Molecular modelling of entangled polymer fluids under flow The ...

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LIST OF FIGURES
3.12 Comparison of multimode pom-pom predictions to experimental data
for first normal stress difference in true exponential shear from Venerus
(2000). Solid curves are pom-pom predictions, shapes are data points
and the dashed curve is the FLV curve for first normal stress difference
in simple shear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.13 Free parameter fit of non-linear parameters of melt 1 using only nearly
exponential shear data collected by Zülle (1987). . . . . . . . . . . . . . 66
3.14 Comparison of pom-pom predictions using spec II with uniaxial extension
data for melt 1 from Meissner (1972). . . . . . . . . . . . . . . . . . 67
3.15 The 8 modes of melt 1 (see table 3.1) in nearly exponential shear for
α = 0.01sec −1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.16 The 8 modes of melt 1 (see table 3.1) in uniaxial extension for ˙ɛ =
0.01sec −1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.17 Linear response of two batches of melt1810H: a)data collected by Venerus
(2000) (melt 1810H) b) data collected by Suneel et al. (Submitted) (melt
1810Hb). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.18 Experimental data and predictions for uniaxial extension of melt 1810Hb
(filled shapes) and simple shear (open shapes) made using spec Ib which
was obtained by fitting only to exponential shear data. . . . . . . . . . . 72
3.19 Experimental data and predictions for true exponential and (filled shapes)
and simple shear (open shapes) of melt 1810Hb made using spec IIb
which was obtained by fitting only to uniaxial extension data. . . . . . . 73
4.1 Two possibilities for the effect of a step deformation on the entanglement
network. (a) The number of entanglements points is fixed and so the tube
persistence length grows. (b) The tube persistence length remains fixed
so Z grows in proportion with the primitive path length. . . . . . . . . . 76
4.2 The effect of CCR on an unstretched segment (a) and a stretched segment
(b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.3 Mechanism by which CCR relaxes chain stretch . . . . . . . . . . . . . . 78
4.4 Theory predictions of steady state shear stress as a function of shear rate
(c ν = 0.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.5 Transient predictions for shear stress and normal stress against strain,
γ, for start-up of simple shear. Model parameters: Z = 20, c ν = 0.1
with shear rates from ˙γτ R = 21 to linear response. . . . . . . . . . . . . 90
4.6 S(q) in steady shear for a range of shear rates. The two higher rate Rouse
Weissenberg number are 0.42 and 6, respectively. Model parameters:
Z = 20 and c ν = 0.1. Contours lines map the same value on each plot. . 91