Page 478 - Introduction to Continuum Mechanics

8

Non-Newtonian Fluids

In Chapter 6, the linear viscous fluid was discussed as an example of a constitutive equation
of an idealized fluid. The mechanical behavior of many real fluids appears to be adequately
described under a wide range of circumstances by this constitutive equation which is referred
to as the constitutive equation of a Newtonian fluid. Many other real fluids exhibit behaviors
which are not accounted for by the theory of Newtonian fluid. Examples of such substances
include polymeric solutions, paints, molasses, etc.
For a steady unidirectional laminar flow of water in a circular pipe, the theory of Newtonian
fluid gives the experimentally confirmed result that the volume discharge Q is proportional to
the (constant) pressure gradient in the axial direction and to the fourth power of the diameter
d of the pipe, that is [see Eq. (6.13.6)]

However, for many polymeric solutions, it was observed that the above equation does not hold.
For a fixed d, the Q versus \dp/dx \ relation is nonlinear as sketched in Fig. 8.1.

Fig. 8.1

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