Fluid Viscosity and Its Relationship to Deformation Rate

Fluids are substances that continuously deform under an applied shear stress. One of the most important properties of a fluid is its viscosity, which represents its resistance to flow. When a fluid flows, different layers move at different speeds, leading to a "shear" or "deformation." The rate at which this deformation occurs is known as the rate of deformation or shear strain rate.

The question asks about a fluid whose viscosity changes with this rate of deformation or shear strain. Let's analyze the different types of fluids mentioned in the options to find the correct answer.

Newtonian Fluid Properties

A Newtonian fluid is a fluid for which the shear stress is directly proportional to the shear strain rate. This means that its viscosity remains constant, regardless of how much shear stress is applied or how fast it is deformed. The relationship can be expressed by Newton's Law of Viscosity:

$$\tau = \mu \frac{du}{dy}$$

• Here, $\tau$ represents the shear stress.
• $\mu$ is the dynamic viscosity, which is a constant for a Newtonian fluid at a given temperature and pressure.
• $\frac{du}{dy}$ is the velocity gradient or the shear strain rate.

Common examples of Newtonian fluids include water, air, gasoline, and most oils under normal conditions. Their viscosity does not change with the rate of deformation.

Non-Newtonian Fluid Characteristics

A Non-Newtonian fluid is a fluid whose viscosity changes with the rate of deformation or shear strain. Unlike Newtonian fluids, the relationship between shear stress and shear strain rate is not linear and constant. The viscosity of these fluids can either increase or decrease depending on the shear rate, or they might require a certain amount of stress before they even begin to flow.

Non-Newtonian fluids are further classified based on how their viscosity changes with shear rate:

• Shear-thinning (Pseudoplastic) Fluids: Their viscosity decreases as the shear strain rate increases. Examples include paint, blood, ketchup, and some polymer solutions. When stirred or shaken (high shear), they become less viscous and flow more easily.
• Shear-thickening (Dilatant) Fluids: Their viscosity increases as the shear strain rate increases. A classic example is a mixture of cornstarch and water (oobleck). When force is applied quickly (high shear), it becomes very stiff and acts almost like a solid.
• Bingham Plastic Fluids: These fluids behave like a rigid body at low stresses but flow like a viscous fluid once a certain yield stress is exceeded. Examples include toothpaste, mayonnaise, and some types of mud.

The definition provided in the question perfectly describes a Non-Newtonian fluid.

Ideal Fluid Definition

An Ideal Fluid is a theoretical concept in fluid dynamics. It is defined as a fluid that is incompressible (its density does not change) and non-viscous (it has zero viscosity, meaning it offers no resistance to flow). Ideal fluids are used to simplify calculations in fluid dynamics, but they do not exist in reality. Therefore, its viscosity does not "change" with deformation, as it's considered zero.

Bernoulli Fluid Principle

The term "Bernoulli Fluid" is not a classification of a fluid type itself. Instead, it refers to a fluid (often an ideal fluid or a real fluid under specific conditions like steady, incompressible, inviscid flow along a streamline) that adheres to Bernoulli's Principle. Bernoulli's Principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. It describes the conservation of energy in fluid flow, not a specific type of fluid whose viscosity changes with deformation.

Conclusion on Fluid Types

Based on the analysis of different fluid types, the fluid whose viscosity changes with the rate of deformation or shear strain is definitively a Non-Newtonian fluid. This characteristic distinguishes them from Newtonian fluids, whose viscosity remains constant under varying shear rates.