3.2.3. Evaluation of Tribological Performance

In this section, the results of the tribological evaluation are outlined. The comparison of the Stribeck curves for the different DLIP textures S1–S4 introduced in this study show no difference in terms of coefficient of friction (see Figure A1 in Appendix A.1). Therefore, texture S1 with a period of 8 μm and a depth of around 1.5 μm is chosen for further tribological evaluation. The idea is that three samples with the same parameters as for S1 but with differently structured regions are compared to each other and to an untextured, polished reference sample. The textured samples differ in the area which is textured. The objective of this experiment is to understand whether it makes a difference if

the surface textures directly end at the tribocontact or at some distance away from it. As showed in Section 2.3.3, the setup of the tribometer is such that a ball rotates on the samples in a point contact. Therefore, the position of the tribocontact is known a priori. Hence, three differently structured samples are compared: a fully textured sample, a textured sample where only the region of the tribocontact is textured and the opposite case, namely a textured sample where the region of the tribocontact is blank but everything else is textured. The diameter of the tribocontact is around 250 μm such that the region of the tribocontact is chosen to have a width of 500 μm. The introduced textured samples are called "selectively textured samples". One can distinguish between "fully textured", "triboregion only" and "triboregion blank".

Besides the four Stribeck curves, Figure 9 also shows schematics of the samples described and evaluated in this section. It shows typical Stribeck curves for the three cases compared to the one of a polished reference sample. The polished sample has the highest coefficient of friction for all lubricating regimes. The coefficient of friction for the case "triboregion blank" is smaller , especially for the mixed lubrication regime, but the difference is negligible. However, this is not the case for the samples where the region of the tribocontact is textured ("fully textured" or "triboregion only"). Their difference again is negligible but compared to the other two samples, the reduction of the COF, especially for the mixed lubrication regime, is significant. This result might be a bit surprising. In the following section an attempt is made to explain this behavior.

**Figure 9.** Experimental results from tribological evaluation of selectively structured samples. The Stribeck curves of three different samples with the same laser texture S1 (*λ* = 8 μm, depth = 1.5 μm) but with differently structured regions ("fully textured", "triboregion blank" or "triboregion only") are compared to the Stribeck curve of a polished reference sample.

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

In the previous section it was shown that it makes a difference whether the triboregion is textured or not (meaning that after wear textures end directly at the tribocontact). In this section, we outline one possible effect that explains this behavior. The focus of this section lies on the transition region out of the laser textures into the tribocontact. However, the setup of the tribometer does not allow a precise observation of the transition region and the oil flow in it. Therefore, a different setup is applied to elucidate the phenomena occurring in this transition region. Nonetheless, the alternative setup has certain limitations:


Figure 10a shows a side view of a sample with the lens on top. Figure 10b corresponds to the setup explained in Section 2.3.4 and shows a top view of the textures through the glass lens. The picture illustrates the tribocontact, the lubrication front with the indicated flow direction and the final meniscus at the lens.

**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.

The temporal course of the fluid flow is shown in Figure 11. In Figures 11a–c it is possible to see the fluid front moving from left to right and the tribocontact. In Figure 11a, the front is approaching the tribocontact. In Figure 11b, it is possible to see that a lee-region is formed behind the contact point of the lens where initially no oil arrives. In Figure 11c, this region is also filled with oil. In Figure 11d, the fluid front has passed the field of view and a meniscus "climbing" the glass lens has formed. The driving force for this meniscus is the surface tension. It stops when an equilibrium state has been reached. This phenomenon can explain how oil is "pulled out" of the surface textures. As long as a continuous oil supply through the textures is guaranteed, the meniscus can grow until equilibrium state. Hence, it marks one possible explanation for the transition of the oil out of the textures into the tribocontact. This phenomenon can only occur when the textures are present exactly where the triboregion begins which explains why the case "triboregion blank" is worse in terms of reduction of COF than the case "triboregion only".

**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.

#### **4. Conclusions**

In this study, the fluid transport in DLIP textures was evaluated. From the numerical investigations it was shown that the capillary force plays an important role in small channels and the spreading factor is higher in channels with a width of 10 μm compared to channels with a width of 30 μm. DLIP textures were created with two different periods (4 μm and 8 μm) and three depths (1.5 μm, 1.0 μm and 0.7 μm). First, the fluid transport in these textures was evaluated. It was found that all textures show a Washburn-like behavior with the fastest transport in the texture with a period of 4 μm and a depth of 1 μm. In a second step, the tribological performance of four different DLIP textures was evaluated. It was shown that the level of COF could be reduced significantly compared to a polished reference but only negligible differences were found between the four textures. In a third step, the effect of differently structured zones was evaluated. For this test, one representative DLIP texture was chosen. In the evaluation, three samples with the same texture but with differently structured zones were compared to a polished reference sample. The samples differed as follows. One sample was fully textured (case "fully textured"), on one sample only the triboregion was textured (case "triboregion only") and on the third sample the triboregion was blank and the rest was textured (case"triboregion blank"). The resulting Stribeck curves showed similar behavior for the polished sample and case"triboregion blank" and a much lower COF but also similar behavior for case "fully textured" and case "triboregion only". The result shows the necessity of available textures directly at the position where the tribocontact ends. At this position the requirement for capillary forces breaks down if the channel is fully filled because then there is no meniscus at the gas–liquid interface. Therefore, in a last step, one possible explanation for this behavior was outlined. For this, a glass lens was chosen as a substitute for the tribological counterpart and was put manually into the tribocontact. Then, the fluid flow around the lens and the building meniscus could be observed. The prerequisite for the building meniscus is that the structures end in the tribocontact such that the fluid can flow until the contact point of the lens. For the abovementioned case "triboregion blank" this is not the case which might explain the higher COF. One limitation is that the lens experiments were conducted under static conditions but the effects in the tribometer are highly dynamic. However, the principle of this hypothesis also holds for the dynamic case.

**Author Contributions:** Conceptualization, all authors; Methodology, T.S. and H.M; Software, H.M. and T.S.; Validation, T.S. and H.M.; Formal Analysis, T.S. and H.M.; Investigation, T.S. and H.M.; Resources, all authors; Data Curation, T.S.; Writing—Original Draft Preparation, T.S.; Writing—Review and Editing, all authors; Visualization, T.S.; Supervision, T.K., H.M. and A.F.L; Project Administration, T.K. and A.F.L.; Funding Acquisition, T.K., H.M. and A.F.L.

**Funding:** This research was funded by the European Union's Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie grant agreement No. 675063. The work of A.F.L. is also supported by the German Research Foundation (DFG) under Excellence Initiative program by the German federal and state governments to promote top-level research at German universities.

**Acknowledgments:** The author H.M. thanks the Collaborative Research Center CRC 1194 "Interaction between Transport and Wetting Processes" by the German Research Foundation (DFG). The authors also thank Gerd Dornhöfer, Joachim Klima and Sarona Frank from the Robert Bosch GmbH for the fruitful discussions. Furthemore, they thank Marius Hofmann for his contribution in this study.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
