Comparing the wall slip and the constitutive approach for modelling spurt instabilities in polymer melt flows

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Abstract

At high flow rates during polymer melt extrusion, pressure oscillations can be observed. The phenomenon is usually referred to as spurt, due to the irregular - in bursts - emergence of the melt out of the die. Spurt, or equivalently, the associated pressure oscillations have been modelled successfully through the mechanism of relaxation-oscillations by Molenaar and Koopmans. The presence of a non-monotone flow curve is at the heart of this modelling. In this paper the curve is deduced from conservation laws combined with a die wall boundary condition and specific constitutive equations. Subsequently, three 'model curves' are compared. Model A, a Newtonian fluid with a 'switch function' defining an alternating stick-slip boundary condition. Model B is a non-monotone constitutive equation i.e. a Johnson-Segalman-Oldroyd (JSO) fluid with a no-slip condition. Model C consists of two Newtonian fluids in concentric die regions and a no-slip condition. It is shown that Models A and C are able to describe spurt that is in qualitative agreement with experiments reported in literature. Model B, however, does not lead to spurt, in spite of the non-monotone nature of the steady stress-strain rate curve! These results tend to show that there are many options to describe experimental flow curves with equations based on geometrical, operational and polymer property parameters. Accordingly, from a mathematical point of view, and in view of the equivalence in results between model A and C, it can be concluded that the existing controversy between slip or no-slip (i.e. constitutive) supporters is not a fundamental one. © 1998 Elsevier Science B.V.

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Den Doelder, C. F. J., Koopmans, R. J., Molenaar, J., & Van De Ven, A. A. F. (1998). Comparing the wall slip and the constitutive approach for modelling spurt instabilities in polymer melt flows. Journal of Non-Newtonian Fluid Mechanics, 75(1), 25–41. https://doi.org/10.1016/S0377-0257(97)00081-5

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