## Viscosity versus shear rate

There is a close relationship between viscosity and shear rate, which is the rate at which a liquid deforms under shear force.

Shear rate is a physical quantity that describes the deformation rate of a liquid. It represents the deformation velocity per unit time. It is the ratio between the Shear velocity and the geometric constraint on the liquid. The shear rate is usually expressed as the ratio of the displacement difference per unit time (shear velocity) to the distance between two parallel layers (shear distance). The unit is usually the reciprocal of the second (s^(-1)).

Viscosity is the internal viscous resistance of a liquid, which measures the degree of stickiness or fluidity of a liquid. The greater the viscosity, the stickier the liquid and the more difficult it is to flow. Viscosity is usually expressed as the ratio of force per unit area to the difference in velocity per unit time (shear rate). The unit is usually PASCAL seconds (Pa·s) or millipascal seconds (mPa·s).

**Viscosity versus shear rate**

The relationship between viscosity and shear rate can be described by Newton’s laws of fluid. A Newtonian fluid is an idealized fluid with a constant viscosity that is independent of the shear rate. According to Newtonian fluid laws, viscosity is equal to the ratio of stress to shear rate.

In Newtonian fluids, changes in the shear rate do not affect the magnitude of the viscosity, whether the shear rate is small or large. The viscosity of a Newton fluid remains the same, no matter how fast or how it is cut. However, for non-Newtonian fluids, such as shear-thinning and shear-thickening fluids, the viscosity will change as the shear rate changes. This means that the viscosity of a non-Newtonian fluid is a function of the shear rate, which can increase or decrease as the shear rate increases. The relationship between viscosity and shear rate of non-Newtonian fluids can be described and predicted by rheological tests and appropriate rheological models.