## Newtonian and Non Newtonian Fluids

**INTRODUCTION**: An ideal fluid has zero viscosity. Shear force is not involved in its deformation. An ideal fluid has to be also incompressible. Shear stress is zero irrespective of the value of du/dy. Bernoulli equation can be used to analyses the flow.

Real fluids having viscosity are divided into two group’s namely Newtonian and non Newtonian fluids. In Newtonian fluids a linear relationship exists between the magnitude of the applied shear stress and the resulting rate of deformation. It means that the proportionality parameter (in equation, τ = µ (du/dy)), viscosity, µ is constant in the case of Newtonian fluids (other conditions and parameters remaining the same). The viscosity at any given temperature and pressure is constant for a Newtonian fluid and is independent of the rate of deformation. The characteristics are shown plotted in Fig. Two different plots are shown as different authors use different representations

Non Newtonian fluids can be further classified as simple non Newtonian, ideal plastic and shear thinning, shear thickening and real plastic fluids. In non-Newtonian fluids the viscosity will vary with variation in the rate of deformation. Linear relationship between shear stress and rate of deformation (du/dy) does not exist. In plastics, up to a certain value of applied shear stress there is no flow. After this limit it has a constant viscosity at any given temperature. In shear thickening materials, the viscosity will increase with (du/dy) deformation rate. In shear thinning materials viscosity will decrease with du/dy. Paint, tooth paste, printer’s ink is some examples for different behaviors. These are also shown in Fig. Many other behaviors have been observed which are more specialized in nature. The main topic of study in this text will involve only Newtonian fluids.

**Viscosity and Momentum Transfer: **In the flow of liquids and gases molecules are free to move from one layer to another. When thevelocity in the layers are different as in viscous flow, the molecules moving from the layer atlower speed to the layer at higher speed have to be accelerated.

Similarly the molecules movingfrom the layer at higher velocity to a layer at a lower velocity carry with them a higher valueof momentum and these are to be slowed down. Thus the molecules diffusing across layerstransport a net momentum introducing a shear stress between the layers. The force will bezero if both layers move at the same speed or if the fluid is at rest.When cohesive forces exist between atoms or molecules these forces have to be overcome,for relative motion between layers. A shear force is to be exerted to cause fluids to flow.Viscous forces can be considered as the sum of these two, namely, the force due tomomentum transfer and the force for overcoming cohesion. In the case of liquids, the viscousforces are due more to the breaking of cohesive forces than due to momentum transfer (asmolecular velocities are low). In the case of gases viscous forces are more due to momentumtransfer as distance between molecules is larger and velocities are higher.