Newtonian & Non-Newtonian liquids:

The coefficient of viscosity of a liquid is given by

\( \displaystyle{\eta=-\frac{F}{A\cdot\frac{du}{dz}}} \),

or, \( \displaystyle{\eta=-\frac{\frac{F}{A}}{\frac{du}{dz}}} \).

where, \( F \) is the dragging force acting in contact area \( A \) of two adjacent layers, \( \frac{du}{dz} \) is the velocity gradient along the perpendicular direction of the liquid flow.

The above equation is known as Newton’s law of streamline motion of the viscous liquid.

So the liquid for which the shearing stress is \( \frac{F}{A} \) is proportional to the velocity gradient \( \frac{du}{dz} \) is called Newtonian liquid. For a Newtonian liquid, the coefficient of viscosity \( \eta \) is a constant at a given temperature and pressure and is also independent of the velocity gradient. Almost all pure liquids and homogeneous solutions are Newtonian liquids.

The liquid for which shearing stress \( \frac{F}{A} \) is not proportional to the velocity gradient \( \frac{du}{dz} \) is called non-Newtonian liquid. In case of the non-Newtonian liquid, the ratio of shearing stress to the velocity gradient is called apparent viscosity, which is not constant at a given temperature and pressure and decreases with the increase of velocity gradient. Non-homogeneous liquids like blood, paints, colloids etc. are non-Newtonian liquids.