Newtonian fluid

Newtonian Fluid

A Newtonian fluid is a fluid in which the viscous stresses arising from its flow, at every point, are linearly proportional to the local strain rate—the rate of change of its deformation over time. This relationship is described by Isaac Newton's law of viscosity, which states that the shear stress between adjacent fluid layers is proportional to the velocity gradients between the two layers.

Graph showing the behavior of different types of fluids, including Newtonian fluids.

Characteristics

The defining characteristic of a Newtonian fluid is its constant viscosity, regardless of the stress applied to it. This means that the fluid's viscosity does not change with the rate of flow or shear rate. Common examples of Newtonian fluids include water, air, and mineral oil.

Viscosity

Viscosity is a measure of a fluid's resistance to deformation at a given rate. For Newtonian fluids, this property remains constant, which simplifies the mathematical modeling of their flow. The viscosity of a Newtonian fluid is only dependent on temperature and pressure, not on the forces acting upon it.

Mathematical Description

The relationship between shear stress (_) and shear rate (du/dy) in a Newtonian fluid is given by:

_ = _ (du/dy)

where:

• _ is the shear stress,
• _ is the dynamic viscosity,
• du/dy is the velocity gradient perpendicular to the direction of shear.

Comparison with Non-Newtonian Fluids

Unlike Newtonian fluids, non-Newtonian fluids have a viscosity that changes with the rate of shear or stress. These fluids can be further classified into several types, such as pseudoplastic, dilatant, Bingham plastic, and thixotropic fluids.

Pseudoplastic Fluids

Pseudoplastic fluids, also known as shear-thinning fluids, decrease in viscosity with an increase in shear rate. An example of a pseudoplastic fluid is ketchup.

Dilatant Fluids

Dilatant fluids, or shear-thickening fluids, increase in viscosity with an increase in shear rate. An example of a dilatant fluid is a mixture of cornstarch and water.

Applications

Newtonian fluids are often used as a baseline in fluid dynamics studies due to their simple behavior. Understanding the flow of Newtonian fluids is crucial in various engineering applications, including aerodynamics, hydraulics, and lubrication.

Related pages

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