D] second invariant of the rate of strain tensor p Pressure [mu] Newtonian viscosity [eta] non-Newtonian viscosity
n power-law index T Temperature b temperature sensitivity coefficient of viscosity m consistency index R calender radius [x.
In the laboratory experimental measurements, the density and non-Newtonian viscosity
behavior of drilling mud are evaluated.
In this section, the model of the non-Newtonian viscosity
was introduced first, and the formulation for the plastic melt flow was then derived for optimization.
where [eta]([absolute value of [gamma]]) is the apparent non-Newtonian viscosity
given by the power-law model, which is a function of the magnitude [absolute value of [gamma]] of the rate-of-strain tensor [bar.
gamma]] Shear rate [eta] Non-Newtonian viscosity
[rho] Density [tau] Stress tensor Table 1.
Figure 5 shows that with increased chain branching or raised molecular weight or polydispersity, the onset of non-Newtonian viscosity
occurs at lower shear rates and at lower frequencies.
The effects of a non-Newtonian viscosity
of a polymer on the amount of die swell can be much larger than the Newtonian examples presented here.
Eyring's model considers that the mechanisms of deformation are progressively activated according to a statistic of the clearing over energy barriers, An activated non-Newtonian viscosity
is thus defined.
the non-Newtonian viscosity
as a function of [DELTA]P, N, s, and position, is obtained when Eqs 19 and 17 as well as the relationships U = [pi] D N and Z = [kappa] [pi] D are plugged into the power-law model: [eta] = m[[gamma].
Figures 1A-C demonstrate that Eq 3 with the rheological parameters shown in Table 1 reproduce well the simple shear experimental data for non-Newtonian viscosity
for all three polymer melts.
The effects of non-Newtonian viscosity
may be significant.
However, in a non-Newtonian viscosity
range E should be determined at constant shear stress (8).