Ideal Non Newtonian Fluids

Ideal Fluid
    
Consider a hypothetical fluid having a zero viscosity ( μ = 0). Such a fluid is called an ideal fluid and the resulting motion is called as ideal or in viscid flow. In an ideal flow, there is no existence of shear force because of vanishing viscosity.

 
All the fluids in reality have viscosity (μ > 0) and hence they are termed as real fluid and their motion is known as viscous flow.

Under certain situations of very high velocity flow of viscous fluids, an accurate analysis of flow field away from a solid surface can be made from the ideal flow theory.

Non-Newtonian Fluids

There are certain fluids where the linear relationship between the shear stress and the deformation rate (velocity gradient in parallel flow) as expressed by the  is not valid. For these fluids the viscosity varies with rate of deformation.

Due to the deviation from Newton's law of viscosity they are commonly termed as non-Newtonian fluids. Fig. 1 shows the class of fluid for which this relationship is nonlinear.
 


(i) The abscissa in Fig. 1 represents the behaviour of ideal fluids since for the ideal fluids the resistance to shearing deformation rate is always zero, and hence they exhibit zero shear stress under any condition of flow.

(ii) The ordinate represents the ideal solid for there is no deformation rate under any loading condition.

(iii) The Newtonian fluids behave according to the law that shear stress is linearly proportional to velocity gradient or rate of shear strain τ = μd/dy. Thus for these fluids, the plot of shear stress against velocity gradient is a straight line through the origin. The slope of the line determines the viscosity.

(iv) The non-Newtonian fluids are further classified as pseudo-plastic, dilatants and Bingham plastic.

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