Analytical solution to calendering in eccentric cylindrical coordinates

Calendering is the process in which molten material is dragged through the nip region to produce a film or sheet. By nip region, we mean the area between two corotating rolls. Here, we analyze the calendering problem in eccentric cylindrical coordinates with the simplest fluid, Newtonian. We first assume the velocity profile as vθ(ξ,θ). We arrive at the analytical solution for the velocity profile and pressure distribution when the fluid passes between parallel rolls. We then get the flow rate (and, thus, the sheet thickness) by integrating the velocity profile between the parallel rolls. We include a worked example to teach how to use our main result.