On the Extrusion of a Very Viscous Liquid

Abstract

Abstract An approximation to a state of affairs occurring in the extrusion of rubber is the two-dimensional slow flow of a very viscous liquid from a half plane into a semi-infinite strip. The region surrounding the orifice or juncture of the strip and plane corresponds to the region where the extruded rubber is forced from a die box into a die. Methods are developed and carried out for numerically obtaining the stream function, the velocity components, and the pressure in this region. The general pattern of the streamlines is determined, and it is found in what way and to what extent the flow pattern in the strip near the orifice differs from plane Poiseuille flow and how far into the strip this difference is significant. Incidental to this work, it was necessary to determine the first several complex roots of sin A = ± 2 3 π A . This information is useful apart from the flow problem, and the results are tabulated.