APPARENT VISCOSITY:

In power-law fluids, no constant of proportionality between shear stress and shear rate exists. Therefore, instead of talking about the coefficient of viscosity, which we use with newtonian fluids, it is more common to refer to the apparent viscosity, va, defined as shear stress/shear rate:

Va = SS / SN For a newtonian fluid, Va = V:
SS = V * SN
so V = SS / SN = Va (by definition) for an ostwald-de waele fluid:

Va = SS / SN = K * (SN) **(n-1)

So for these fluids, Va still depends on sn. For a b.p.:

SS = SS0 + V * SN

So Va = SS / SN = ( SS0 / SN ) + V

Once again, Va is dependent on SN at very high SN values:

SS0 / SN > 0,

So Va > V ie., A Bingham plastic asymptotically approaches newtonian behaviour at high shear rates. This is how the plot looks:

Another way to look at rheological equations of state is on a log plot.

For a newtonian fluid:

LOG(SS) = LOG(V) + LOG(SN)

For Ostwald-de Waele fluid s:

LOG(SS) = LOG(K) + n.LOG(SN)

Linear plots are obtained for both types of fluids:

The above models are rather idealized. Actual fluids might exhibit a combination of characteristics. The b.p., for example, might exhibit either p.p. or dilatant behaviour above ss = ss0. The Ostwald-de Waele fluids, too, might show non-linear behaviour even on a log plot, with n being dependent upon shear rate.

TIME-DEPENDENT FLUIDS:

Certain materials exhibit highly irregular behaviour where flow properties, such as apparent viscosity, change with the time of shearing. In some cases the change is reversible, and the viscosity eventually recovers its initial value after a sufficiently long period after cessation of shear. In other cases it is irreversible. Examples of reversible behaviour are `thixotropy' and `rheopexy'.

For further details,see any text book on fluid dynamics or on rheology.

Other fluids: Some materials outwardly appear solid,but under stress the deformation is not instantaneous,and sometimes only partly reversible.such materials are called viscoelastic.

Some others appear liquid and capable of indefinite deformation but which on release of the deforming stress show some recovery of shape; these materials are called elasticoviscous.

We shall not deal any further with these fluids.they are merely mentioned here in passing, as it were. 

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