5. Viscoelastic Lubrication Using the Second-Order Fluid

The chapter explores the behavior of thin-film lubrication flows between solid surfaces, a phenomenon prevalent in various natural and engineered systems. It begins by discussing the fundamental role of lubrication in reducing friction and enhancing movement in both biological joints and mechanical components. The text then introduces the second-order fluid model, which is used to incorporate viscoelasticity into lubrication equations through long-wave expansions. This model simplifies the analysis by allowing the use of Tanner’s theorem, which provides exact expressions for liquid pressure and stresses without solving the full viscoelastic problem. The chapter delves into the governing equations and the lubrication approximation, comparing Newtonian and viscoelastic lubrication flows. It highlights how viscoelastic effects lead to non-trivial pressure variations across the film thickness, unlike Newtonian lubrication where pressure remains uniform. The applications section presents several case studies, including pressure drop along a channel, lift on sliding objects, and drag forces. These examples illustrate how viscoelasticity can enhance lift forces and affect drag, depending on the geometry and motion of the objects. The chapter concludes by discussing the limitations of the second-order fluid model and suggests future directions for research, particularly in the context of interfacial flows and thin liquid films.