# Role of Surface Topography in the Superhydrophobic Effect—Experimental and Numerical Studies

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## Abstract

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## 1. Introduction

_{SV}, γ

_{SL}, and γ

_{LV}are surface tensions for interfaces between solid S, liquid L, and vapor V, respectively. This equation is valid only for perfectly flat surfaces. When the real topography of the solid substrate surface is included in Equation (1), the wetting phenomenon becomes much more complex. Depending on the chemistry and roughness of the surface, wetting can be divided into two main regimes: (1) homogeneous wetting (Wenzel model) and (2) heterogeneous wetting (Cassie–Baxter model) [4]. Homogeneous wetting can be described with the Wenzel equation:

_{1}, f

_{2}are surface area fractions and ${\theta}_{1}$, ${\theta}_{2}$ are contact angles on phase 1 and 2. Hence, it is possible to consider air bubbles trapped in hollows on the surface as a second phase, simply by assuming that the air phase has a contact angle of 180°. Therefore, the Cassie–Baxter equation with surface roughness considered can be written as follows [7]:

## 2. Materials and Methods

^{®}finish 77702) was obtained from Akzo Nobel, The Netherlands. It was used in combination with the Aerodur

^{®}HS 37092 2-component amine-cured epoxy primer (Akzo Nobel, Sassenheim, The Netherlands). To modify the topcoat, Fluorosil

^{®}OH C7-F (Siltech, Toronto, ON, Canada), a liquid fluoroalkyl and alkylcarbinol functionalized silicone based on non-PFOS fluoroalkyl chains was utilized. Silicone-based additives are promising for modification of polyurethanes due to the higher energy of bonds (Si-O-Si, 550 kJ·mol

^{−1}) and (Si-C, 369 kJ·mol

^{−1}) present in the silicone chain, in comparison to the energy bonds (C-C, 347 kJ·mol

^{−1}), (C-O, 340 kJ·mol

^{−1}) and (N-C, 335 kJ·mol

^{−1}) existing in polyurethane. Hydrophobicity of the alkyl groups present in the Fluorosil additive causes increased interfacial energy between silicone and polyurethane matrix. A decrease in interfacial energy is achieved via the migration of silicon to the coating surface. This results in altered surface properties including increased hydrophobicity and chemical resistance, even at a low silicon content. [53]. The hydrophobic nanosilica Aerosil

^{®}R805 (Evonik, Hanau, Germany) used in this study has a specific surface area of 125–175 m

^{2}·g

^{−1}and a nominal particle size of 15 nm. It was produced by treating nano-silica with organosilane. The aim of the modified nanosilica addition was to roughen the surface with low surface energy materials and to achieve dual-scale (micro and nano) hierarchical structure. This is one of the essential factors in generating hydrophobic coatings and especially important for obtaining surfaces with low water sliding angles [54]. All the materials mentioned above were used as received. The modified PUR coatings were deposited on 2024 aluminum alloy (WMH Group, Essen, Germany).

^{®}Pilot XIII air spray gun (Wuppertal Vohwinkel, Germany) and left to dry for 3 h. Meanwhile, PUR topcoats with 3 wt.% of nanosilica and Fluorosil additive (5 wt.%) were prepared by mixing using a magnetic stirrer. Before spraying, nano-silica suspensions on the modified PUR coating were prepared by means of an ultrasonic gun (VCX 750, Sonics and Materials Inc., Newtown, CT, USA) for 30 min. The suspension was then sprayed on top of the already applied primer and left to dry for 24 h.

^{−1}and the jump speed was 10 mm·s

^{−1}. The laser spot width was 5µm, so it was possible to obtain overlapping lines for displacement values lower than the beam width. The fabricated surfaces had different patterns and geometry; nine surfaces of parallel laser beam lines with different width and distances between each other were produced. The depth of the grooves was 8 µm. All combinations of groove width and peak width from 5, 10 and 20 µm were manufactured, which resulted in 9 different surface patterns. Samples were denoted as X by Y, where X is peak width and Y is groove width. For example, sample 20by10 has a surface pattern with 20 µm peak width and 10 µm groove width.

^{−2}. Air and liquid water properties were imported from the Fluent database. Water surface tension was set to a value of 0.072 N·m

^{−1}with the continuum surface force model. The wall adhesion option was enabled, so that the contact angle with the material surface could be set. Implicit body force correction in the momentum equation was included, due to the existence of large body forces (gravity, surface tension force) in the studied phenomenon. A standard operating condition of 1013.25 hPa pressure and 1.225 kg·m

^{−3}air density were set. The following boundary conditions were set:

- -
- Velocity inlet with 0 m·s
^{−1}velocity magnitude on the upper edge - -
- Outflow on the sides of simulation domain
- -
- Wall with No Slip condition and static contact angle on the lower boundary representing the material’s surface.

^{−7}s, due to Courant number limitation. The simulation was initialized with initial values of 0 Pa pressure and 0 m·s

^{−1}velocity. A circle with a radius of 1.06 mm located 0.05 mm above the material’s surface was patched with a volume fraction of 100% water, and rest of the simulation domain was patched with air. Such a radius was picked to achieve 5µL volume, similar to the droplet size in experimental testing. The droplet was set on the surface after calculating 100,000 timesteps of the droplet falling on the surface and stabilization. In Figure 3, the initial configuration of the simulation was presented. Simulation was performed with 5° mesh rotation after 100,000 timestep intervals. The roll-off angle was determined when the droplet shifted more than the distance of 2 grooves from the initial position. The 2 grooves shift condition for evaluating roll-off was picked after a series of modeling for the samples, which exhibited high droplet adhesion. In those cases, the droplet did not roll off after 90° rotation, and it did not move even one groove distance.

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**SEM images of modified polyurethane coatings after laser patterning: (

**a**,

**c**) sample ‘5by5’, (

**b**,

**d**) sample ‘20by20’.

**Figure 3.**Volume fraction of fluid (red—water, blue—air) presenting: (

**a**) Initial droplet configuration and (

**b**) droplet after stabilization.

**Figure 4.**Measurement of contact angle: (

**a**) initial volume fraction image (red—water, blue—air), (

**b**) grayscale volume fraction image (black—water, white—air), and (

**c**) contact angle measured with drop analysis plugin.

**Figure 5.**Volume fraction of the fluid in the grooves: blue—water and red—air. Visible air pockets trapped in the grooves.

**Figure 6.**Volume fraction of the fluid in the grooves: blue—air and red—water. (

**a**) Water phase does not reach the next bulge on circular pattern, (

**b**) Water-air interface with the spiked pattern.

Sample | SCA [°] | CAH [°] | RoA [°] |
---|---|---|---|

Reference PUR | 85 | 39 | 87 |

Modified PUR | 107 | 35 | 80 |

5by5 | 114 | 18 | 90 |

10by5 | 119 | 20 | 45 |

20by5 | 115 | 25 | 90 |

5by10 | 118 | 23 | 40 |

10by10 | 121 | 26 | 90 |

20by20 | 136 | 5 | 5 |

5by20 | 133 | 24 | 40 |

10by20 | 131 | 18 | 35 |

20by10 | 115 | 27 | 70 |

Sample | Experiment | Model | Model (140° Surface Contact Angle) | Model Miwa et al. [43] | ||||
---|---|---|---|---|---|---|---|---|

Apparent Contact Angle [°] | Roll-off-Angle [°] | Apparent Contact Angle [°] | Roll-off-Angle [°] | Apparent Contact Angle [°] | Roll-off -Angle [°] | 107 CA [°] | 140 CA [°] | |

5by5 | 114 | >90 | 107 | >90 | 113 | >90 | - | - |

10by10 | 121 | >90 | 116 | >90 | 122 | >90 | - | - |

20by20 | 136 | 5 | 132 | 30 | 138 | 10 | 66 | 27 |

Surface Pattern | Roll-Off Angle [°] | Apparent Contact Angle [°] | |
---|---|---|---|

Rectangle | >90 | 128 | |

Rounded rectangle | >90 | 133 | |

Circles | >90 | 130 | |

Spikes | 10 | 167 | |

Rounded spikes | 35 | 166 |

Surface PatternL_D [µm] | Roll-Off Angle[°] | Apparent Contact Angle[°] | |

5_5 | >90 | 145 | |

10_5 | >90 | 146 | |

15_5 | >90 | 147 | |

20_5 | >90 | 149 |

Surface Pattern L_D [µm] | Roll-Off Angle [°] | Apparent Contact Angle [°] | |

5_12 | 15 | 172 | |

10_12 | 10 | 169 | |

15_12 | 10 | 175 | |

20_12 | 5 | 170 |

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**MDPI and ACS Style**

Haj Ibrahim, S.; Wejrzanowski, T.; Przybyszewski, B.; Kozera, R.; García-Casas, X.; Barranco, A.
Role of Surface Topography in the Superhydrophobic Effect—Experimental and Numerical Studies. *Materials* **2022**, *15*, 3112.
https://doi.org/10.3390/ma15093112

**AMA Style**

Haj Ibrahim S, Wejrzanowski T, Przybyszewski B, Kozera R, García-Casas X, Barranco A.
Role of Surface Topography in the Superhydrophobic Effect—Experimental and Numerical Studies. *Materials*. 2022; 15(9):3112.
https://doi.org/10.3390/ma15093112

**Chicago/Turabian Style**

Haj Ibrahim, Samih, Tomasz Wejrzanowski, Bartłomiej Przybyszewski, Rafał Kozera, Xabier García-Casas, and Angel Barranco.
2022. "Role of Surface Topography in the Superhydrophobic Effect—Experimental and Numerical Studies" *Materials* 15, no. 9: 3112.
https://doi.org/10.3390/ma15093112