Abstract
In [1,2] we develop a comprehensive theory of one space dimensional closure models (closed systems of 1-D equations for the unknown, or modal, variables) for free viscoelastic jets. These closure models are derived via asymptotics from the full 3-D boundary value problem under the conditions of a Von Kármán-like flow geometry, a Maxwell-Jeffreys constitutive model, elliptical free surface cross section, and a slender jet scaling. The focus of the present paper is to determine the consequences and predictions of the lowest order system of equations in this asymptotic analysis. For the special cases of elliptical inviscid and Newtonian free jets, subject to the effects of surface tension and gravity, our model predicts oscillation of the major axis of the free surface elliptical cross section between perpendicular directions with distance down the jet, and draw-down of the cross section, in agreement with observed behavior. In the absence of surface tension the transformation from a cross section with major axis in one direction to a cross section with major axis in the perpendicular direction occurs only once, in agreement with the observation of Taylor [4]. In viscoelastic regimes, our model predicts swell of the elliptical extrudate and distortion of the elliptical extrudate cross section from the dimensions of the die aperture.
Published Version
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