where o (Pa):shear stress, [o.sub.0] (Pa): yield stress (minimum force required for the fluid to move, and is related to the internal structure of the material to be broken ),K (Pa sn):coefficient consistency (proportionality constant indicating the degree of non-Newtonian viscosity
), (s-1): shear rate and, n (-):index of rheological behavior (indicating the proximity of the fluid to a Newtonian fluid.
The standard Hershel-Bulkley model becomes discontinuous at less shear rates and causes instability during numerical solution due to the fact that the non-Newtonian viscosity
becomes unbounded at small shear rates.
models were also found effective for transient study of flow in complex geometries like arch of aorta and region of bifurcation [6,7].
In industrial production there are many coating liquids with a non-Newtonian viscosity
behavior, such as polymeric solutions or dispersions.
In the laboratory experimental measurements, the density and non-Newtonian viscosity
behavior of drilling mud are evaluated.
Scheraga, H.A.: 1955, Non-Newtonian viscosity
of solutions of ellipsoidal particles.
Meunier, "Viscoelastic free-boundary problems: non-newtonian viscosity
vs normal stress effects," Physical Review Letters, vol.
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]] = [gradient][bar.u] + [gradient][[bar.u].sup.T], given by:
NOMENCLATURE [C.sub.p] Specific heat capacity D Rate of strain tensor F Volume concentration function [kappa] Conductivity P Pressure t Time T Temperature [T.sub.g] Glass transition temperature [T.sub.m] Melting temperature [U.sub.x] Velocity [DELTA][U.sub.x] Velocity difference V Velocity vector [dot.[gamma]] Shear rate [eta] Non-Newtonian viscosity
[rho] Density [tau] Stress tensor Table 1.
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.
If the non-Newtonian viscosity
[eta] were constant (i.e.