Non-Newtonian region

For the straight line in Fig. 2.5 where m = 1.0, this equation expresses direct proportionality between and y, the condition of Newtonian behavior. In the non-Newtonian region where m < 1, Eq. (2.11) may describe the data over an order of magnitude or so. Next we consider the relationship between the constant K and viscosity. If Eq. (2.11) is solved for K and the resulting expression multiplied and divided by 7 ", we obtain... 

Moreover, a further conclusion can be drawn from Fig. 10, namely, that the evaluation of molar mass is impossible in the non-Newtonian region because samples with different molar mass all exhibit the same viscosity at a given shear rate. 

Accordingly, plots of a t)/a(0) vs t from different shear rates should superimpose. Experimentally the curves do not superimpose when the shear rate is in the non-Newtonian region, the initial rate of relaxation being increasingly more rapid for higher shear rates. The normal stress decays more slowly than shear stress, but behaves similarly with respect to the effect of previous shearing flow in the non-Newtonian region. 

When the shear rate at steady state is in the non-Newtonian region for the fluid, the recoil is smaller than J°a0 for both broad and narrow molecular weight distributions (362). 

The dynamic moduli for infinitesimal superimposed deformations parallel and transverse to the flow direction in steady shearing flow should be unaffected by flow if the shear rate is sufficiently small. According to the theory of simple fluids, the superimposed dynamic moduli for shearing flows in the non-Newtonian region must change in order to conform with the relations (370,372 ... 

The experiments show that the time-temperature dependence of viscosity in the non-Newtonian region of flow may be represented as ... 

For Newtonian fluids the viscosity is independent of time. However, for most non-Newtonian fluids the viscosity at a shear rate high enough to place the fluid in the non-Newtonian region evolves with time as schematically indicated by the lower curve of Figure 13.39. The viscosity decreases with time until steady-state conditions are reached. This phenomenon is called thixotropy. The cause of this behavior lies in the fact... 

The molecular entanglements increase as the average molecular weight increases. The lower Newtonian region becomes smaller because the interactions occur at lower shear rates, and the non-Newtonian region persists to higher shear rates, as illustrated in Fig. 3.38. 

Table 2.2 Flow Activation Energies Found Independent of Shear Stress in the Non-Newtonian Regions for Representative Amorphous Linear, Polymers...

FIG. 12 Plot of apparent viscosity r/ vs apparent shear rate / for HDPE at 230°C L /D = 40.1, Instron capillary rheometer II, specially designed capillary rheometer III, first non-Newtonian region IV, second Newtonian region V, second non-Newtonian region. (From Ref. 31.)... 

Figure 5.3 (b) Apparent viscosity versus apparent shear rate for HDPE at 230 "C LjD = 40). I Instron capillary rheometer II specially designed capillary rheometer IE first non-Newtonian region IV second Newtonian region V second non-Newtonian region [2]... 

The transition from the shear-thinning to the upper Newtonian region occurs when the Darcy velocity exceeds given by Eq. 5.44. Because there is a singjle non-Newtonian region, =n<. j and... 

The elastic properties of a viscoelastic medium also change when particles are added. These changes are qualitatively similar to those of the viscosity (Mewis and de Bleyser, 1975). In the non-Newtonian region, elasticity increases less than viscosity. Hence filled polymers are always less elastic than the suspending polymers under processing conditions. Reviews available on suspensions in non-Newtonian media include Metzner (1985) and Kamal and Mutel (1985). 

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