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Reply to: ‘On the ‘‘viscosity overshoot’’ during the uniaxial extension of a low density polyethylene’
Journal of Non-Newtonian Fluid Mechanics 171–172 (2012) 106
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Reply to: ‘On the ‘‘viscosity overshoot’’ during the uniaxial extension of a low density polyethylene’
In the work by Burghelea et al. [1] data points from one of our measurements (originating from Ref. [2]) were inserted in their Fig. 9a and b. All the measurements performed by Burghelea et al. [1] were conducted at 140 °C, where our measurements were conducted at 130 °C. There are no references to this temperature in the work by Burghelea et al. [1] and our data were not time-temperature super-positioned to the 140 °C. The time–temperature shift factor for the used material (LDPE Lupolen 1840D) can be obtained from Resch [3]. Here the ratio between the zero-shear rate viscosities at 140 °C and 130 °C are 0.63 giving a time–temperature superposition shift factor aT = 0.62. This ratio between the zero-shear rate viscosities is multiplied on our extensional viscosities to shift these to 140 °C. The data are shown in the corrected Fig. 9a and b in the following. We have kept the figure caption identical with the original one. In Fig. 9a our extensional rate of e_ ¼ 0:01 s1 (at 130 °C) corresponds to a rate of e_ ¼ 0:016 s1 at 140 °C, applying the shift factor aT = 0.62. This rate is virtually identical to e_ ¼ 0:015 s1 , within the experimental accuracy on the determination of the rates presented in Burghelea et al. [1]. Our data from Fig. 9a are inserted in Fig. 9b (the upper triangles) as well. We have also included our measurements (the lower triangles) at a rate of e_ ¼ 0:03 s1 (at 130 °C) corresponding to a rate of e_ ¼ 0:048 s1 at 140 °C in Fig. 9b, as the extension by Burghelea et al. [1] are reported to be at a rate of e_ ¼ 0:025 s1 . A rate in between e_ ¼ 0:016 s1 and e_ ¼ 0:048 s1 . Finally, notice that our measurements all are performed at an aspect ratio (height to width) of 0.28. This is substantially lower the smallest aspect ratio used by Burghelea et al. [1] of 0.62. To quote Rasmussen et al. [2] page 373: ‘A low initial aspect ratio is
required for measuring on LDPE melt at high elongation rates in the FSR. At low aspect ratio, the location of the neck in the circular sample, during the extension, is predictably placed in the middle of the filament, creating the symmetry plane, where the laser sheet is located. By contrast, with a high aspect ratio, an unexpected neck located closer to one of the end plates typically occurs. As a consequence, the filament will break asymmetrically and the symmetry plane at the mid filament is lost.’ Therefore the study by Burghelea et al. [1] cannot be used to discuss the flow in our measurements. References [1] T.I. Burghelea, Z. Stary´, H. Münstedt, On the ‘‘viscosity overshoot’’ during the uniaxial extension of a low density polyethylene, Journal of Non-Newtonian Fluid Mechanics 166 (2011) 1198–1209. [2] H.K. Rasmussen, J.K. Nielsen, A. Bach, O. Hassager, Viscosity overshoot in the start-up of uniaxial elongation of low density polyethylene melts, Journal of Rheology 49 (2) (2005) 369–381. [3] J. Resch, PhD thesis, University of Erlangen-Nürnberg, 2009.
Henrik Koblitz Rasmussen a ⇑ Ole Hassager b, a Department of Mechanical Engineering , Technical University of Denmark, DK-2800 Kgs, Lyngby, Denmark b Department of Chemical and Biochemical Engineering, Technical University of Denmark, DK-2800 Kgs, Lyngby, Denmark ⇑ Corresponding author. E-mail address: [email protected] (O. Hassager)
Fig. 9. Comparison between the integral viscosity measurements (full lines), space averaged viscosity (squares) and the elongational viscosity obtained following a procedure similar (see text) to that of Rasmussen et al. [16] (circles): (a) e_ ¼ 0:015 s1 (Wi = 16.5). (b) e_ ¼ 0:025 s1 (Wi = 27.5). The triangles are data extracted manually from Fig. 4 from [16] and they refer to e_ H ¼ 0:01s1 (Wi = 18.75). The full arrows indicate the onset of the primary geometric inhomogeneity of the sample and the dashed arrows indicate the onset of the secondary necking instability. 0377-0257/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jnnfm.2012.01.004
Contents lists available at SciVerse ScienceDirect
Journal of Non-Newtonian Fluid Mechanics journal homepage: http://www.elsevier.com/locate/jnnfm
Reply to: ‘On the ‘‘viscosity overshoot’’ during the uniaxial extension of a low density polyethylene’
In the work by Burghelea et al. [1] data points from one of our measurements (originating from Ref. [2]) were inserted in their Fig. 9a and b. All the measurements performed by Burghelea et al. [1] were conducted at 140 °C, where our measurements were conducted at 130 °C. There are no references to this temperature in the work by Burghelea et al. [1] and our data were not time-temperature super-positioned to the 140 °C. The time–temperature shift factor for the used material (LDPE Lupolen 1840D) can be obtained from Resch [3]. Here the ratio between the zero-shear rate viscosities at 140 °C and 130 °C are 0.63 giving a time–temperature superposition shift factor aT = 0.62. This ratio between the zero-shear rate viscosities is multiplied on our extensional viscosities to shift these to 140 °C. The data are shown in the corrected Fig. 9a and b in the following. We have kept the figure caption identical with the original one. In Fig. 9a our extensional rate of e_ ¼ 0:01 s1 (at 130 °C) corresponds to a rate of e_ ¼ 0:016 s1 at 140 °C, applying the shift factor aT = 0.62. This rate is virtually identical to e_ ¼ 0:015 s1 , within the experimental accuracy on the determination of the rates presented in Burghelea et al. [1]. Our data from Fig. 9a are inserted in Fig. 9b (the upper triangles) as well. We have also included our measurements (the lower triangles) at a rate of e_ ¼ 0:03 s1 (at 130 °C) corresponding to a rate of e_ ¼ 0:048 s1 at 140 °C in Fig. 9b, as the extension by Burghelea et al. [1] are reported to be at a rate of e_ ¼ 0:025 s1 . A rate in between e_ ¼ 0:016 s1 and e_ ¼ 0:048 s1 . Finally, notice that our measurements all are performed at an aspect ratio (height to width) of 0.28. This is substantially lower the smallest aspect ratio used by Burghelea et al. [1] of 0.62. To quote Rasmussen et al. [2] page 373: ‘A low initial aspect ratio is
required for measuring on LDPE melt at high elongation rates in the FSR. At low aspect ratio, the location of the neck in the circular sample, during the extension, is predictably placed in the middle of the filament, creating the symmetry plane, where the laser sheet is located. By contrast, with a high aspect ratio, an unexpected neck located closer to one of the end plates typically occurs. As a consequence, the filament will break asymmetrically and the symmetry plane at the mid filament is lost.’ Therefore the study by Burghelea et al. [1] cannot be used to discuss the flow in our measurements. References [1] T.I. Burghelea, Z. Stary´, H. Münstedt, On the ‘‘viscosity overshoot’’ during the uniaxial extension of a low density polyethylene, Journal of Non-Newtonian Fluid Mechanics 166 (2011) 1198–1209. [2] H.K. Rasmussen, J.K. Nielsen, A. Bach, O. Hassager, Viscosity overshoot in the start-up of uniaxial elongation of low density polyethylene melts, Journal of Rheology 49 (2) (2005) 369–381. [3] J. Resch, PhD thesis, University of Erlangen-Nürnberg, 2009.
Henrik Koblitz Rasmussen a ⇑ Ole Hassager b, a Department of Mechanical Engineering , Technical University of Denmark, DK-2800 Kgs, Lyngby, Denmark b Department of Chemical and Biochemical Engineering, Technical University of Denmark, DK-2800 Kgs, Lyngby, Denmark ⇑ Corresponding author. E-mail address: [email protected] (O. Hassager)
Fig. 9. Comparison between the integral viscosity measurements (full lines), space averaged viscosity (squares) and the elongational viscosity obtained following a procedure similar (see text) to that of Rasmussen et al. [16] (circles): (a) e_ ¼ 0:015 s1 (Wi = 16.5). (b) e_ ¼ 0:025 s1 (Wi = 27.5). The triangles are data extracted manually from Fig. 4 from [16] and they refer to e_ H ¼ 0:01s1 (Wi = 18.75). The full arrows indicate the onset of the primary geometric inhomogeneity of the sample and the dashed arrows indicate the onset of the secondary necking instability. 0377-0257/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jnnfm.2012.01.004