Polymer Physics

7.3 Viscoelastic Phenomena of Polymer Flow

In shear flows, polymer melt experiences significant elastic deformations, and the
normal stress difference reflects its resistance to the shear stress. As illustrated in
Fig.7.13, the direction of flow is labeled as “1”, the direction of velocity gradient is
labeled as “2”, and the direction of equal velocity (normal to the book) is labeled as
“3”. Since the deformation along direction 1 is large, part of the normal stress
initially along direction 2 will be added onto direction 1, resulting in the order of
normal stresses as

s 11 >s 33 >s 22 (7.24)

Therefore, thefirst normal stress differenceis defined as

N 1 s 11 s 22 > 0 (7.25)

and thesecond normal stress differenceis defined as

N 2 s 22 s 33 < 0 (7.26)

Their common relations are

N 1  5 N 2 (7.27)

N 1 ;N 2 /g^02 (7.28)

Owning to large normal stress differences, the following-listed viscoelastic
phenomena are unique in polymer flows.

Fig. 7.13 Illustration of normal stress distributions (a) before and (b) after the shear flow acting
on the polymer fluid

140 7 Polymer Flow