Mathematical study of viscoelastic polymer during roll-over-web coating

Roll-coating, also known as roll-to-roll coating or web coating is a continuous and high-speed method used in various industrial applications to apply a thin and uniform layer of material onto a substrate. This process is commonly employed in industries such as electronics, photovoltaic, printing, packaging, and other fields where precise and consistent coating is essential. Here we present an asymptotic analysis of forward roll coating over a rigid substrate for low Weissenberg number viscoelastic fluids. The analysis uses lubrication theory coupled with regular perturbation theory assuming a simplified Phan-Thien-Tanner (SPPT) constitutive equation and small values of the extensibility parameter e. The analytical expressions of velocity fields, pressure gradient and pressure fields are obtained while the load carrying force, and power input are estimated by numerical solutions (4th order Runge-Kutta). Increases in both Wi and e increases the pressure gradient in the nip region and increases in viscoelasticity reduce the overall force on the roll. Further, SPTT model predicts 14% lower pressure for Wi(= 0.8) in the nip region when compared to Newtonian model.