As for a viscoelastic-fluid flow accompanied by DR, both timescale and lengthscale of turbulent-eddy motions are known to be different from those in Newtonian flows
. Therefore, a modification of [f.sub.[mu]] for viscoelastic flow is necessarily required.
* Method D is a control method for determining the viscosity of materials that have an equivalent viscosity no greater than approximately 3000 cP, and is limited to materials that have or approach Newtonian flow
The BHR Group has incorporated some of the work into pipeline modelling into SLURP which models all the various options of transporting liquids in pipes - from single phase Newtonian flow
to fully developed plug flow.
Due to their hydrophilic component, polyol, the PEPO thickeners provide more Newtonian flow
Computations for the KNN element were time consuming, and took about 4 h for Newtonian flow
(n = 1.0), and 21 h for non-Newtonian flow (n = 0.3).
The results for the Newtonian flow
are discussed first followed by those for the shear-thinning case.
A second beneficial feature for implementing PIV in molten plastic flow involves the shear thinning characteristics of the fluid that blunt the flow profile when compared with an equivalent Newtonian flow
. For example, the velocity profile, u(y), for pressure-gradient-driven flow of a power-law fluid in a parallel-wall channel of width 2B is given by the following:
Although the flow pattern between the viscoelastic fluid flow and the Newtonian flow
is similar, the flow deflection occurs in the case of the viscoelastic fluid, which may be due to the influence of the viscoelastic force of the fluid.
Clearly, the average droplet radii first increase and then reduce after a critical shear rate, indicating that coalescence of the droplets occurs in the flow with lower shear rates (Newtonian flow
), while higher shear rates promotes break-up of the droplets in the non-Newtonian flow.
The streamline patterns for power law fluids were qualitatively similar to low Re Newtonian flow
(18), where a single primary vortex fills up the entire cavity.
Instead, an apparent radius was calculated from the analytical Newtonian flow
conductance of a tapered segment.
In Generalized Newtonian flow
(GNF), the fully developed flow condition in a duct is rectilinear with no secondary flow (i.e., no velocity components normal to the axial direction).