1. Transport phenomena Ch.8 Polymeric liquid

2. Non-Newtonian Behaviors
1. Shear thinning & thickening
: Nonlinear relation between shear rate & stress
 Viscosity depending on shear rate
Shear thinning
Newtonian
Shear thickening
Interaction between
flow & structure

3. Non-Newtonian Behaviors
2. Elasticity
: Solid like response to deformation
Elastic solid Viscous liquid
Force
Force
Viscoelastic fluid : Force
Oscillatory shear
When 
Ex) Water
Storage modulus Loss modulus

4. Non-Newtonian Behaviors
3. Yield stress(Bingham plastic fluid)
: Behaves as a rigid body at low stresses but flows as a viscous fluid at high stress
(ex. Toothpaste, Mayonnaise)
Planar pressure driven flow
yield stress

5. Non-Newtonian Behaviors
4. Normal stress effect

6. Constitutive model Shear thinning & thickening
Generalized Newtonian fluid
- Power law viscosity
:  Shear thinning
! Infinite viscosity for
- Carreau model
Planar pressure driven flow, power law fluid
For ,
By symmetry,

7. Constitutive model Elasticity Spring - dashpot : Maxwell model
: Relaxation time

8. Constitutive model Maxwell model : start-up shear flow, constant
Stationary shear flow
: Newtonian (no shear thinning & normal stress)

9. Constitutive model
Maxwell model : Oscillatory shear

11. Constitutive model Scalar equation to tensor equation ??? ???
1) Galilean invariance
???
???
Total time derivative!

12. Constitutive model Scalar equation to tensor equation
1) Galilean invariance
Total time derivative

13. Constitutive model
Rotational invariance

14. Constitutive model
Rotational invariance
Position
Velocity

15. Constitutive model
Rotational invariance
Velocity
Shear rate?

16. Constitutive model
Rotational invariance
Velocity
Shear rate?

17. Constitutive model Rotational invariance Transformation rule of tensor
Shear rate?
Transformation rule of tensor
Then, how about time derivative?