Polymers- Flow Mechanics

Question 1

Types of flow

Answer 1

Bulk
Elongational
Shear

Question 2

Bulk flow equation

Answer 2

K=P/(ΔV/V)
K is bulk modulus (volumetric stiffness)
P is hydrostatic pressure
ΔV/V is volumetric strain rate

Question 3

Elongational flow

Answer 3

Describes flow of polymer melt being pulled through a tube at a constant temperature. Force F required to pull melt with varying CSA, A, creating a tensile stress σt in the melt
σt=F/A
Velocity, ν, at which melt moves varies for a constant volumetric flow rate, Q.
Q=νA

Question 4

Elongational viscosity

Answer 4

In terms of the applied force and either velocity or CSA gradient in the z direction
λ=(F/A)/(dν/dz)
λ=(F/ν)/(dA/dz)

Question 5

When is the response to an applied tensile stress in a polymer Newtonian or non-Newtonian?

Answer 5

Lower than 10^3 Pa Newtonian

Higher than 10^3 Pa non-Newtonian

Question 6

Tension thinning and stiffening in polymers

Answer 6

Both non-Newtonian. Most do tension thinning where if stretched either side of a notch there will be necking. Some do tension stiffening and there is uniform draw instead. This is the case for branched PE as the side chains act as hooks restricting flow which is why it dominates the film market

Question 7

Power law for shear flow

Answer 7

τ=Cγ•^n
C is related to shear viscosity
τ is shear stress
n is constant (<1 for polymer melts)
γ• has dot on top and is shear strain rate

Question 8

Graph of shear stress vs shear strain rate for polymer melts

Answer 8

Curve forming cave from origin. Originally close to Newtonian straight line but bends away

Question 9

Equation for fluid down a capillary

Answer 9

τw=(R/2)dP/dz
Large scale pressure gradient is -ΔP/ΔL
τw is shear stress at wall
R is radius of capillary 
L is length of capillary

Question 10

Formulae for velocity, volumetric flow rate and shear strain rate for non-Newtonian flow down a circular pipe

Answer 10

Very complicated formulae in lecture 2 page 12