Significance of slip velocity and viscosity variation on squeezed film couple-stress properties between a rough plate and a cylinder

This study examines the impact of surface roughness and viscosity variation on the couple stress squeeze film characteristics between a cylinder and a rough plate with slip velocity. Two distinct one-dimensional roughness patterns—longitudinal and transverse—are considered. Using Christensen's theory, the stochastic modified Reynolds equation is derived for Stokes couple stress fluid, incorporating viscosity variation with pressure. The standard perturbation technique is applied to solve the average Reynolds equation, yielding closed-form expressions for the mean fluid film pressure, load-carrying capacity, and squeeze film time. Various parameters are varied, and the results are discussed through graphical representations in 2D and 3D. This study highlights the importance of viscosity variation, couple stresses, and surface roughness in optimizing squeeze film performance. While increased viscosity and couple stresses enhance load-bearing capacity and film time, slip velocity detracts from these properties. Additionally, surface roughness has a significant impact, with transverse roughness improving, and longitudinal roughness reducing, the squeeze film characteristics. Applications of this study include improving the design and performance of bearing systems, lubrication in mechanical seals, and hydraulic systems where surface roughness and viscosity variation play a significant role in operational efficiency.