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

List of Tables
1.1 The tensorial description of some simple flows . . . . . . . . . . . . . . . 4
2.1 Summary of the transformation from a discrete system to a continuous
variable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 The pom-pom constitutive equation- differential approximation . . . . . 39
3.1 Non-linear spectrum of melt 1 fitted to extensional rheology, from Inkson
et al. (1999). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.2 Non-linear spectrum of melt 1810H obtained by fitting to planar extension
data from Hachmann (1997). . . . . . . . . . . . . . . . . . . . . . . 60
3.3 Criterion of equation 3.22 applied to the linear spectrum of melt 1 and
two non-linear spectra for melt 1. Spec I is a fit to uniaxial extension
[Inkson et al. (1999)] and Spec II is a fit to the transient nearly exponential
shear stress data collected by Zülle et al. (1987) . . . . . . . . . 65
3.4 Criterion of equation 3.22 applied to the linear spectrum of melt 1810Hb
and two non-linear spectra. Spec Ib is a fit to exponential shear data and
Spec IIb is a fit to the transient uniaxial extensional data from Suneel
et al. (Submitted). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.1 Closed system of equation including describing the dynamics of an ensemble
of entangled linear polymers including: contour length fluctuations,
retraction, constraint release and variable number of entanglements. 85
4.2 Material parameters for two polybutadiene solutions [Menezes and Graessley
(1982)] and a polystyrene solution [Hua et al. (1999)]. Material parameters
are as quoted in the original papers, fitted parameters are obtained
from linear oscillatory shear and calculated parameters are computed
from the other parameters. . . . . . . . . . . . . . . . . . . . . . . 93
viii