What Is Newtonian Viscosity

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3.3 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; ...................( ) 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 modeling purposes. In …show more content…

Hence, the value of n determines the classes of the fluid which is as follow: n = 1 (Newtonian Fluid) n > 1 shear-thickening (Dilatant fluids) n < 1 shear-thinning (pseudo-plastics)
These three types of power-law models are clarified butter in Figure. 2-2.
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. 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, …show more content…

(a) shear-thinning fluid ( n < 1). (b) Newtonian fluid ( n = 1). (c) shear-thickening fluid ( n > 1).
3.4.2 Carreau shear thinning model
Another well-known shear thinning model is proposed by Carreau25 is provided here:

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 = 2.415s, n = 0.3568, = 0 0.56P and = 0.0345P  


3.4.2 Cross Model
As discussed in the previous section, the power-law model does not have the capability of handling Newtonian regions of shear-thinning fluids at very low and high shear rates,In order to overcome this drawback of the power-law model, Cross (1965) proposed a model that can be described as:

where is the instantaneous viscosity, andis viscosities at very low and high shear rate , is the time constant ,m is model constants and is the shear rate .The values for the constants are, , m =1.089m ,=0 0.56P and =0.0345P 
Cross model produces Newtonian viscosities at very low and shear rates compared to the Power Law model (Kim, 2002).
3.4.3 Bingham Plastic

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