Biomedical Engineering Reference
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can be an advantage, for example in applications where solutions are required to spread
easily on a surface. Shear thinning is ascribed to the disruption of the network junctions:
the rate of network breakdown under shear exceeds the rate at which the intermolecular
associations take place. However, the Cox
Merz rule ( Chapter 4 ; Cox and Merz, 1958 ;
Graessley, 1974 ) is no longer obeyed. This rule states that the dynamic viscosity
-
η
*(
ω
)
can be superposed on data of the steady shear viscosity
, at equivalent low angular
frequencies or shear rates. The rule is observed for almost all simple polymer solutions of
high molecular mass or melts, and here the superposition extends further into the shear
thinning range as well (Ferry, 1980 ). In associating polymer solutions, the shear viscosity
is larger than the dynamic viscosity, the Newtonian plateau of the steady shear viscosity
extending further than the dynamic viscosity plateau, as shown in Figure 6.9b . The
opposite effect to this was seen in other structured liquid systems such as the xanthan
polysaccharides ( Chapter 5 ).
In some cases shear thickening (dilatancy) also occurs, as shown in Figure 6.9a .
Shear thickening is also observed in HMPAm polymers with a statistical distribution of
hydrophobes along the chains in the presence of 0.1M NaCl. Telechelic HEUR
solutions also exhibit shear thickening effects (Lundberg et al., 1991 ). With increasing
shear rates, viscosity increases and attains a maximum, and then falls again at higher
shear rates.
In the case when the whole sample is uniformly sheared in volume, i.e. the shear is not
localized into shear bands, and there are no wall slippage effects, Witten and Cohen
( 1985 ) outlined a mechanism of shear thinning in which
ðγÞ
flow produced an increase in
inter-chain associations at the expense of those within the chain. They then calculated
how chain elongation produced by
flow altered the balance between these intra- and
20
70
(b)
(a)
40
10
5
10
( )
η
η ( )
η
* (
)
η
ω
* ( ω )
2
10 -2
10 -1
10 0
10 1
10 2
10 -2
10 -1
10 0
10 1
10 2
(s -1 ), ω ( rad s -1 )
(s -1 ),
ω ( rad s -1 )
Steady-state viscosity ðγÞ and dynamic complex viscosity η *( ω ) as a function of the shear rate or
angular frequency for two samples of the HM poly(acrylamide) DiHexAm: (a) M w =4.2×10 5 gmol 1 ,
hydrophobic block length 3.2 units, 18 hydrophobic blocks per chain at c=2%w/w;(b)M w =1.4×10 5
gmol 1 , 6 hydrophobic blocks per chain at c = 9% w/w. Adapted with permission from Regalado et al.
( 1999 ) © 1999 American Chemical Society.
Figure 6.9
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