, M.M. Compound capillary rise. J. Fluid Mech.
**2012**, 709, 622–647. [Google Scholar] [CrossRef] - Das, S.; Mitra, S.K. Different regimes in vertical capillary filling. Phys. Rev. E
**2013**, 87, 063005. [Google Scholar] [CrossRef] - Tanner, L.H. The spreading of silicone oil drops on horizontal surfaces. J. Phys. D Appl. Phys.
**1979**, 12, 1473. [Google Scholar] [CrossRef] - de Gennes, P.G. Wetting: Statics and dynamics. Rev. Mod. Phys.
**1985**, 57, 827–863. [Google Scholar] [CrossRef] - Delgadino, M.G.; Mellet, A. On the Relationship between the Thin Film Equation and Tanner’s Law. Commun. Pure Appl. Math.
**2021**, 74, 507–543. [Google Scholar] [CrossRef] - Ganci, S.; Yegorenkov, V. Historical and pedagogical aspects of a humble instrument. Eur. J. Phys.
**2008**, 29, 421–430. [Google Scholar] [CrossRef] - Boatwright, A.; Hughes, S.; Barry, J. The height limit of a siphon. Sci. Rep.
**2015**, 5, 16790. [Google Scholar] [CrossRef] - Wang, K.; Sanaei, P.; Zhang, J.; Ristroph, L. Open capillary siphons. J. Fluid Mech.
**2022**, 932, R1. [Google Scholar] [CrossRef] - Yu, K.; Cheng, Y.-G.; Zhang, X.-X. Hydraulic characteristics of a siphon-shaped overflow tower in a long water conveyance system: CFD simulation and analysis. J. Hydrodyn. Ser. B
**2016**, 28, 564–575. [Google Scholar] [CrossRef]

**Figure 1.**Characterization of Heliamphora minor and fabrication of biomimetic trichomes. (

**a**) Optical images of H. minor; (

**b**) sectional view of pitcher inside wall, above is a pubescent zone and below is a smooth zone; (

**c**) stereomicroscope of the red-box-indicated region in (

**b**); (

**d**) SEM image of the yellow-box-indicated region in (

**c**), trichomes of length L and base diameter d are arranged with a mutual pitch, p; (

**e**) statistical analysis of L, p, d with normal distribution fitting; (

**f**) illustration of sample resources from pitcher inside wall. The orange and blue boxes indicate the sample from the pubescent zone and smooth zone, respectively; (

**g**) water contact angle on surface of smooth zone; (

**h**) water contact angle changing on surface of pubescent zone, which gradually decreases to ~0°; (

**i**) high-speed front view of water injected from syringe wicking on pubescent zone, the red dotted line indicates the fringe front; (

**j**) high-speed side view of water wicking and filling the trichomes’ intervals, the red dotted line indicates the border of dry and wet regions; (

**k**) schematic of bottom-up 3D printer based on photo-initiated polymerization of resin using liquid crystal display as UV source; (

**l**) SEM images of 3D-printing fabricated biomimetic trichomes array, the left is top view and the right is side view; (

**m**) energy-dispersive spectrometry of printed surface, Si and Ti elements are from SiO

_{2}and TiO

_{2}nanoparticles, which turn the surface superhydrophilic. The inset is a zoomed-in view of the surface. Scale bars: 1 cm in (

**a**,

**b**); 1 mm in (

**c**,

**d**,

**i**,

**j**); 500 µm in (

**l**); 50 µm in (

**m**).

**Figure 2.**Capillary wicking on biomimetic trichomes array. (

**a**) Schematic of capillary wicking on modified surface of superhydrophilic trichomes as the climbing water reaches a height of H. The SEM image shows the biomimetic trichomes array; (

**b**) Oblique view of the wicking process on L = 2 mm, p = 500 µm, d = 200 µm trichomes array; (

**c**) Side view of final wicking state. The film thickness, e, decreases with increasing H; (

**d**) Climbing height, H, changes with time, t, on trichomes arrays of different pitches with fixed L = 2 mm and d = 200 µm; (

**e**) Number of climbed intervals (n) changing with t. To the right are side views of p = 900 µm, 1300 µm, and 1800 µm from top to bottom; (

**f**) Thickness of different intervals changing with t as the water climbs. Scale bars: 500 µm in (

**a**), 2 mm in (

**b**,

**c**).

**Figure 3.**Microscopic capillary wicking dynamics and meniscus profile. (

**a**) Microscopic view of capillary wicking on biomimetic trichomes array. The red dotted line indicates the meniscus front; (

**b**) Schematic of capillary force on the perimeter of the trichomes and the film thickness in the nth interval. e

_{n}= α

_{n}L, where α

_{n}is the ratio between trichome thickness and length, and the meniscus front extends on the substrate to a distance of x from the (n + 1)th row; (

**c**) Self-similarity of film profiles for trichomes arrays of different lengths. The ratio, α

_{n}, changing with n, collapses into a narrow region, implying a similar tendency across the arrays; (

**d**) Catenary line schematic of meniscus AB in the nth interval (left), and force analysis of a small arc PQ in the meniscus of length Δφ (right). The tension force, T, and gravity, G, are two major forces acting on two end points, and the tangential deflection angle is θ; (

**e**) Meniscus profile of different trichome thickness to length ratios, α. Normalized z* = z/p and y* = y/p are used; (

**f**) Film profile reconstructed from Micro-CT scanning. Both cross-sectional views in the y–z plane and perpendicular to z axis follow the catenary line, which results in a pressure gradient that is large at the bottom and small at the top. The blue false color indicates the water phase; (

**f**) Meniscus extending with time, t, in a single interval at H ≈ 13 mm. The insets are in situ snapshots corresponding to the arrow-indicated point. Scale bars: 500 µm in (

**a**,

**f**,

**g**).

**Figure 4.**Macroscopic capillary wicking dynamics and generality of scaling law for different liquids. (

**a**) Capillary wicking height, H, changes with time, t. The dynamics of capillary rise in a closed tube of diameter, d = 0.45 mm, is plotted in gray for comparison, and the logarithm coordinates are used to present the scaling law. The inset enlarges the transition regime between the inertia-dominated regime (H~t) and the viscosity-dominated thin-film spreading regime (H~t

^{1/10}). The scaling law fits the transition regime of capillary wicking that is H~t

^{2/3}when the capillary is H~t

^{1/2}; (

**b**) Properties of different liquids including surface tension, viscosity, and density; (

**c**) Capillary wicking dynamics of different liquids in a trichomes array, with parameters of L = 2 mm, p = 500 μm, and d = 200 μm; (

**d**) Dimensionless capillary wicking height with respect to normalized time. The trends of viscous liquids deviate from that of dyed water (indicated by the red dotted line) in the late stage due to the thin film and as the slow flow of the Reynolds number decreases, meaning viscous dissipation plays an important role in influencing the dynamics.

**Figure 5.**High-flux open siphon application and mass transportation through capillary wicking. (

**a**) Schematic of open siphon construction, the straight surface is bent into an “n” shape with the inlet height difference h

_{in}and outlet height difference h

_{out}, transparent glass was used for the observation of the water flow injected from inlet. The red dotted line to the left indicates the bending position; (

**b**) Comparison between bare and trichomes-array-modified devices shows that no siphon forms on the bare side wall, while spontaneous wicking on the trichomes connects the two sides; (

**c**) Flux measurement of different two-sided height differences for different h

_{in}. Meniscus deformation leads to large Laplace pressure, which enhances the flux, deviating from the fitting tendency; (

**d**) Schematic of mass transportation and thin-film evaporation (I) leading to solute crystallization (II), (III) is the final state. (

**e**) Side and front views of film thinning and solute crystallization. From left to right, the solutes are FeCl

_{3}, CuSO

_{4}, and glucose, respectively. Above the red dotted line is crystallized solute, which reflects light. Scale bars: 1 cm in (

**b**).

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## Share and Cite

**MDPI and ACS Style**

Chen, F.; Cheng, Z.; Jiang, L.; Dong, Z.
Capillary Wicking on *Heliamphora minor*-Mimicking Mesoscopic Trichomes Array. *Biomimetics* **2024**, *9*, 102.
https://doi.org/10.3390/biomimetics9020102

**AMA Style**

Chen F, Cheng Z, Jiang L, Dong Z.
Capillary Wicking on *Heliamphora minor*-Mimicking Mesoscopic Trichomes Array. *Biomimetics*. 2024; 9(2):102.
https://doi.org/10.3390/biomimetics9020102

**Chicago/Turabian Style**

Chen, Fenglin, Ziyang Cheng, Lei Jiang, and Zhichao Dong.
2024. "Capillary Wicking on *Heliamphora minor*-Mimicking Mesoscopic Trichomes Array" *Biomimetics* 9, no. 2: 102.
https://doi.org/10.3390/biomimetics9020102