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A COMPARISON BETWEEN THE KINETIC THEORY OF - page 17 / 25

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Here is a convected time derivative of , is the solvent contribution to the stress tensor,   is the rate-of-strain tensor, and is a time constant ( being the hydrodynamic drag coefficient for a bead moving through the solvent, and H is the spring constant). This simple result is of limited value, because it cannot describe the observed non-Newtonian viscosity or the normal stress coefficient in steady-state shear flow. In linear viscoelasticity, it cannot describe the observed spectrum of relaxation times.

For the FENE-P model, described at the beginning of §2, we find [11]

(3.2)

where

(3.3)

and is a dimensionless quantity—about 50—that is a measure of the extent to which the molecule can be stressed; the parameter is given by . This model gives a viscosity that goes as and a first normal stress coefficient as , both of which are in fair agreement with experiment. It also gives an elongational viscosity that goes to as the elongation rate goes to , and to as the elongation rate tends toward . This seems to be

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