Rheological aspects of thermoplastic foam extrusion

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Abstract
Several rheological aspects of thermoplastic foam extrusion are described by a phenomenological model of the flow in an extrusion die. The macroscopic effects of the phase change, from a homogeneous polymer melt that contains a blowing agent, to a foam, are described in terms of two dimensionless parameters. α is defined as the ratio of the pressure gradient in the melt phase to the average pressure gradient in the foam phase. Θ represents the ratio of the pressure drop in the melt phase to the pressure drop in the foam phase. The position at which the phase change initiates, the exit contribution to the Bagley ends pressure correction, and the true wall shear stress in the melt phase are related to α and Θ. The quality of the foam produced is discussed in terms of the extrusion conditions and their effect on the foaming position in the die. It is demonstrated that the ends pressure correction cannot be neglected on the basis of a long die alone. Asymptotic conditions for which the phase change has negligible effect on the melt flow rate are predicted. α is calculated from the data of Han and Villamizar, who measured the pressure distribution in the die and observed the phase change directly. The prediction of α from theory is complicated by the lack of suitable constitutive relations for the foam phase. Since Θ only requires knowledge of the pressure at which the phase change initiates, it is relatively easy to evaluate.

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