Roll coating analysis of a third grade fluid

This paper studies the roll-coating process of an incompressible viscoelastic fluid, where the roll and the web have equal velocities. The lubrication approximation theory is used to simplify the equations of motion. Solutions for velocity profile, pressure gradient, flow rate per unit width, and shear stress at the roll surface are obtained by using a regular perturbation method. Integrated quantities of engineering interest are also calculated. These include the maximum pressure, separation point, roll/sheet separating force, power transmitted to the fluid by the roll, and coating thickness. It is found that these quantities increase substantially and monotonically as the fluid's material constant increases.