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Scaling effects in microscale ﬂuid ﬂow at rough solid surfaces
The flow of lubricant between two solid surfaces at contact is studied via lattice Boltzmann simulations. Through a simple order of magnitude estimate, it is shown that high Reynolds number flows may occur in usual engineering applications such as metal forming processes, even at scales as small as the surface roughness asperities. This contradicts the common assumption of a laminar lubricant flow and brings about the possibility of a roughness-induced transition towards an unsteady flow/turbulence. The impact of parameters such as the (average) roughness height and the (average) roughness wave length on the transition is studied. It is shown that it is not the roughness height alone which determines the onset of flow instability. Rather, it is the combined effect of the roughness height and wave length which is essential. In particular, keeping the roughness height constant, it is possible to trigger flowinstability by an increase in the roughnesswave length. This observation is rather unexpected, as it also occurs in cases where the increase in the wave length is achieved by introducing a smoother surface. Our results are in qualitative agreement with results on rough wall turbulence in that they show that a local Reynolds number (based on the roughness height alone) does not capture the roughness effects on the flow characteristics. Moreover, a comparison of simulation results on the viscous shear stress and the Reynolds stress clearly shows that these two quantities are not proportional to each other. In other words, the eddy viscosity model does not apply to the situation studied in this work.