**1. Introduction**

As early as in ancient Egypt, tribology, which includes friction, wear, and lubrication, has been put to use to reduce frictional losses and mitigate interfacial damage between rubbing surfaces. During the construction of the pyramids, the Egyptians had already realized that the efforts involved in transporting heavy stones could be significantly reduced when putting rolling elements underneath the stones. Most probably, this can be considered as the first evidence that rolling friction is lower than pure sliding friction. Over the centuries, prominent researchers including Da Vinci, Newton, Amontons, Coulomb among many others have studied frictional phenomena under different aspects [1,2]. During their investigations, they realized that friction is governed by the interplay of various mechanochemical phenomena taking place simultaneously on the contact interface. To shed more light on the involved processes, they initially tried to describe the frictional behavior of dry sliding contacts from a phenomenological point of view by establishing a mathematical relationship between

the applied normal load and the resulting friction force. The definition of the coefficient of kinetic friction (COF) goes back to Amontons and Coulomb, who independently figured out that the resulting friction force is proportional to the normal load for dry sliding contacts [3]. The constant relating both forces is the kinetic COF. This simple, linear relationship often oversimplifies the complexities found in actual tribological interfaces, where time-dependent, non-equilibrium thermodynamic processes contribute to the resulting COF [4]. The Amontons-Coulomb's model of dry friction assumes that the kinetic COF does not depend on the nominal contact area and on the magnitude of the sliding velocity. These observations have been refined by Bowden and Tabor, who realized that the COF, in fact, does not depend on the nominal contact area but rather on the real contact area between the asperity peaks, thus connecting the resulting friction force with the real contact area and shear strength of the interface [5].

The real contact area strongly depends on the roughness of the interacting surfaces [6,7]. Since the surfaces are effectively in contact only at the tips of distinct asperities, all individual contact spots have to be summed up to determine the entire contact area. Having a closer look at the surface roughness, it becomes obvious that multiple scales are involved. Dependent on the respective instrument and magnification used to measure the surface topography, different geometric features become visible ranging from nanometer- to millimeter-scale [8]. This immediately demonstrates that the frictional properties of a contact pair depend on multi-physics phenomena occurring in multiple length scales, and therefore the accurate determination of the friction force relies on the solution of a multi-scale problem. Apart from the geometric and fractal aspects of surface roughness, mechanochemical effects on different scales also affect the resulting frictional behavior. Thinking about the atomic and molecular levels, the bonding strength directly correlates with the friction force. Furthermore, the atomic/molecular arrangement and order phenomena influence friction and wear. Considering order and crystal structures, chemical imperfections and lattice defects play a significant role in the subsequent materials and hence frictional properties. This impressively underlines that frictional behavior is also influenced by chemical contributions occurring on different scales. From an engineering point of view, friction and wear are also affected on micrometer- and millimeter-scale when tolerances of manufacturing processes are considered. This short paragraph ultimately demonstrates that tribology is highly inter-disciplinary and definitely encompasses the research and solution of multi-physics and multi-scale problems.

A detailed look into nature shows that it often makes use of multi-scale/hierarchical surfaces to optimize physical properties [8–11]. A well-studied phenomenon is the drag reduction observed for dolphins and sharks induced by their skin containing features of at least two different scales [12,13]. In addition, the ability to tune adhesion properties by hierarchical surface textures as observed for beetles, flies, geckos among others, is another prominent example of the important role of interfacial geometry [14–16]. Moreover, the lotus leaf, for instance, combines a specific surface roughness on different scales with modified surface chemistry to enable self-cleaning properties and superhydrophobicity [17,18].

Inspired by these strategies provided by nature and the direct impact of the surface topography on tribological performances, specific surface textures have been utilized for more than three decades to optimize friction and wear. The pioneering systematic work in this field has been carried out by Etsion and co-workers showing the potential benefits of surface textures in different lubricated machine components (seals and piston rings among others) [19,20]. Afterwards, this topic has experienced tremendous interest and attention in the tribological community. In the last years, several review papers have summarized the state-of-the-art regarding the influence of surface texturing on friction and wear in laboratory experiments and machine components [21–24]. Interestingly, the majority of the published research works make use of purely single-scale textures. The positive effects of single-scale textures depend to a large extent on the type of contact (conformal or nonconformal) and lubrication regime. Under full-film hydrodynamic lubrication, surface textures may function as micro-hydrodynamic bearings which boost the fluid pressure, thus increasing the overall load-carrying

capacity [25–28]. This is particularly significant for contacts with parallel and flat surfaces, such as those encountered in mechanical seals and parallel thrust bearings. Furthermore, the subambient pressure zones formed in textures close to the contact inlet due to the fluid cavitation phenomenon responsible for the aforementioned micro-hydrodynamic bearing effect may also contribute to drawing additional lubricant into the contact (inlet-suction effect) [27,29,30]. However, it needs to be pointed out that an inappropriate choice of texture parameters (i.e., texture depth, width, and density) may lead to detrimental effects due to the excessive increase of the cavitation zones, which may reduce the local film thickness and the load carrying capacity [31]. Under mixed lubrication, surface textures typically fulfill multiple functions. Besides contributing to improved hydrodynamic pressure they also reduce the real contact area and they are able to store lubricant thus acting as a secondary oil supply. Moreover, textures can trap wear particles thus reducing abrasive wear. Under boundary lubrication, surface texturing reduces the real area of contact and can induce the formation of pressure-induced boundary layers, thus lowering friction and wear [32,33]. The proper combination of the aforementioned aspects leads to a significant reduction of friction and wear, and/or to shift the transition between different lubrication regimes [34–36]. Considering dry friction, the reduction of the real contact area as well as the storage of wear particles can be named as the main effects contributing toward improved tribological properties [37–39].

Although nature provides numerous examples of the successful use of multi-scale textures for friction reduction, the transfer of these ideas to engineering applications has been scarcely realized. Therefore, it can be expected that multi-scale surface textures bear the tremendous potential to further optimize friction and wear properties in machine components. In this context, this review article aims at summarizing the existing articles in the field of multi-scale surface textures to improve friction and wear. First, potentially suited fabrication techniques will be reviewed, as well as discussing the advantages and shortcomings of these techniques. Afterwards, the article reviews the research conducted in biologically inspired multi-scale surface textures and their effect on friction and wear. The next section will summarize the numerical methods used to model multi-scale surfaces to predict potential friction and wear reductions. Finally, this article intends to outline the mechanisms responsible for the improved friction and wear behavior promoted by multi-scale textures as well as provide future research directions for improved texture designs.

## **2. Fabrication Strategies for Multi-Scale Surface Textures**

Historically, numerous methods have been utilized to create surface textures for tribological applications. In this context, surface textures can be defined as geometric features following a deterministic pattern, which is intended to be engineered to induce certain surface functionalities [40]. Moreover, textures can have a preferential direction or be arranged in a random fashion [40]. The fabrication methods can be roughly divided into mechanical, chemical, physical, and thermal methods [41]. Examples for each group can be found in Table 1. A detailed overview of the individual families of surface texturing methods has been given in the form of tree structures by Costa and Hutchings [41]. The benefits and limitations of each texturing technique have to be considered regarding productivity, efficiency, geometric flexibility, accuracy, material flexibility, among others. The general geometry and accuracy of the produced textures significantly affect the tribological behavior of the generated surfaces [22,23]. In this regard, the pitch, depth, edge angle, and line accuracy of the texture features are all factors influencing the tribological performance [22]. Accuracy is especially important for multi-scale textures since textures have to be combined suitably and both patterns should be left intact during the texturing process. For patterned surfaces in general and particularly for multi-scale surfaces, the real area of contact and hence the resulting friction force is significantly influenced by the arrangement of the textural features [40]. Efficiency is a critical factor when thinking about large-scale production. This is especially true in case of patterning many components in industrial chains, which directly asks for a rather cheap and efficient texturing method [41]. Of a vast variety of texturing methods, laser texturing is the most advanced technique, which can be traced back to its high flexibility

in terms of materials and geometries, high speed, good accuracy, and excellent control over the textures' geometry [20,22,41–43]. Furthermore, laser texturing belongs to the methods which remove material from the surface and therefore creates more durable and shear resistant textures compared to other methods that add material to the surface (i.e., protrusions) [22].

**Table 1.** General classification and examples for each type of texturing method [41].


Having the generation of multi-scale surface textures in mind, they can be fabricated in a multi-step [44–49] or single-step [50–52] process. Naturally, single-step processes are less time-consuming, easier to integrate into production lines, and therefore more efficient. Moreover, multi-step processes, which consist of different steps but using the same equipment to produce textures on different scales, are more practical and efficient than combining two or more different texturing techniques to produce multi-scale surfaces. It has to be pronounced that every surface inherently shows texture features on several scales. During laser surface texturing, for example, ablated particles can be redeposited on the surface, creating a random nano-roughness [53]. However, this review shall be limited to such techniques, which deliberately engineer multi-scale surfaces.

In the literature, several review papers can be found summarizing methods to create surface textures for tribological applications [40–42]. Hence, here only techniques with a special connection to multi-scale surface texturing will be presented.
