Shear viscosity

Shear Viscosity is a fundamental property of fluids that describes their internal resistance to shear stress. It is a measure of how a fluid's velocity changes in different layers when it is in motion, indicating how easily the fluid flows. The concept of shear viscosity is crucial in the fields of fluid dynamics and rheology, the study of the flow of matter.

Definition

Shear viscosity, often denoted by the symbol η, is defined as the ratio of shear stress (τ) to the shear rate (γ̇) in a fluid. Mathematically, it is expressed as:

\[η = \frac{τ}{γ̇}\]

where τ is the force per unit area applied parallel to the fluid layer, and γ̇ is the rate of change of velocity per unit distance perpendicular to the direction of the force.

Units

The SI unit of shear viscosity is the Pascal second (Pa·s), which is equivalent to N·s/m² or kg/(m·s). In the CGS system, the unit is the poise (P), named after Jean Léonard Marie Poiseuille. 1 P = 0.1 Pa·s.

Types of Fluids Based on Shear Viscosity

Fluids can be classified based on how their viscosity changes with the shear rate:

• Newtonian Fluids: Fluids for which the viscosity remains constant regardless of the shear rate. Examples include water and air.
• Non-Newtonian Fluids: Fluids whose viscosity changes with the shear rate. This category includes:

 * Pseudoplastic: Viscosity decreases with an increase in shear rate.
 * Dilatant: Viscosity increases with an increase in shear rate.
 * Bingham Plastic: A yield stress is required before the fluid starts to flow, after which it behaves like a Newtonian fluid.

Measurement

Shear viscosity can be measured using a device called a viscometer or rheometer, which applies a known shear stress to a fluid and measures the resulting shear rate, or vice versa. Common types of viscometers include the capillary viscometer, rotational viscometer, and falling ball viscometer.

Applications

Understanding and controlling the shear viscosity of fluids is essential in various industrial and scientific applications, including:

• Lubrication
• Polymer processing
• Food manufacturing
• Paint formulation
• Petroleum extraction and processing

See Also

• Viscosity
• Fluid dynamics
• Rheology
• Newtonian fluid
• Non-Newtonian fluid