Non-Newtonian Fluids

Non-Newtonian FlowGoalsDescribe key differences between a Newtonian and non-Newtonian fluidIdentify examples of Bingham plastics (BP) and power law (PL) fluidsWrite basic equations describing shear stress and velocities of non-Newtonian fluidsCalculate frictional losses in a non-Newtonian flow system

Non-Newtonian FluidsNewtonian FluidNon-Newtonian Fluid is the apparent viscosity and is not constant for non-Newtonian fluids.

- Apparent ViscosityThe shear rate dependence of categorizes non-Newtonian fluids into several types.Power Law Fluids:Pseudoplastic (viscosity) decreases as shear rate increases (shear rate thinning)Dilatant (viscosity) increases as shear rate increases (shear rate thickening)Bingham Plastics: depends on a critical shear stress (t0) and then becomes constant

Non-Newtonian FluidsNewtonianBingham Plastic:Pseudoplastic:Dilatant:sludge, paint, blood, ketchuplatex, paper pulp, clay solns.quicksand

Modeling Power Law FluidsOswald - de Waelewhere:K = flow consistency indexn = flow behavior indexNote: Most non-Newtonian fluids are pseudoplastic n

Modeling Bingham PlasticsRigid

Frictional Losses Non-Newtonian FluidsRecall:Applies to any type of fluid under any flow conditions

Laminar FlowMechanical Energy Balance000

MEB (contd)Combining:

Momentum Balance00

Power Law FluidBoundary Condition

Velocity Profile of Power Law FluidCircular Conduit

Upon Integration and Applying BC

Power Law (contd)Need bulk average velocity

Power LawResults Hagen-Poiseuille for Power Law Fluid Recall

Laminar Friction FactorPower Law FluidDefine a Power Law Reynolds Number

Turbulent Flow

ExampleA concentrated suspension flows through 75 m of 3 cm ID pipe at a bulk velocity of 5 cm/sec. From rheological data, it is determined that the fluid has a power law behavior with n=2 and an apparent viscosity of 18 poise at a shear rate of 10/sec. Find the pressure drop in the pipe.

Bingham PlasticsBingham plastics exhibit Newtonian behavior after the shear stress exceeds to. For flow in circular conduits Bingham plastics behave in an interesting fashion.

Bingham PlasticsUnsheared CoreSheared Annular Region

Bingham Plastic Friction FactorHedstrom Number(Non-linear)

Turbulent Bingham Plastic Flow