Averaged inertia analysis in couple stress fluids in squeeze film under piezo-viscous lubrication between annular parallel disks

This study explores effect of inertia on piezo-viscous pressure and the flow of a couple stress fluids in the squeeze film lubrication between annular parallel disks. Based on the Stokes micro-continuum theory, the governing equations are derived by retaining the nonlinear inertia terms by taking the average inertia principle along the vertical direction. The resulting Reynolds equation for piezo-viscous pressure, which includes inertial impact, is solved using perturbations with piezo-viscosity parameter as a perturbation parameter. Results reveal that the piezo-viscous effect increases load support compared to the iso-viscous case, and an increase in the couple stress parameter improves the load-carrying capacity due to the greater resistance caused by micro-structural interactions within the fluid. Additionally, the Reynolds number significantly influences the flow regime, affecting pressure distribution, load-carrying capacity, and response time. The findings have implications for lubrication systems in high-speed rotary machinery, aerospace components, and precision engineering applications where both pressure-induced viscosity variations and inertial effects are significant.