3.4 Newtonian Fluid Fluid such as water , air, ethanol and benzene are Newtonian. The shear stress is plotted against shear rate at a given temperature; the figure 6 shows a straight line with a constant slope that is independent of shear rate. This slope is called the viscosity of the fluid. The simplest constitutive equation is Newton‟s law of viscosity; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 8 ) where μ = the Newtonian viscosity and γ = shear rate or the rate of strain.
The Newtonian fluid is the basis for classic fluid mechanics Munson et al. 1998. Gases and liquids like water and mineral oils exhibit characteristics of Newtonian viscosity. Blood is often assumed to be Newtonian fluid for…show more content… Unfortunately, one of the evident disadvantages of the power-law model is that it fails to portray the viscosity of many non-Newtonian fluids in very low shear rate regions and very high. Since is generally less than one,goes to infinity at a very low shear rate (see Figure 3-5) rather than to a constant, , as is often observed experimentally.Viscosity for many suspensions and dilute polymer solutions becomes constant at a very high shear rate. This cannot be solved via the power-law model (Kim, 2002).
Figure 3-5 Flow curves of power-law fluids,(a) shear-thinning fluid ( n < 1). (b) Newtonian fluid ( n = 1),(c) shear-thickening fluid ( n > 1).
3.5.2 Carreau model
Another well-known shear thinning model is proposed by Carreau25 is provided here: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 11 ) is the instantaneous viscosity, are the zero and infinite viscosities, is the time constant, is the shear rate and is the rate law index. The values for the constants are = 3.313s, n = 0.3568, = 0.56P and = 0.0345P (Cho YI et al,1991).
3.5.2 Cross