Introduction The flow factor method according to Patir and Cheng is an established modification of the Reynolds equation for calculating fluid flows between rough surfaces. The method allows the consideration of roughness without having to discretize the computational domain in the same order of magnitude as the present roughness peaks. This way, it is possible to consider the influence of roughness on the flow with sufficient accuracy and moderate computing time [1 - 7]. The conventional determination of flow factors assumes that the fluid viscosity is constant [1, 2]. In case of a shear thinning fluid, this assumption is not valid. Now, the viscosity is a function of the shear rate and varies for every film thickness, which differs from the averaged film thickness and also in gap height direction. Accordingly, the viscosity is not negligible anymore and the flow factor depends on the viscosity behavior of the fluid, too. Herbst has already investigated the influence of various shear-thinning oils on the flow factors as a function of the fluid film height, but not as a function of the pressure gradient [7]. However, the flow factor according to Patir and Cheng assuming Newtonian viscosity is widely used in many branches of industry and is also applied for non-Newtonian fluids like engine oils. This contribution aims to evaluate the error introduced by neglecting the non-Newtonian viscosity behavior in the calculation of flow factors especially for different pressure gradients and the associated consequences for the design of tribological systems. In the first part of this contribution the flow factor method according to Patir and Cheng is highlighted and the approach for the derivation of the flow factors is explained. Moreover, it is demonstrated how the viscosity varies in gap heights direction for non-Newtonian fluids. To consider the described viscosity variations for the flow factor calculation, in the next section of this contribution a simulation model based on the Reynolds equation according to Dowson and Herbst’s preliminary work is presented. The mathematical principles and the used algorithm are to be discussed as well [7,8]. Subsequently, the results determined with the simulation model will be presented. Here, the error caused by neglecting non-Newtonian viscosity behavior is evaluated for different gap heights, pressure gradients and fluid properties. Finally, the consequences for the design of tribological systems arising from the obtained results will be discussed. Flow calculation for rough surfaces In various technical applications the influence of roughness on the flow between two surfaces is not negligible. This applies for example to the piston bushing contact in hydraulic machines, combustion engines or other tribological systems where the gap height is small Science and Research 5 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0007 unikationswissenhe Sprachwissenent \ Altphilologie Kommunikationsistorische Sprachanagement \ Alttik \ Bauwesen \ schaft \ Tourismus ie \ Kulturwissenichte \ Anglistik \ \ BWL \ Wirtschaft On the Validity of the Flow Factor Concept with Respect to Shear-thinning Fluids Marius Hofmeister, Jonas Schütz, Katharina Schmitz* submitted: 03.09.2023 accepted: 24.06.2024 (peer-review) Presented at the GfT Conference 2023 This contribution aims to determine the error introduced by assuming constant viscosities in the calculation of the flow factors for non-Newtonian fluids. For this purpose, a simulation model based on the generalized Reynolds equation according to Dowson is used to evaluate shear thinning effects for various oils as well as different technical surfaces. Keywords Dowson, flow factors, non-Newtonian fluids, simulation, generalized Reynolds equation, shear thinning effects, technical surfaces Abstract * Marius Hofmeister, M. Sc. Jonas Schütz, B. Sc. Univ.-Prof. Dr.-Ing. Katharina Schmitz Institut für fluidtechnische Antriebe und Systeme (ifas) der RWTH Aachen Campus-Boulevard 30, 52074 Aachen es on the flow factor method according to Patir and Cheng. For the determination of the flow factors, first, a representative area between the two rough surfaces is selected like shown in Figure 1. This area is discretized in the order of magnitude of the present roughness peaks. For calculating ϕ p,x , the flow in y-direction is set to zero and a pressure gradient is applied in x-direction. [1, 3] The resulting flow is calculated by means of the Reynolds equation and corresponds to the term for rough surfaces in eqn. 2. Subsequently, the flow is determined for ideally smooth surfaces and an average gap height, which equals the one of the rough gaps. Finally, the pressure flow factor is the ratio of the flow between rough surfaces and the one for ideally smooth surfaces. To account for surface irregularities, the process should be performed several times for different areas of the surface. [1, 2] eqn. 2 The pressure flow factor in y-direction is calculated analogously by changing the direction of the pressure gradient and the boundary conditions. This way, one considers roughness effects depending on the flow direction. In general, the procedure for the determination is comparable to that of the pressure flow. In contrast to the pressure flow, no pressure gradient is applied for the determination of shear flow but a relative velocity between the surfaces shown in Figure 1. Since the flow factor is a tensor, the method described should be carried out parallel or transverse to the surface orientation, as otherwise there is an coupling between the flow for xand y-direction.This contribution only focuses on the pressure flow, so that the shear flow factor is not described in detail. . p,x = 1 y T 3 12 y 0 rough surface 3 12 smooth surface Science and Research 6 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0007 in relation to the present roughness peaks. One possibility to consider the influence of roughness on the flow is the discretization of the entire computational domain in the order of magnitude of the present roughness peaks. Subsequently, the flow and pressure field can be calculated for defined boundary conditions by means of numeric models like the Reynolds equation or Navier Stokes equation. However, this approach is associated to a high computational effort and is therefore impracticable. One way to avoid these high computational costs is to use the flow factor method according to Patir and Cheng. This method represents the information about the influence of roughness on the flow by only two scalar values: the pressure flow factor ϕ p and the shear flow factor ϕ s . These values are integrated to the Reynolds equation for 2-dimensional" flow visible in eqn. 1 and correct the deviations in flow rate caused by the rough surface for pressure flow and shear flow. In this manner, the influence of roughness is considered without discretizing the computational domain in the order of magnitude of the present roughness peaks, which is beneficial regarding discretization and computational effort. [1, 2] eqn. 1 An alternative to the flow factor method is the homognized Reynolds equation, which is independent from effects arising from the orientation of the chosen coordinate system [9]. However, this contribution only focuss- . ( ) Pressure build up = p,x 3 12 Pressure flow s,x ,1 ,2 2 ,1 Shear flow L y L x surface 2 no flow no flow x fluid film h surface 1 p B p A y Figure 1: Computational Domain When deriving the pressure and shear flow factors, a constant viscosity is assumed in gap height direction and along the flow direction. This assumption is only valid for Newtonian fluids. In case of a non-Newtonian fluid, the viscosity depends on the present shear rate, which varies along the gap height and the flow direction. This phenomenon is illustrated by Figure 2. Here, two gaps with the different heights h and H are visible. The same pressure gradient is applied to both gaps. The corresponding velocity, shear and viscosity profiles are indicated by black and green arrows for a Newtonian and a non- Newtonian fluid, respectively. The viscosity of both fluids is the same for a shear rate of zero. For both gaps and the Newtonian fluid, the pressure gradient leads to a parabolic velocity profile and therefore to a linear shear profile. Since the varying shear rate along the gap height has no influence on the viscosity of the Newtonian fluid, the viscosity is constant for the entire gap height and both gaps. The shear dependent viscosity course of the non-Newtonian fluid is visible in Figure 3. In this case, the non- Newtonian fluid is shear-thinning and can be described by the Cross equation (eqn. 7). For low shear rates the Cross fluid behaves like a Newtonian fluid. For a specific shear rate, the viscosity starts to decrease rapidly until the second Newtonian plateau is reached. [10] Since the viscosity of the non-Newtonian fluid decreases with increasing shear rate, the viscosity varies along the gap, which in turn influences the velocity and the shear profiles so that maximum velocity is higher for the non- Newtonian fluid. Furthermore, the flow velocity and the maximum shear rate is higher for the gap with the greater height H. The overall higher shear rates lead to a stronger decrease of viscosity. Applied to the flow between rough surfaces, this means that the viscosity is variable in gap height direction, but also changes for each gap height in flow direction. Thus, eqn. 2 is not valid and leads to errors if the varying viscosity is not considered. Flow simulation model To avoid the errors in flow factor calculation caused by the non-Newtonian viscosity behavior, a novel simulation model is built up. Since the fluid viscosity varies along the gap height direction, as described in the previous section, the conventional Reynolds equation cannot be used. However, the Reynolds equation according to Dowson offers the possibility to discretize the viscosity course in the gap height direction. The corresponding equation is given in eqn. 3. Analogous to the common Reynolds equation, the Reynolds equation, according to Dowson, consists of a term for pressure flow, shear flow and a term for pressure build up.[8] Science and Research 7 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0007 1st Newtonian plateau 2nd Newtonian plateau shear rate viscosity Figure 3: Qualitative viscosity course for a Cross fluid Figure 2: Velocity, shear rate, and viscosity profiles for Newtonian/ non-Newtonian fluids and different gap heights The shear rate is derived from the flow profile. Based on an arbitrary fluid model, the viscosity profile for each volume is calculated. Any model that gives a clear relationship between viscosity and shear rate can be used as a fluid model. In the context of this contribution only shear-thinning fluids, which can be described by the Cross or Carreau equation, are considered. The viscosity values calculated based on the shear profile are used to correct the Dowson integrals and the Reynolds equation is solved again. This procedure repeats until the deviation of two flow profiles determined in consecutive cycles is below a specified limit. As mentioned before, in the context of this contribution only pressure flow is considered and no shear flow occurs. With the described algorithm it is possible to calculate the flow Q rough,η(γ ˙ ) for non-Newtonian fluids and therefore the flow factor ϕ mod,x for the same. The modified flow factor does not only depend on the gap heights and the surface properties but also on the pressure gradient and the viscosity properties of the considered fluid. eqn. 6 To evaluate the error caused by assuming constant fluid viscosity, the normalized pressure flow factor ϕ N given in eqn. 7 is used. This measure represents the ratio of the pressure flow factor ϕ p,x determined with the common method by assuming constant viscosities and the pressure flow factor ϕ mod calculated with the model introduced before. eqn. 7 Results and discussion The described algorithm is used for the calculation of the normalized pressure flow factor ϕ N for the simplified . , = rough, ( ) 3 12 , rough, ( ) = ( , ( , ), ( )) = , Science and Research 8 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0007 eqn. 3 For the calculation of the shear rate γ ˙ for every value of z eqn. 4 is used.[8] eqn. 4 Unlike the Reynolds equation, in eqn. 3 and eqn. 4 the viscosity is not specified explicitly, but is considered by means of the Dowson integrals mentioned in eqn. 5. The Dowson integrals result from the derivation of the Reynolds equation from the Navier Stokes equation, if a variable viscosity in gap height direction is assumed.[8] eqn. 5 Eqn. 3 is integrated in the algorithm visible in Figure 4. The algorithm starts with an initialization process. Here, the boundary conditions are defined, the computational domain is discretized and divided into a specified number of volumes in xand y-direction. Additionally, each volume is subdivided in z-direction, whereby this discretization only refers to the values for fluid viscosity. Furthermore, during the initialization process the Dowson integrals are calculated for an initially constant viscosity. In the next step, the Reynolds equation according to Dowson is solved for the entire computational domain and the pressure field is calculated. The velocity profile is determined for each volume using eqn. 4. ( ) Pressure build-up = ,4 1 2 0 Pressure flow ,1 ,2 2 1 0 ,1 Shear flow = = 1 1 0 + ,2 ,1 0 = 1 = = 1 = = flow profile shear profile viscosity profile end pressure profile Reynolds equation start Dowson integrals Initialization Dowson integrals Dowson integrals Dowson integrals Boundary Conditions Discretization max(|v -v |) j,i-1 j,i < v res no yes Figure 4: Algorithm for the calculation of flow for rough surfaces and non-Newtonian fluids rough gap visible in Figure 5. This gap consists of two areas, each with the gap height h and H, respectively. In this example, the relationship between h and H is given by the following equation: H = h + 1 μm. The height h¯ of the second gap visible in Figure 5 corresponds to the average height of the rough gap and is the mean value of h and H. The flow direction points into the drawing plane for both gaps. As the orientation of the surface roughness in this simplified gap runs exclusively in the x-direction along the pressure gradient, the calculated flow factor corresponds to that in the main axis direction. Therefore, no further components of the flow tensor away from the main axes need to be taken into account. The fluid used in the simulation is a shear-thinning oil that can be described by the Cross model and the parameters given in eqn. 8. The value r refers to the ratio of the viscosity η 0 for zero shear and the viscosity at the 2 nd Newtonian plateau. The factor m indicates how rapidly the transition between 1 st and 2 nd Newtonian plateau takes place. The K variable determines the shear rate where shear-thinning starts to be noticeable.[10] eqn. 8 The overall dimensions of the computational domain are 10 by 10 mm. The domain is divided into 20 volumes in xand y-direction. Each volume is subdivided in 51 sections in z-direction. The Dowson integrals from eqn. 5 are solved by Trapezoidal numerical integration. The corresponding results for the normalized flow factor ϕ N and the Reynolds number are visible in Figure 6. The normalized flow factor is equal to one for a pressure gradient tending towards zero and therefore equals the flow factor determined according to Patir and Cheng for constant viscosity. With increasing pressure gradient, the normalized flow factor increases rapidly and reaches a maximum. After passing the maximum, ϕ N decreases slowly. It can thus be seen that for a non-Newtonian fluid, the flow factor depends not only on the gap height but also on the pressure gradient respectively the shear rate. The Reynolds number is low for the entire set of parameters and therefore the prerequisite for using of the Reynolds equation Re ≪ 1 is true. The course of the normalized pressure flow factor ϕ N can be divided into four sections. Within the first section where the pressure gradient is nearly zero, the corresponding shear rate is also close to zero. Therefore, the shear rate has no effect on the fluid viscosity and for every gap height shown in Figure 5 the viscosity is the same. In this case, the normalized pressure flow factor = + 1 1 + ( ) ϕ N equals the flow factor according to Patir and Cheng. This phenomenon is also indicated by the circles in the viscosity diagram Figure 7. Since the gap heights differ from each other, an increased pressure gradient leads to varying shear rates for each gap height. Due to the comparably low hydraulic resistance for gap heights H, here, the shear rate is the highest and therefore the viscosity loss is the largest. This leads to a higher flow rate for H compared to h and h¯ and an increase of the normalized flow factor. If the pressure gradient increases even further, the shear thinning also starts to become noticeable for gap h¯. Accordingly, the curve begins to fall again in section III. For high pressure gradients tending to an infinite value, the viscosity for each gap has reached the second Newtonian plateau. Now, the viscosity is the same for each gap and the normalized flow factor approaches one again. Science and Research 9 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0007 H h h rough gap smooth gap H h B B ¹⁄ B ¹⁄ B Figure 5: Simplified rough gap Figure 7: Fluid model for fluid 1 0 10 20 30 40 50 1 1.005 1.01 1.015 0 0.00076 0.0015 0.0023 0.003 0.0038 Reynolds Number I II dp/ dx 0 → dp/ dx → 1.025 ∞ III IV Pressure gradient dp/ dx in bar/ mm Normalized Flow Factor ϕ N Figure 6: Results for the normalized flow factor s = 1,34 10 , = 0,68 = 40 mPa s, = 0,49 Besides the simplified gap from Figure 5 the technical surface visible in Figure 12 was investigated, too. The surface was measured by means of a digital microscope with a lateral resolution of 350 nm and a minimal vertical resolution of 10 nm. Figure 12 shows a section of the technical surface with the dimensions 0.5 mm by 0.5 mm. For the simulation the entire surface scan with the dimensions 1 mm by 1 mm was used. As can be seen, there are several grooves on surface 1 that are neither parallel nor transverse to the x-axis and would therefore also influence the flow in the y-direction for a pressure gradient in x-direction. However, surface 2 has a very similar surface orientation in the opposite direction, which cannot be seen in this figure as it is covered by surface 1. Overall, the surfaces are positioned in relation to each other so that the x-direction of the calculation area corresponds to the main flow direction. To represent the influence of roughness correctly, the computational domain must be meshed much finer for the measured surface in comparison to the simplified Science and Research 10 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0007 A further parameter investigated in the context of this paper, is the gap height, which was varied as shown in Figure 9. The gap heights is reduced stepwise until the h vanishes. The results for the gap heights variation and the same fluid parameters as used before are visible in Figure 8. The results show that ϕ N increases with decreasing gap height. In this example the highest value for ϕ N is 1.096 and is reached for h¯ = 0.5 μm. In Figure 10, the influence of different fluid parameters on the normalized pressure flow factor is evaluated. For this purpose, the m value of the Cross equation was varied as shown in Table 1. The corresponding viscosity courses are visible in Figure 11. The simulation results show that an increased m value leads to a stronger expression of the maxima for ϕ N . For example, the maximum value of ϕ N is 1.215 for fluid 3 with m = 1.34 and an average gap height h¯ of 0.5 µm. In comparison, the maximum value for fluid 1 and the same gap height is significantly smaller and is 1.044. 0 10 20 30 40 50 1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 Re = 1e-5 Re = 5e-5 Re = 1e-4 Re = 2e-4 Re = 3e-4 Pressure gradient dp/ dx in bar/ mm h = 1 m μ h = 0.75 m μ h = 0.5 m μ h = 2 m μ h = 1.25 m μ h = 1.75 m μ h = 1.5 m μ Normalized Flow Factor ϕ N Figure 8: Results for different gap heights H h h rough gap smooth gap H h B B ¹⁄ B ¹⁄ B h rough gap smooth gap H B B ¹⁄ B Figure 9: Gap heights reduction 0 5 10 15 20 25 Pressure gradient in bar/ mm dp/ dx 1 1.05 1.1 1.15 1.2 1.25 Normalized Flow Factor Φ N Fluid 1 Fluid 2 Fluid 3 0.5 m μ 0.75 m μ 1 m μ 1.25 m μ 1.5 m μ 1.5 m μ 1.5 m μ 1.25 m μ 1 m μ 0.75 m μ 0.5 m μ 1.25 m μ 1 m μ 0.75 m μ 0.5 m μ Figure 10: Results for different fluid parameter 0 5 10 15 20 Shear rate in 1/ s 20 30 40 Viscosity η in mPas Fluid 1 Fluid 2 Fluid 3 Figure 11: Investigated fluid models Fluid 1 Fluid 2 Fluid 3 in Pa·s 40 0,49 0,000134 0,68 0,34 1,34 Table 1: Cross parameter for Fluid 1-3 gap. To find the optimal mesh size a, convergence analysis was conducted. The corresponding results are visible in Figure 14. As can be seen, the deviation in flow rate decreases significantly for a mesh with 80 volumes in each direction. Therefore the resolution of 300 by 300 volumes implemented for previous simulations is sufficient to map the flow between the selected surface accurately. The results for the normalized pressure flow factor ϕ N and the technical surface are visible in Figure 13. Again, the fluid properties of fluid 1 are used and the corresponding Reynolds numbers are given.The effects shown for the simplified gap can also be observed for the technical surface. The previously defined four areas in the flow factor course exist also for the technical surface. It can be seen that a decrease in the gap height leads to an increase in the maximum normalized flow factor exactly the same as in the previous examples. Differences exist essentially in the expression of the maximum values for ϕ N . Thus, the maximum value of ϕ N for the simplified gap and a gap height of 1 µm is 1.050, while for the technical surface and the same gap height only a value of 1.027 is obtained. The comparison between simplified gap and technical surface illustrates that the characteristic of the surface also has a significant impact on the normalized pressure flow factor. Summary and outlook This contribution first highlighted the concept of flow factors according to Patir and Cheng and described the derivation of the pressure flow factor. Subsequently, the variation of viscosity for non-Newtonian fluids in z-direction and for different gap height was illustrated. Furthermore, the errors caused by this viscosity variation were addressed. Science and Research 11 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0007 Figure 13: Results for technical rough surface 6 8 10 12 14 20 40 60 80 100 140 180 225 275 350 500 700 900 1100 1300 1500 Cells per direction 0.7 0.8 0.9 1 1.1 1.2 Normalized flow deviation to 1500 Figure 14: Convergence analysis Figure 12: Technical rough surface Nomenclature B gap width H, h gap height h¯ averaged gap height J i Dowson integral K K-constant Cross model L i length m m-constant Cross model p i pressure r r-constant Cross model t time u i velocity of surface i x,y,z x,y,z-coordinates γ ˙ shear rate η dynamic viscosity η 0 dynamic viscosity at γ ˙ = 0 ρ density ϕ N normalized pressure flow factor ϕ mod modified pressure flow factor ϕ p,x pressure flow factor x-direction ϕ s,x shear flow factor x-direction References [1] Patir, N.; Cheng, H. S., An Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic. J. lubr. technol., Vol. 1, 1978, pp. 12- 17 [2] Patir, N.; Cheng, H. S.. Application of Average Flow Model to Lubrication Between Rough Sliding Surfaces. J. lubr. technol.Vol. 2, 1979, pp. 220-229 [3] Elrod, H. G., A General Theory for Laminar Lubrication With Reynolds Roughness. J. lubr. technol., Vol. 1, 1979, pp. 8-14 [4] Harp, S. R.; Salant, R. F., An Average Flow Model of Rough Surface Lubrication With Inter-Asperity Cavitation. J. lubr. technol., Vol. 1, 2001, pp. 134-143 [5] Hasim Khan; Prawal Sinha. Thermal Elastohydrodynamic Lubrication of Line Contact Rough Surfaces Using Flow Factor Method. Contemp. Eng. Sci., Vol. 3, 2010, no. 3, pp. 113-138 [6] Kumar, R.; Azam, M. S.; Ghosh, S. K., Influence of stochastic roughness on performance of a Rayleigh step bearing operating under Thermo-elastohydrodynamic lubrication considering shear flow factor. Tribol. Int., 2019, pp. 264-280 [7] Herbst HM. Theoretical modeling of the cylinder lubrication in internal combustion engines and its influence on piston slap induced noise, friction and wear. Graz (Austria): Graz University of Technology, 2008. [8] Dowson, D., A Generalized Reynolds Equation for Fluidfilm Lubrication, Int. J. Mech. Sci., Vol. 4, 1962, pp. 159- 170 [9] Rom, M.; Müller, S., A Reduced Basis Method for the Homogenized Reynolds Equation Applied to Textured Surfaces, Commun. Comput. Phys., Vol. 24, 2018, No. 2, pp. 481-509 [10] Bukovnik, S., Thermo-elasto-hydrodynamic lubrication model for journal bearing including shear rate-dependent viscosity. Lubrication Science, Vol. 19, 2007, pp. 231-245 Science and Research 12 Tribologie + Schmierungstechnik · volume 71 · issue 2/ 2024 DOI 10.24053/ TuS-2024-0007 To consider the described viscosity variations for the flow factor calculation, a simulation model based on the Reynolds equation according to Dowson and preliminary works from Herbst was introduced. Mathematical principles as well as the used algorithm were discussed. To understand the fundamental mechanism influencing the flow factor calculation with respect to non-Newtonian fluids, initially, a simplified rough gap was generated. The corresponding results showed that neglecting the variable viscosity behavior of non-Newtonian fluids leads to significant errors. Furthermore, it could be shown that the error increases with decreasing gap height. The error is especially huge for fluids, whose viscosity change rapidly for varying shear rates. A further parameter influencing the error in flow factor calculation is the pressure gradient. Besides the simplified gap, a realistic technical surface was investigated, as well. Here, the same effects that were previously evaluatedcould be demonstrated. The presented method can be used to estimate the error in the flow factor calculation caused by neglecting shear thinning in the conventional method. In a further step, the phenomena and dependencies shown are to be investigated in more detail in to be able to estimate the maximum deviations from the flow factor according to Patir and Cheng as a function of surface properties, fluid properties, gap height and pressure gradient without complex simulation. This way users can estimate wether high deviation in flow factor can be expected for their specific tribological system. Since the error is especially high for small gap height, the future implementation of a contact model is desirable. This way, the gap height between the two rough surfaces can be reduced even more. Additionally, the influence of flow channel formation on the error could be investigated with an appropriate deformation model. Moreover, the investigation of further non-Newtonian fluids apart from Cross fluids is planned. In this context, the evaluation of ionic liquids that are showing strong shear thinning behavior is also feasible. This contribution only focused on the pressure flow between rough surfaces. For this reason, the simulation model shall be extended by a calculation routine for shear flow. Acknowledgement Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - Exzellenzcluster 2186 “The Fuel Science Center”.