Fluids Carreau-Yasuda

For an analysis of converging flow with a Navier slip condition for Newtonian, power-law, and Carreau-Yasuda fluids, see... 

Figure 12.8. Streamlines for a Carreau-Yasuda fluid with n = 0.3 and w = 4.0. The dashed line is the streamline for a Newtonian fluid ((v = 0), while the dotted line is the streamline for the corresponding power-law fluid. Reprinted from Joshi and Denn, /. Non-Newtonian Fluid Mech., 114,185 (2003).

Figure 14.2. Simulation of the mixing pattern for two identical Carreau-Yasuda fluids with n = 0.1 after passing through a static mixer with six blades with a twist angle of 180°. Reprinted with permission from Galaktionov et al., Int. Polym. Proc., XVIII, 138 (2003).

Basic Protocol 2 is for time-dependent non-Newtonian fluids. This type of test is typically only compatible with rheometers that have steady-state conditions built into the control software. This test is known as an equilibrium flow test and may be performed as a function of shear rate or shear stress. If controlled shear stress is used, the zero-shear viscosity may be seen as a clear plateau in the data. If controlled shear rate is used, this zone may not be clearly delineated. Logarithmic plots of viscosity versus shear rate are typically presented, and the Cross or Carreau-Yasuda models are used to fit the data. If a partial flow curve is generated, then subset models such as the Williamson, Sisko, or Power Law models are used (unithi.i). 

Finally, the shear rate as deflned by Equation 2.36b is clearly the appropriate argument for the viscosity function only for one-dimensional flows like the one used here. We need a quantity that reduces to dvx/dy for the one-dimensional flow but is properly invariant to the way in which we choose to deflne our coordinate system. The appropriate function, which follows directly from the principles of matrix algebra, is one half the second invariant of the rate of deformation, which is usually denoted Ud- Ud is shown in Table 2.6, where it is identical to the dissipation function O divided by r] for the special case of Newtonian fluids. (It is important to keep in mind that the function /) in Table 2.6 is the proper form for the dissipation only for a Newtonian fluid, whereas IId is a universally valid definition that depends only on the velocity field.) For an arbitrary flow field, then, the power-law and Carreau-Yasuda equations would be written, respectively. 

A second dimensionless group, w = qP/l abY, arises for the Carreau-Yasuda (C-Y) shear-thinning fluid, Equation 2.40b ... 

We investigate the influence of different destabilizing parameters on the primary breakup of non-Newtonian jets to analyze the primary breakup process. During our research our numerical simulations have constantly been improved. The more accurate Carreau-Yasuda viscosity model was implemented in FS3D and validated against experimental data. The earlier simulations used aqueous PVP solutions as model fluids due to their status as model fluid inside SPP 1423 and the good... 

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