A theory of roll coating of viscous and viscoelastic fluids

A theory for roll coating of a fluid onto a moving sheet is developed utilizing the usual “lubrication approximations.” The effects of fluid and operating parameters on coating thickness and pressure distribution are determined for a Newtonian fluid, and for a purely viscous non‐Newtonian fluid obeying the Power Law. The results for these cases are obtained analytically, and are rather straightforward. A viscoelastic fluid is considered, of a type which shows typical non‐Newtonian shear behavior observed in polymer melts and solutions and which also exhibits normal stress behavior. Analytical solutions are not possible, but a perturbation method, using a viscoelastic perturbation parameter related to a Deborah number, yields an approximate solution. Only terms to first order in the perturbation parameter are given. Subject to that degree of approximation, the following conclusions are drawn: Non‐Newtonian shear behavior reduces the pressure distribution, and increases the coating thickness. Elasticity of the type usually observed in polymer solutions makes only a minor contribution to the roll‐separating (load‐carrying) force. The contribution is positive, but smaller than the corresponding negative contribution due to the non‐Newtonian shear effects. An increase in load‐carrying capacity would require a different viscoelastic fluid than the type considered here—one that is essentially Newtonian in shear but, independently, capable of developing significant normal stresses.