Viscoelastic lubrication with Phan-Thein-Tanner fluid (PTT)

We analyze the lubrication flow of a viscoelastic fluid to account for the time dependent nature of the lubricant. The material obeys the constitutive equation for Phan-Thein-Tanner fluid (PTT). An explicit expression of the velocity field is obtained. This expression shows the effect of the Deborah number (De =lambda U/L, lambda is the relaxation time). Using this velocity field, we derive the generalized Reynolds equation for PTT fluids. This equation reduces to the Newtonian case as De --> 0. Finally, the effect of the Deborah number on the pressure field is explored numerically in detail and the results are documented graphically.