A mathematical model to study the effect of the air jet in the film blowing process

Abstract

The aerodynamic effect of the air jet that supports the polymeric films produced in the film blowing process is studied theoretically. The nonlinear coupling between the air and the polymer is examined by assuming steady, axisymmetric, and isothermal flow for both phases. The governing equations for the polymer are simplified by following the thin-film approximation and the corresponding ones for the air are derived by applying a boundary-layer type analysis. The latter are solved analytically by first applying the Mangler transformation that reduces the boundary layer equations for the axisymmetric case to those for a plane boundary layer. Then a similarity solution is obtained, allowing the shear stress and the pressure on the outer polymer/air interface to be evaluated in terms of the film shape only. The final set of ordinary differential equations for the film is solved numerically using finite differences. The results show that the force caused by the airflow has a significant effect on the film shape and the characteristics of the final product. Copyright © 2009 Society of Plastics Engineers.