<string language="el">On the stick-slip flow from slit and cylindrical dies of a Phan-Thien and Tanner fluid model. II. Linear stability analysis</string>
engURIhttp://hdl.handle.net/10795/3411physical sciencesapplied researchuniversity researchDuring extrusion of viscoelastic fluids various flow instabilities may arise resulting in
a distorted free surface. In order to investigate the factors generating these instabilities
we performed a linear stability analysis at zero Reynolds number around the steady
solution of the cylindrical or planar stick-slip flowfor a viscoelastic fluid following the
affine exponential Phan-Thien Tanner (PTT) model. Stick-slip flow is an important
special case of the extrudate swell problem, since the latter reduces to it in the limit
of infinite surface tension but avoids the complications of a free-boundary flow. The
linear stability analysis is performed for various values of the rheological parameters
of the PTT model in order to determine the effects of all material properties. It is
found that the flow becomes unstable as the Weissenberg number increases above
a critical value, due to a Hopf bifurcation suggesting that the flow will become
periodic in time. Both the critical value of theWeissenberg number and the frequency
of the instability depend strongly on the rheological parameters of the viscoelastic
model. The corresponding eigenvectors indicate that the perturbed flow field has a
spatially periodic structure, initiated at the rim of the die, extending for up to 5–7 die
gaps downstream, but confined close to the surface of the extrudate, in qualitative
agreement with existing experiments. This suggests that instability is generated by
the combination of the singularity in the velocity and stress fields at the die lip and the
strong extension that the extruded polymer undergoes near its surface. The elasticity
alone can be responsible for the appearance of instabilities in the extrusion process
of viscoelastic fluids and the often used assumptions of wall slip or compressibility,
although they might be present, are not required. Finally, the mechanisms that produce
these instabilities are examined through energy analysis of the disturbance flow29 pp.Digital Library of the Operational Programme "Education and Lifelong Learning" abstract types
TextViscoelastic fluidsLinear stability analysisPTTRheological parametersExtruded polymer3142518application/pdfhttp://repository.edulll.gr/edulll/bitstream/10795/3411/2/3411_POF_paper1.pdfΠανεπιστήμιο Θεσσαλίας. Τμήμα Μηχανολόγων Μηχανικών. - Δημοσιεύσεις.URIhttp://hdl.handle.net/10795/3411LOMv1.0creator2016-05-25T11:15:19ZLOMv1.0validator2016-05-25T11:15:19ZLOMv1.0grenonoCopyright EYD-EPEDBM (Operational Programme "Education and Lifelong Learning")