Multiscale analysis and texture design for hydrodynamically lubricated interfaces with variable viscosity and density liquids

In this work, a numerical framework is developed for the analysis and design of textured interfaces with piezoviscous, compressible and shear-thinning lubricants. This framework is based on a modified viscosity approach alongside homogenization as a mathematical technique for the upscaled solution of the Reynolds equation to alleviate the inherent computational difficulties to model roughness. Good agreement is observed between (i) direct numerical simulations, (ii) nonlinear Reynolds equation results and (iii) homogenized Reynolds equation results. Furthermore, the developed numerical framework has been used in conjunction with a topology optimization algorithm to design different surface textures that are dependent on the fluid rheology. These textures are shown to (i) minimize energy dissipation, or (ii) increase the traction to amplify the grip between the surfaces depending on the respective lubrication application.