As many existing studies show, the turbulent eddy motions and ordered structures in drag-reducing viscoelastic flows are known to exhibit time and spatial scales that are different from those of Newtonian flows [3, 4].
where the suffixes "visc" and "Newt" stand for the friction-coefficient values in the viscoelastic and Newtonian flows, respectively, at the same bulk Reynolds number.
It is worth noting that the relative error in the case of the polymer solution displacement is of the same order as that for the Newtonian flow
. Values of the average tip velocity from the numerical and experimental results are shown in Table 3.
[28, 29] demonstrated that neutrally buoyant rigid spherical particles moved laterally, a phenomenon that would not be observed in Newtonian flows
. For shear thinning fluids, particles tended to move in the direction of the shear stress gradient, from the center toward the outer wall.
The viscoelastic flows tend to be more three-dimensional and more complex than the Newtonian flows
. That also explain why the large flow deflection occurs at the low Reynolds number of the viscoelastic.
For the immiscible PCL/PLA blend, the [G*.sub.components] should nearly be changeless in the Newtonian flow
(<0.3 [s.sup.-1]) because the entangled structure of the bulk polymers is stable.
For a standard Newtonian flow
in a duct with equal domain size, the proposed algorithm is between 8 and 15 times faster.
However, we assume Newtonian flow
(n = 1) in the whole stage of flash generation.
The subscript n denotes the Newtonian flow
while the subscript p denotes the second-order fluid flow.
For various physical parameters, the numerical values of the friction factor (in terms of the wall velocity gradient, f"(0)), Nusselt number (in terms of heat transfer rate, -[theta](0)), and local Sherwood number (in terms of mass transfer rate, -[phi]'(0)) are shown in Tables 4 and 5, for both cases of Newtonian ([beta] [right arrow] [infinity]) and non- Newtonian flows
. From Table 4, it is seen that the magnitude of the friction factor and the heat and mass transfer rates reduce with an increase in the slip parameter, [lambda].
Making use of a suggestion made by Lumley (1973, 1978) to account for drag reduction caused by long-chain molecules, the authors of the present paper proposed some years ago that the viscous sublayer for non-Newtonian turbulent flows is generally thicker than for equivalent Newtonian flows
and put forward a quantitative model to calculate this effect (Wilson and Thomas; 1985; Thomas and Wilson, 1987).
Additionally, similar inertial effects on the Reynolds numbers scale between [10.sup.-6] and [10.sup.-3] were also noted while this magnitude is well below the regime where inertia is known to play an important role in Newtonian flows