An in situ investigation of the draw resonance phenomenon in film casting of a polypropylene melt - Burghelea, Teodor I.; Grieß, Hans Jürgen; Münstedt, Helmut (Journal of Non-Newtonian Fluid Mechanics, 2012)
An experimental investigation of the stability of the casting process of a polypropylene film is presented. By combined in situ measurements of the width of the cast film and Digital Particle Image Velocimetry (DPIV) measurements of the velocity distributions within the polymer film, several flow regimes are identified: stable, oscillatory and chaotic. Measurements of the velocity distribution along and across the extruded film corresponding to each drawing regime are presented. The intermittent physical rupture of the film's edges observed within the chaotic drawing regime is explained by the emergence of a " V-shaped" region of high axial gradients of the axial velocity component which indicates a highly inhomogeneous distribution of tensile stresses.By measurements of the statistics of the fluctuations of both the film's width and velocity a continuous (second order) imperfect bifurcation towards oscillatory states is found. The fluctuation data acquired before the chaotic regime is reached can be fitted by the stationary Landau-Ginsburg equation. The observation of a stable limit cycle at the onset of the bifurcation identifies it as a supercritical Hopf bifurcation. The experimentally found scaling of the onset and amplitude of the bifurcation with the Weissenberg number indicates that elasticity destabilizes the drawing process. This can be explained by the thinning behavior of the material in both shear and extension.The spectral analysis of the fluctuations of both film's width and point-wise velocity provides a quantitative description of the harmonics excited beyond the bifurcation point. The transition to chaotic states is accompanied by a major reorganization of the power spectra consistent with a period doubling bifurcation of a stable limit cycle. © 2012 Elsevier B.V.
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Keywords: Chaos; Coat hanger die; Draw resonance; Film casting; Imperfect bifurcation