Newtonian and non-Newtonian fluid Branch:-Chemical , 2ed Year En.no.:-130420105001 130420105002 130420105003 130420105004

Two Categories of Flow & Deformation Newtonian (Newtonian Law of Flow) “the higher the viscosity of a liquid, the greater is the force per unit area (shearing stress) required to produce a certain rate of shear” Shear – as a stress which is applied parallel or tangential to a face of a material, as opposed to a normal stress which is applied perpendicularly. Shear stress Measured in (SI unit): pascal Commonly used symbols: τ Expressed in other quantities: τ = F / A

Two Categories of Flow & Deformation Newtonian (Newtonian Law of Flow) A Newtonian fluid (named for Isaac Newton) is a fluid whose stress versus rate of strain curve is linear and passes through the origin. The constant of proportionality is known as the viscosity. A simple equation to describe Newtonian fluid behavior is where τ is the shear stress exerted by the fluid ("drag") [Pa] μ is the fluid viscosity - a constant of proportionality [Pa·s] du is the velocity gradient perpendicular to the direction dy of shear [s−1]

Two Categories of Flow & Deformation Newtonian (Newtonian Law of Flow) Cartesian coordinate system where, by the convention of tensor notation, τij is the shear stress on the ith face of a fluid element in the jth direction ui is the velocity in the ith direction xj is the jth direction coordinate

Two Categories of Flow & Deformation Newtonian (Newtonian Law of Flow) For a Newtonian fluid, the viscosity, by definition, depends only on temperature and pressure (and also the chemical composition of the fluid if the fluid is not a pure substance), not on the forces acting upon it. If the fluid is incompressible and viscosity is constant across the fluid, the equation governing the shear stress is expressed in the Cartesian coordinate system

Newtonian Fluids water air ethyl alcohol Common denominator: simple fluids air ethyl alcohol

Two Categories of Flow & Deformation Non-Newtonian A non-Newtonian fluid is a fluid whose flow properties are not described by a single constant value of viscosity. Many polymer solutions and molten polymers are non- Newtonian fluids, as are many commonly found substances such as ketchup, starch suspensions, paint, blood and shampoo. In a Newtonian fluid, the relation between the shear stress and the strain rate is linear (and if one were to plot this relationship, it would pass through the origin), the constant of proportionality being the coefficient of viscosity.

Two Categories of Flow & Deformation Non-Newtonian A In a non-Newtonian fluid, the relation between the shear stress and the strain rate is nonlinear, and can even be time- dependent. Therefore a constant coefficient of viscosity cannot be defined. A ratio between shear stress and rate of strain (or shear- dependent viscosity) can be defined, this concept being more useful for fluids without time-dependent behavior.

Non-Newtonian Fluids blood ketchup toothpaste Nature of Non-Newtonian fluids: slurries, significantly viscous fluids, highly concentrated solutions, polymer melts blood ketchup toothpaste

Non-Newtonian Fluids paint molten metal whipped cream More examples of non-Newtonian fluids. paint molten metal whipped cream

Two Categories of Flow & Deformation Non-Newtonian Examples There are fluids which have a linear shear stress/shear strain relationship which require a finite yield stress before they begin to flow. That is the shear stress, shear strain curve doesn't pass through the origin. These fluids are called 1. Bingham plastics. clay suspensions, drilling mud, toothpaste, mayonnaise, chocolate, and mustard. The classic case is ketchup which will not come out of the bottle until you stress it by shaking.

Two Categories of Flow & Deformation Non-Newtonian Examples These fluids are called 1. Pseudoplastic Flow Polymers in solutions such as tragacant, sodium alginate, methylcellulose Viscosity decreases with an increase in shear thinning Caused by the re-alignment of polymer and/or the release of solvents associated with the polymers 2. Dilatant Flow Volume increases when sheared Shear thickening Suspension containing high-concentration of small deflocculated particles

Two Categories of Flow & Deformation Non-Newtonian Examples There are also fluids whose strain rate is a function of time. Fluids that require a gradually increasing shear stress to maintain a constant strain rate are referred to as rheopectic. An opposite case of this, is a fluid that thins out with time and requires a decreasing stress to maintain a constant strain rate (thixotropic).

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