# Simulation Approach for Hydrophobicity Replication via Injection Molding

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Mathematical Formulation

_{xv}is the stress tensor which takes all the terms associated with viscosity. Energy equation (Equation (3)) relates the temperature field (T) and internal energy (e) to pressure and the rate of work done on the fluid by viscous effects ($\dot{Q}$) [16].

_{0}is the zero shear viscosity or the ‘Newtonian limit’ in which the viscosity approaches a constant at very low shear rates, $\dot{\gamma}$ is the shear rate (1/s), τ* is the critical stress (Pa) level at the transition to shear thinning, and n is the power law index.

_{1}(Pa s) and A

_{1}(-), determined by curve fitting coefficients, and A

_{2}(K) is calculated with Equation (6):

_{3}(K) and D

_{3}(K/Pa) are data-fitted coefficients

_{2}(K) is data-fitted coefficient.

_{0}(K) are empirical coefficients that must be defined for each polymer. By comparing Equations (5) and (6), we can conclude that the model is identical for zero shear rate where μ = μ

_{0}.

#### 2.2. Mold Properties for Plastic Injection

^{3}plus the volume of channels. The projected nanostructured area is around 2(πd

^{2}/4) ≈ 1100 mm

^{2}.

#### 2.3. Polymer Properties for Plastic Injections

#### 2.4. Simulation Setup

^{®}Xeon

^{®}Gold 6230 Processor and 32 GB of RAM.

#### 2.4.1. SolidWorks Plastics Macro Simulation

^{2}= 4620 N but pressure is not constant in all points at the same given time). Packing of the polymer was defined with a holding pressure and with a cooling time of up to 20 s each. This was done in order to decide when to open the mold and check if replication was complete. Obviously, this cooling time is required to be minimized in industry in order to maximize production and reduce cost per part.

#### 2.4.2. Fluent Approach for Nanoreplication

^{−15}s should be taken into the account to accurately capture the plastic–air interface in the injection process. Parameters used for mesh generation included a growth rate of 1.2 capturing curvature and with smooth transition ratio of 0.25.

#### 2.4.3. Polyflow Approach for Nanoreplication

## 3. Results

#### 3.1. Fluent

^{−6}s [14].

#### 3.2. Polyflow

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Yoo, Y.; Kim, T.; Choi, D.; Hyun, S.; Lee, H.; Lee, K.; Kim, S.; Kim, B.; Seo, Y.; Lee, J.; et al. Injection molding of a nanostructured plate and measurement of its surface properties. Curr. Appl. Phys.
**2009**, 9, e12–e18. [Google Scholar] [CrossRef] - Christiansen, A.B.; Clausen, J.S.; Mortensen, N.A.; Kristensen, A. Injection moulding antireflective nanostructures. Microelectron. Eng.
**2014**, 121, 47–50. [Google Scholar] [CrossRef][Green Version] - Kim, S.; Jung, U.T.; Kim, S.; Lee, J.; Choi, H.S.; Kim, C.; Jeong, M.Y. Nanostructured multifunctional surface with antireflective and antimicrobial characteristics. ACS Appl. Mater. Interfaces
**2015**, 7, 326–331. [Google Scholar] [CrossRef] [PubMed] - Baruah, S.; Pal, S.K.; Dutta, J. Nanostructured Zinc Oxide for Water Treatment. Nanosci. Nanotechnol. Asia
**2012**, 2, 90–102. [Google Scholar] [CrossRef][Green Version] - Oh, H.J.; Park, J.H.; Lee, S.J.; Kim, B.I.; Song, Y.S.; Youn, J.R. Sustainable fabrication of micro-structured lab-on-a-chip. Lab Chip
**2011**, 11, 3999–4005. [Google Scholar] [CrossRef] [PubMed] - Barthlott, W.; Neinhuis, C. Purity of the sacred lotus, or escape from contamination in biological surfaces. Planta
**1997**, 202, 1–8. [Google Scholar] [CrossRef] - Yamamoto, M.; Nishikawa, N.; Mayama, H.; Nonomura, Y.; Yokojima, S.; Nakamura, S.; Uchida, K. Theoretical Explanation of the Lotus Effect: Superhydrophobic Property Changes by Removal of Nanostructures from the Surface of a Lotus Leaf. Langmuir
**2015**, 31, 7355–7363. [Google Scholar] [CrossRef] [PubMed] - Fagade, A.A.; Kazmer, D.O. Early cost estimation for injection molded components. J. Inject. Molding Technol.
**2000**, 4, 97–106. [Google Scholar] - Muntada-López, O.; Pina-Estany, J.; Colominas, C.; Fraxedas, J.; Pérez-Murano, F.; García-Granada, A. Replication of nanoscale surface gratings via injection molding. Micro Nano Eng.
**2019**, 3, 37–43. [Google Scholar] [CrossRef] - Pina-Estany, J.; Colominas, C.; Fraxedas, J.; Llobet, J.; Perez-Murano, F.; Puigoriol-Forcada, J.M.; Ruso, D.; Garcia-Granada, A. A statistical analysis of nanocavities replication applied to injection moulding. Int. Commun. Heat Mass Transf.
**2017**, 81, 131–140. [Google Scholar] [CrossRef][Green Version] - Pina-Estany, J.; Granada, A.A.G. 3D Simulation of Nanostructures Replication via Injection Molding. Int. Polym. Process.
**2017**, 32, 483–488. [Google Scholar] [CrossRef] - Pina-Estany, J.; Granada, A.A.G. Molecular dynamics simulation method applied to nanocavities replication via injection moulding. Int. Commun. Heat Mass Transf.
**2017**, 87, 1–5. [Google Scholar] [CrossRef] - Biosca, A.; Borrós, S.; Clemente, V.P.; Hyre, M.R.; Granada, A.G. Numerical and experimental study of blow and blow for perfume bottles to predict glass thickness and blank mold influence. Int. J. Appl. Glas. Sci.
**2019**, 10, 569–583. [Google Scholar] [CrossRef] - Boleda, T.B.; Guardia, C.C.; García-Granada, A.-A. Hydrophobic Hierarchical Structures on Polypropylene by Plastic Injection Molding. 2019. Available online: https://meaagg.com/PLASTFUN/Poster-Nanotoday.pdf (accessed on 2 March 2021).
- Peydró, M.A.; Parres, F.; Crespo, J.E.; Varón, D.J. Study of rheological behavior during the recovery process of high impact polystyrene using cross-WLF model. J. Appl. Polym. Sci.
**2010**, 120, 2400–2410. [Google Scholar] [CrossRef] - Anderson, J.D., Jr. Fundamentals of Aerodynamics; Tata McGraw-Hill Education: New York, NY, USA, 2010. [Google Scholar]
- Vasquez, S. A Phase Coupled method for Solving Multiphase Problems on Unstructured Mesh. In Proceedings of the ASME FEDSM’00: ASME 2000 Fluids Engineering Division Summer Meeting, Boston, MA, USA, 11–15 June 2000. [Google Scholar]
- Patankar, S.V. Numerical Heat Transfer and Fluid Flow; CRC Press: Boca Raton, FL, USA, 2018. [Google Scholar]
- Jemcov, A.; Maruszewski, J.P. 12 Algorithm stabilization and acceleration in computational fluid dynamics: Exploiting recursive properties of fixed point algorithms. Comput. Fluid Dyn. Heat Transf. Emerg. Top.
**2011**, 23, 459. [Google Scholar] - Choudhary, M.K.; Venuturumilli, R.; Hyre, M.R. Mathematical Modeling of Flow and Heat Transfer Phenomena in Glass Melting, Delivery, and Forming Processes. Int. J. Appl. Glas. Sci.
**2010**, 1, 188–214. [Google Scholar] [CrossRef] - Chouffart, Q. Experimental and Numerical Investigation of the Continuous Glass Fiber Drawing Process; Université de Liège: Liège, Belgium, 2018. [Google Scholar]
- Loaldi, D.; Regi, F.; Baruffi, F.; Calaon, M.; Quagliotti, D.; Zhang, Y.; Tosello, G. Experimental Validation of Injection Molding Simulations of 3D Microparts and Microstructured Components Using Virtual Design of Experiments and Multi-Scale Modeling. Micromachines
**2020**, 11, 614. [Google Scholar] [CrossRef] [PubMed]

**Figure 3.**Viscosity (

**a**) versus shear rate for different temperatures’ fitting WLF model and (

**b**) curve fit for VFT model as a function of temperature for shear rates below 1(1/s).

**Figure 6.**Evolution of Polyflow replication for T = 230 °C and Tm = 90 °C at different times from left to right of t = 0, 0.01, 0.05, 0.1, 0.5, 1, 5, 10, 15 s.

**Figure 7.**Y coordinate evolution of the bottom-middle corner point on different conditions vs. time (s).

**Figure 8.**Simulation at ending time (15 s) on conditions (

**a**) T = 230 °C, Tm = 30 °C and (

**b**) T = 270 °C, Tm = 90 °C and SEM micrograph (

**c**) T = 230 °C, Tm = 30 °C and (

**d**) T = 270 °C, Tm = 90 °C.

**Figure 9.**Experimental results of (

**a**) best replication in silicone, (

**b**) acceptable replication in PP with hot mold, and (

**c**) incomplete replication in PP with cold mold.

ρ (kg/m^{3}) | α (W/(m K)) | k (J/kg K) | |
---|---|---|---|

Steel mold | 7800 | 20 | 460 |

PP polymer | 850 | 0.15 | 3100 |

D1 (Pa·s) | D2 (K) | D3^{1}(K/Pa) | A1 (-) | A3 (K) | τ (Pa) | n (-) | T*^{1}(K) | A2^{1}(K) |
---|---|---|---|---|---|---|---|---|

7.4 × 10^{31} | 113.15 | 0 | 32.7 | 51.6 | 26,260 | 0.272 | 113.15 | 51.6 |

^{1}With data provided, D3 is zero and therefore, T* and A2 are constant and do not depend on pressure.

A^{1}(log(Pa s)) | B^{1}(K*log(Pa s)) | T_{0}(K) |
---|---|---|

0.2 | 1110 | 113.15 |

^{1}A should be 0.2 + 3 in order to get viscosity in (cPo) instead of (Pa s) in Polyflow.

CPU Time (s) | Simulated Time (s) | Mesh Size (mm) | Nodes (-) | Time Step (s) | Hard Disk Required (MB) | |
---|---|---|---|---|---|---|

SolidWorks Plastics | 1320 | 50 | 1 | 10,500 | 0.012 ^{1} | 93 |

Ansys Fluent | 43,200 | 1 × 10^{−6} | 0.001 | 1092 | 1 × 10^{−15} | 80,000 ^{2} |

Ansys Polyflow | 600 | 15 | 0.001 | 813 | 5 × 10^{−3} | 534 |

^{1}For SolidWorks Flow time step is 0.012 and for Pack, it is 0.5 s.

^{2}Writing only one out of 1-million-time steps.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Baldi-Boleda, T.; Sadeghi, E.; Colominas, C.; García-Granada, A.
Simulation Approach for Hydrophobicity Replication via Injection Molding. *Polymers* **2021**, *13*, 2069.
https://doi.org/10.3390/polym13132069

**AMA Style**

Baldi-Boleda T, Sadeghi E, Colominas C, García-Granada A.
Simulation Approach for Hydrophobicity Replication via Injection Molding. *Polymers*. 2021; 13(13):2069.
https://doi.org/10.3390/polym13132069

**Chicago/Turabian Style**

Baldi-Boleda, Tomás, Ehsan Sadeghi, Carles Colominas, and Andrés García-Granada.
2021. "Simulation Approach for Hydrophobicity Replication via Injection Molding" *Polymers* 13, no. 13: 2069.
https://doi.org/10.3390/polym13132069