The problem of the squeezing of a fluid film with a complex rheology is studied. Thefluid is represented by the Phan-Tien and Tanner (PTT) constitutive equation. The goal ofthe paper is to develop an analytical approach which allows one to describe and quantifythis process, which is often present in classical lubrication problems, but particularlyin human joints. The present approach can potentially supplement time-consuming and costlypurely numerical methods which are also susceptible to misleading artifacts. A parametricstudy reveals the effect of fluid elasticity compared to viscous effects and someexplanation is suggested as to their possible links with joint diseases.

In recent decades, problems related to the squeeze of fluid films in the presence of aporous medium draw attention of researchers and are the subject of many applied studiesfor industry and biomechanics. Our concerns in this paper are the numerical simulation ofthe viscous shear stresses effects on the fluid film characteristics between two discswith one porous. This study is based on the coupling, at the fluid film-porous discinterface, of the Darcy-Brinkman equations in the porous medium and the modified Reynoldsequation describing the flow in the fluid film. The system of equations obtained isdiscretized by the means of finite differences method and solved numerically using thetechnique of Successive Over-Relaxation (SOR). The results show that the viscous sheareffects increase the radial and the axial fluid film velocities as well as the squeezefilm velocity but decrease the response time. Moreover, these effects are enlarged forsmaller viscous shear parameter and for smaller fluid film thickness.