Fluid Classification based on Shear Stress - Time Rate of Shear Strain


In fluid mechanics, fluids can be classified into different categories based on their flow behavior under shear stress. The shear stress is a measure of the force per unit area acting parallel to the surface of the fluid, while the time rate of shear strain represents the rate at which the fluid deforms or flows under the applied shear stress. By analyzing the relationship between shear stress and time rate of shear strain, we can determine the type of fluid behavior.



There are several types of fluids based on their flow behavior, including:

1. Newtonian fluid: A Newtonian fluid exhibits a linear relationship between shear stress and time rate of shear strain. The shear stress is directly proportional to the time rate of shear strain, with a constant of proportionality known as the dynamic viscosity. Examples of Newtonian fluids include water and many common liquids.

2. Bingham plastic: A Bingham plastic behaves like a solid at low shear stresses and starts flowing like a fluid once a certain threshold shear stress, known as the yield stress, is exceeded. The relationship between shear stress and time rate of shear strain is non-linear, with an initial linear elastic region followed by a plastic flow region. Bingham plastics are commonly found in drilling muds and certain food products.

3. Pseudoplastic: A pseudoplastic fluid exhibits a non-linear relationship between shear stress and time rate of shear strain. As the shear stress increases, the time rate of shear strain increases at a faster rate. These fluids are characterized by a decreasing viscosity with increasing shear rate. Examples include paints, gels, and some polymer solutions.

4. Dilatant: A dilatant fluid shows an increase in viscosity with increasing shear rate. The relationship between shear stress and time rate of shear strain is non-linear, with an increasing slope. Dilatant fluids are shear-thickening fluids and can be found in mixtures of cornstarch and water or suspensions of silica particles in a liquid.



In the given shear stress - time rate of shear strain data, the shear stress values increase as the time rate of shear strain increases. This behavior is characteristic of a dilatant fluid. As the fluid experiences higher shear rates, its viscosity increases, resulting in a higher resistance to flow. This can be observed from the increasing slope of the shear stress - time rate of shear strain curve.

Therefore, based on the given data, the fluid can be classified as a dilatant fluid (option D).