1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Transient overshoot extensional rheology of long-chain branched polyethylenes: Experimental and numerical comparisons between filament stretching and cross-slot flow
Rent:
Rent this article for
USD
10.1122/1.4767982
    + View Affiliations - Hide Affiliations
    Affiliations:
    1 Department of Physics, University of Durham, Durham DH1 3HP, United Kingdom and Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
    2 Department of Chemical and Biochemical Engineering, The Danish Polymer Centre, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
    3 Interdisciplinary Research Centre for Polymer Science and Technology (IRC), University of Leeds, Leeds LS2 9JT, United Kingdom and Institute of Condensed Matter, Bio- and Soft Matter, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
    4 Department of Chemical Engineering, University of Cambridge, Cambridge CB2 3RA, United Kingdom and Institut Teknologi Brunei, Jalan Tungku Link, Gadong BE1410, Brunei Darussalam
    5 Department of Mechanical Engineering, The Danish Polymer Centre, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
    6 Department of Chemical and Biochemical Engineering, The Danish Polymer Centre, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
    7 Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
    8 Department of Chemical and Biochemical Engineering, The Danish Polymer Centre, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
    9 Department of Chemistry, University of Durham, Durham DH1 3LE, United Kingdom and Department of Physics, Durham University, Durham DH1 3HP, United Kingdom
    a) Electronic mail: d.m.hoyle@durham.ac.uk
    b) Author to whom correspondence should be addressed; electronic mail: o.g.harlen@maths.leeds.ac.uk
    J. Rheol. 57, 293 (2013); http://dx.doi.org/10.1122/1.4767982
/content/sor/journal/jor2/57/1/10.1122/1.4767982
http://aip.metastore.ingenta.com/content/sor/journal/jor2/57/1/10.1122/1.4767982

Figures

Image of FIG. 1.
FIG. 1.

(a) Schematic outlining the Cambridge MPR core and (b) the dimensions and flow direction for the cross-slot geometry insert as used in the midsection of the MPR. The associated flow directions are indicated by arrows.

Image of FIG. 2.
FIG. 2.

(a) The transient extensional viscosity for a single mode overshoot Pompom model in uniaxial extension. The four set of curves shows the effect of variations in the power law from 10 to 1000 with for various stretch Weissenberg numbers ( ). As is increased so does the amount of alignment needed for the extra relaxation time, , to become dominant. This has the effect of delaying relaxation until a higher Hencky strain has been reached causing a bigger difference between the maximum and the steady-state extensional viscosity. (b) A plot of the measured alignment, , for the same stretch Weissenberg numbers. As is increased so does the strain taken for the measured alignment to approach unity and thus delays the transient overshoot.

Image of FIG. 3.
FIG. 3.

(a) The transient extensional viscosity for a single mode overshoot Pompom model in uniaxial extension. The four set of curves shows the effect of variations in parameter from 1 to 5 with for various stretch Weissenberg numbers ( ). The parameter does not affect the strain needed to achieve an overshoot but it does affect the magnitude of and thus determines the steady-state extensional viscosity. (b) The effect of the branch number q on transient extensional viscosity for a single mode overshoot Pompom model in uniaxial extension. The four set of curves shows the effect of variations in parameter q from 3 to 20 for the same stretch Weissenberg numbers. In the case q = 3 maximum stretch is achieved during the transient, but for larger values q = 10 and 20, remains strictly less than q for all time and the differences are due only to the change to .

Image of FIG. 4.
FIG. 4.

(a) Computed contours of constant principal stress difference for the one mode Pompom model used in Fig. 2 , examining how the power law affects W-cusps in cross-slot flow. The dashed line shows , the solid line , and the dotted line . (b) The effect of varying on the W-cusps in the cross-slot flow using the single mode Pompom models used in Fig. 3 . The dotted line shows , the solid line shows , and the dashed line shows .

Image of FIG. 5.
FIG. 5.

PSD and along the SP streamline as a function of distance from the SP showing variations in (a) and (b) . Negative distance from the SP corresponds to the inlet channel and positive distance the outlet channel.

Image of FIG. 6.
FIG. 6.

A comparison of the steady-state extensional viscosity measurements from the FSR and the CSER for three polyethylene samples detailed in Table I . The open symbols show the FSR results and the closed symbols show the CSER data.

Image of FIG. 7.
FIG. 7.

A comparison between the transient extensional stress response as measured by the FSR (closed) and the SER (open) for HDB6 (left) and HDB4 (right). The figure shows a good agreement of the initial stress growth, until sample rupture limits the SER to Hencky strains of around 4.

Image of FIG. 8.
FIG. 8.

(a) A plot comparing extensional data and OPP theory for Dow150R. Strain rates range from to . The closed symbols show the SER data and the open symbols data from the FSR achieving higher Hencky strains than the SER. The lines show the theoretical prediction from the OPP model. (b) The steady-state extensional viscosity values from the FSR and the CSER are compared to the prediction of the Pompom model fitted to the data.

Image of FIG. 9.
FIG. 9.

The transient (a) and steady-state (b) data for HDB6 are plotted along side the OPP model fitted to the data (lines). For the transient fit, the slower strain rates were measured by the FSR and the higher rates by the SER. The steady-state data came from the FSR and the CSER.

Image of FIG. 10.
FIG. 10.

A comparison of between FIB in cross-slot flow and 2D simulations of the OPP parameterization for LDPE Dow150R. The values of overshoot parameters are and , and the transient extensional rheology is shown in Fig. 8 . The black lines in the simulations represent the black contours of the experimental PSD for initial strain rates of , and from top to bottom.

Image of FIG. 11.
FIG. 11.

A comparison of between FIB in cross-slot flow and 2D simulations of the OPP parameterization for HDPE HDB6. The values of overshoot parameters are and , and the transient extensional rheology is shown in Fig. 9 . The black lines in the simulations represent the black contours of the experimental PSD for initial strain rates of , and from top to bottom.

Image of FIG. 12.
FIG. 12.

A comparison between the OPP simulations and the experimentally measured position of the FIB contours of constant PSD for HDB6 at three flow rates.

Tables

Generic image for table
TABLE I.

Material properties of polyethylenes studied.

Loading

Article metrics loading...

/content/sor/journal/jor2/57/1/10.1122/1.4767982
2012-12-04
2014-04-17
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Transient overshoot extensional rheology of long-chain branched polyethylenes: Experimental and numerical comparisons between filament stretching and cross-slot flow
http://aip.metastore.ingenta.com/content/sor/journal/jor2/57/1/10.1122/1.4767982
10.1122/1.4767982
SEARCH_EXPAND_ITEM