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Experimental Data (Chapter 6)

Steady shear flow

•Linear Polymers

•Limits on measurability

•Material effects - MW, MWD, branching, mixtures, copolymers

•Temperature and pressure

Unsteady shear flow (SAOS, step strain)Steady elongationUnsteady elongation

later . ..

© Faith A. Morrison, Michigan Tech U.

1.E+02

1.E+03

1.E+04

1.E+05

0.01 0.1 1 10 100

η, Poise

Ψ1,(dyn/cm2)s2

1, −sγ�

o1Ψ

oη

( )γη �

( )γ�1Ψ

Figure 6.1, p. 170 Menzes and Graessley conc. PB solution

Steady shear viscosity and first normal stress coefficient

© Faith A. Morrison, Michigan Tech U.

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Steady shear viscosity and first normal stress coefficient

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

0.01 0.1 1 10 100

η, P

oise

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

Ψ1,

dyn

es/c

m2

1, −sγ�

η

Ψ1

Figure 6.2, p. 171 Menzes and Graessley conc. PB solution; c=0.0676 g/cm3

813 kg/mol517 kg/mol350 kg/mol200 kg/mol

© Faith A. Morrison, Michigan Tech U.

Steady shear viscosity and first normal stress coefficient

0.1

1

10

100

0.1 1 10 100

stress, Pa

1, −sγ�Figure 6.5, p. 173 Binnington and Boger; PIB soln

sPa ⋅,η

21, sPa ⋅Ψ

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First normal stress effects: rod climbing

Bird, et al., Dynamics of Polymeric Fluids, vol. 1, Wiley, 1987, Figure 2.3-1 page 63. (DPL)

Newtonian - glycerin Viscoelastic - solution of polyacrylamide in glycerin

02211

4

Second normal stress effects: inclined open-channel flow

R. I. Tanner, Engineering Rheology, Oxford 1985, Figure 3.6 page 104

Newtonian - glycerin Viscoelastic - 1% soln of polyethylene oxide in water

03322 >−ττExtra tension in the 2-direction pulls down the free

surface where dv1 /dx2 is greatest (see DPL p65).

N2 ~ -N1 /10

© Faith A. Morrison, Michigan Tech U.

Second normal stress effects: inclined open-channel flow

from R. I. Tanner, Engineering Rheology, Oxford 1985, Figure 3.7 page 105

polyox WSR-301 in waterSeparan AP-30 in waterOppanol B200 in cetaneNBS Nonlinear Fluid No. 1

1 100.1

1

10

N2 (Pa)

)(21 Paτ−

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Limits on Measurements: Flow instabilities in rheology

Figures 6.7 and 6.8, p. 175 Hutton; PDMS

Figure 6.9, p. 176 Pomar et al. LLDPE

cone and plate flow capillary flow

© Faith A. Morrison, Michigan Tech U.

10

100

1,000

10,000

1.E+05 1.E+06 1.E+07

LPE-1 LPE-2LPE-3LPE-4

(s -1 )34

R

Q

π

2/,2

cmdynesLRP∆

Spurt instability

Figure 6.10, p. 177 Blyler and Hart; PE

2Rb

Q

B

A

Polymer meltreservoir

Piston

Barrel

F

Instron capillary rheometer

© Faith A. Morrison, Michigan Tech U.

6

Steady shear viscosity and first normal stress coefficient - Molecular weight effects

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

0.01 0.1 1 10 100

η, P

oise

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

Ψ1,

dyn

es/c

m2

1, −sγ�

η

Ψ1

Figure 6.2, p. 171 Menzes and Graessley conc. PB solution; various MW

813 kg/mol517 kg/mol350 kg/mol200 kg/mol

© Faith A. Morrison, Michigan Tech U.

log M + constant

1

constantlog 0+

η

Variation of viscosity with molecular weight

Figure 6.12, p. 178 Berry and Fox, 1968; various polymers

slope=3.4-3.5

Mc

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MMc

Unentangledrelaxation is rapid

Entangledrelaxation is retarded

Entanglements strongly affect polymer relaxation

© Faith A. Morrison, Michigan Tech U.