# Avoiding Starvation in Tribocontact Through Active Lubricant Transport in Laser Textured Surfaces

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## Abstract

**:**

^{®}. The results show that narrow channels (width of 10 μ$\mathrm{m}$) allow higher spreading than wide channels (width of 30 μ$\mathrm{m}$). In a second step, fluid transport inside DLIP textures is investigated experimentally. The results show an anisotropic spreading with the spreading velocity dependent on the period and depth of the laser textures. A mechanism is introduced for how lubricant can be transported out of the channels into the tribocontact. The main conclusion of this study is that active lubricant transport in laser textured surfaces can avoid starvation in the tribocontact.

## 1. Introduction

#### 1.1. Solution Approach

^{®}is applied. The two-phase wetting phenomena are described by the phase-field method. In this method, the Cahn-Hilliard equation describing the multiphase system is coupled with the Navier Stokes equations governing the flow phenomena. Due to the diffusive character of the Cahn-Hilliard equation, this method allows a motion of the contact line in combination with a no-slip boundary condition at the solid wall [20]. The first implementation of this method in OpenFOAM

^{®}was done by Cai et al. [21] who validated the numerical model for different test cases and investigated the wetting phenomena of a droplet on a flat substrate. Fink et al. [22] investigated the hydrophobicity of micro-textured surfaces and showed good agreement between the numerical model and experiments, at least for the advancing phase.

#### 1.2. Outline of Article

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Numerical Methods

#### 2.2.1. Phase-Field Approach for Interface Evolution

#### 2.2.2. Governing Equations for the Fluid Flow

#### 2.2.3. Numerical Aspects

^{®}was applied to solve the above system of equations numerically with a finite-volume method. Spatial derivatives are approximated by a high-resolution scheme (Gamma scheme) and time integration is performed by a second-order two time level backward scheme (Gear’s method). The time step is chosen such that the maximum Courant number is 0.1. For further details see [21]. As suggested by Zolper et al. [23], PAO is considered to behave as a Newtonian fluid. In OpenFOAM

^{®}, it is also possible to model fluids with non-Newtonian behavior. However, the multiphase character of the problem in this study makes this more challenging, see for example [24]. Nevertheless, Niethammer et al. [25] show a rigorous treatment of a gas–liquid system with a non-Newtonian liquid phase. In this study, focus is laid on the steady state solution which does not depend on the transient viscosity behavior.

#### 2.3. Experimental Methods

#### 2.3.1. Laser Surface Texturing

#### 2.3.2. Fluid Transport Evaluation

#### 2.3.3. Characterization of Tribological Properties

#### 2.3.4. Surface Characterization

## 3. Results and Discussion

#### 3.1. Numerical Results-Droplet Wetting on Line-Like Textures

#### 3.2. Experimental Results

#### 3.2.1. Fabrication of Line-Like Surface Textures Using DLIP

#### 3.2.2. Fluid Transport Inside Laser Textured Surfaces

#### 3.2.3. Evaluation of Tribological Performance

#### 3.2.4. Transition of Fluid out of Laser Textured Surfaces into Tribocontact

- Due to a necessary amount of light for microscopy a glass lens is used instead of the 100Cr6 ball. The lens has the same radius of curvature and similar wetting properties.
- The phenomena in the tribometer occur under dynamic conditions. In the alternative setup it is only possible to observe effects under static conditions.
- The test samples first run in the tribometer and then the transition effects with the glass lens are observed. Therefore, the tribocontact exists on the sample and the glass lens is put manually into this contact.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

LST | laser surface texturing |

COF | coefficient of friction |

DLW | Direct Laser Writing |

DLIP | Direct Laser Interference Patterning |

## Appendix A

#### Appendix A.1. Tribological comparison of all DLIP textures introduced in this study

**Figure A1.**Tribological comparison of Stribeck curves for all DLIP textures introduced in this study and a polished reference sample.

#### Appendix A.2. Numerical Parameters and Solver Settings

Field | Solver | Preconditioner | Smoother |
---|---|---|---|

pd | PCG | DIC | GaussSeidel |

U | BiCGStab | DILU | none |

C | PBiCG | DILU | none |

Ccoupled | GMRES | Cholesky | none |

Operation | OpenFOAM | Scheme |
---|---|---|

Time derivative | ddt | Euler |

Gradient | grad | Gauss linear |

Divergence | div | Gauss Gamma |

Laplacian | laplacian | Gauss linear uncorrected |

Interpolation | interpolation | linear |

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**Figure 1.**Experimental setup for fluid transport evaluation. In (

**a**) the setup for the fluid transport evaluation inside the laser textures is shown. The fluid propagation in the channel-like textures is observed via a microscope from the top. In (

**b**) the setup for the lens experiments is illustrated. The transparent glass lens is a substitute for the tribological counterpart and allows fluid flow analysis at the transition region between channels and tribocontact.

**Figure 2.**Experimental setup for tribological evaluation. A side view on the left-hand side and a top view on the right-hand side shows the important components of the setup and the contact line (

**4**) on the rotating ball (

**3**).

**Figure 3.**Simulation of oil in channels of different widths at t = $0.039$ $\mathrm{s}$. The left column (

**a**,

**c**,

**e**) illustrates a cut through the domain at the geometrical center of the droplet. The right column (

**b**,

**d**,

**f**) shows one half of the spreaded droplet filling the channels from the bottom.

**Figure 4.**Quantitative evaluation of the numerical results comparing the spreading factor $\chi $ for the different channels widths as a function of the relative time ${t}^{*}$.

**Figure 5.**Microscope pictures and profiles of laser textures evaluated in this study. Textures and profiles of S1 (

**a**) and (

**e**), S2 (

**b**) and (

**f**), S3 (

**c**) and (

**g**) and S4 (

**d**) and (

**h**).

**Figure 6.**Side view of channels from texture S1. This microscopic image demonstrates in an exemplary manner the integrity of the laser produced textures. It can be seen that there are no discontinuities which lead to open structures.

**Figure 7.**Experimental investigation of fluid transport in laser textured surfaces. (

**a**) Specially designed sample with different regions. 1: Reservoir, 2: Laser surface textures, 3: mm-scale (500 $\mathsf{\mu}$$\mathrm{m}$ per bar); (

**b**) fluid front propagating in laser textures at a distance of 500 $\mathsf{\mu}$$\mathrm{m}$.

**Figure 8.**Quantitative results of flow behavior in different Direct Laser Interference Patterning (DLIP) textures (S2–S4). The sample introduced in Figure 7 was used to measure the distance of the fluid column in different channel-like textures as a function of time. The curves show Washburn-like behavior with the fastest transport in channels with smaller period and higher depth.

**Figure 9.**Experimental results from tribological evaluation of selectively structured samples. The Stribeck curves of three different samples with the same laser texture S1 ($\lambda =8\text{}\mathsf{\mu}\mathrm{m}$, depth $=1.5\text{}\mathsf{\mu}\mathrm{m}$) but with differently structured regions (“fully textured”, “triboregion blank” or “triboregion only”) are compared to the Stribeck curve of a polished reference sample.

**Figure 10.**In order to elucidate the flow behavior in the transition region between channels and tribocontact a transparent glass lense made of N-BK7 is used as a substitute for the counterbody. (

**a**) A side view of the glass lens on top of a textured sample; in (

**b**) the lens is manually put into the tribocontact and the flow around the lens is observed through the lens with a microscope.

**Figure 11.**Temporal course of fluid flow around glass lens in tribocontact and building of meniscus. (

**a**) Fluid front approaching the tribocontact; (

**b**) fluid front passing by the tribocontact; (

**c**) fluid filling the channels behind the tribocontact and (

**d**) building meniscus started at the contact of the lens with the sample.

Period | Hatch Distance | Frequency | Pulse Energy | Fluence | Pulse Overlap | |
---|---|---|---|---|---|---|

S1 | $8.0$$\mathsf{\mu}$$\mathrm{m}$ | $16.0$$\mathsf{\mu}$$\mathrm{m}$ | 20 $\mathrm{k}$$\mathrm{Hz}$ | $10.3$$\mathsf{\mu}$$\mathrm{J}$ | $0.82$$\mathrm{J}$/$\mathrm{c}$$\mathrm{m}$ | 96.88% |

S2 | $8.0$$\mathsf{\mu}$$\mathrm{m}$ | $8.0$$\mathsf{\mu}$$\mathrm{m}$ | 10 $\mathrm{k}$$\mathrm{Hz}$ | $3.5$$\mathsf{\mu}$$\mathrm{J}$ | $0.55$$\mathrm{J}$/$\mathrm{c}$$\mathrm{m}$ | 93.75% |

S3 | $4.0$$\mathsf{\mu}$$\mathrm{m}$ | $4.0$$\mathsf{\mu}$$\mathrm{m}$ | 10 $\mathrm{k}$$\mathrm{Hz}$ | $2.6$$\mathsf{\mu}$$\mathrm{J}$ | $0.41$$\mathrm{J}$/$\mathrm{c}$$\mathrm{m}$ | 93.75% |

S4 | $4.0$$\mathsf{\mu}$$\mathrm{m}$ | $4.0$$\mathsf{\mu}$$\mathrm{m}$ | $6.7$$\mathrm{k}$$\mathrm{Hz}$ | $3.5$$\mathsf{\mu}$$\mathrm{J}$ | $0.55$$\mathrm{J}$/$\mathrm{c}$$\mathrm{m}$ | 90.63% |

S1 | S2 | S3 | S4 | |
---|---|---|---|---|

period | $8.0$$\mathsf{\mu}$$\mathrm{m}$ | $8.0$$\mathsf{\mu}$$\mathrm{m}$ | $4.0$$\mathsf{\mu}$$\mathrm{m}$ | $4.0$$\mathsf{\mu}$$\mathrm{m}$ |

depth | $1.5$$\mathsf{\mu}$$\mathrm{m}$ | $1.0$$\mathsf{\mu}$$\mathrm{m}$ | $1.0$$\mathsf{\mu}$$\mathrm{m}$ | $0.7$$\mathsf{\mu}$$\mathrm{m}$ |

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**MDPI and ACS Style**

Stark, T.; Kiedrowski, T.; Marschall, H.; Lasagni, A.F.
Avoiding Starvation in Tribocontact Through Active Lubricant Transport in Laser Textured Surfaces. *Lubricants* **2019**, *7*, 54.
https://doi.org/10.3390/lubricants7060054

**AMA Style**

Stark T, Kiedrowski T, Marschall H, Lasagni AF.
Avoiding Starvation in Tribocontact Through Active Lubricant Transport in Laser Textured Surfaces. *Lubricants*. 2019; 7(6):54.
https://doi.org/10.3390/lubricants7060054

**Chicago/Turabian Style**

Stark, Tobias, Thomas Kiedrowski, Holger Marschall, and Andrés Fabián Lasagni.
2019. "Avoiding Starvation in Tribocontact Through Active Lubricant Transport in Laser Textured Surfaces" *Lubricants* 7, no. 6: 54.
https://doi.org/10.3390/lubricants7060054