Mixing

Distributive and Dispersive Mixing in Extrusion Processes

Polymer Engineering Center

University of Wisconsin-Madison

1

Tim A. Osswald

Mixing

Rayleigh disturbances

Thread formation

Hole formation due tointerfacial instabilities

PelletFilm ribbon formation

Distribution

Dispersion

Coalescence

Morphology withgcompatibilizer

Morphology withoutcompatibilizer

u

2

Distributive Mixing

3

Distributive Mixing

δ0

A0

A0A0

A(t)δ(t)

4

Distributive Mixing

α = 0o

α = 90o A(t)A0

= γ cos αGrowth:

αγ

Orientation:Deformation:

α→ −90o

α→ 90o

γ =� t

0γ̇dt

5

Distributive Mixing

Erwin/Ng (1980)6

A

A0=

�γ

2

�2

A

A0=

�γ

3

�3

A

A0=

� γ

N

�N

A

A0= γ

A

A0→ eγ/2

Distributive Mixing≈ 100

≈ 2,500

≈ 37,000

≈ 5E21

γ →100

Erwin/Ng (1980)7

Schematic diagram of a Kenics static mixer

Distributive Mixing

8

Experimental progression of the layering of colored resins in a Kenics static mixer

Entrance

Exit

Distributive Mixing

9

Schematic diagram of a co-kneater

Distributive Mixing

10

Typical pin and slotted flight type single screw extruder distributive mixing sections.

Distributive Mixing

11

Unwrapped channel contents of a pin barrel extruder.

Distributive Mixing

12

Distributive Mixing

Boundary Element Model of Static Mixer

Gramann/Osswald (2000)13

Distributive MixingBoundary Element Model of Static MixerPressure Distribution

Gramann/Osswald (2000)14

Gramann/Osswald (2000)

Boundary Element Model of Static MixerStreamlines

Distributive Mixing

15

f(t)

F (t)

F (t) =

� t

0f(t)dt

t̄0 t

t = 0

t = t̄

Residence Time Distribution

Residence Time Distribution

CummulativeResidence Time Distribution

Distributive MixingResidence Time Distribution The Perfect Mixer

(1− C0)Q

C0Q

Q

Q QQ

Residence Time Distribution

17

Various rhomboidal single screw extruder distributive mixing sections.

Distributive Mixing

Rios/Osswald (2000)18

Distributive Mixing

Rios/Osswald (2000)19

Distributive Mixing

Rios/Osswald (2000)20

Dispersive mixing of a solid agglomerate

Dispersive Mixing Solid agglomerates (Carbon black) into a polymer (Rubber)

21

Dispersive Mixing

Felongation = 6πηγ̇r2

22

Schematic diagram of an internal batch mixer

Fraction below 50nm

Dispersive Mixing

Manas/Tadmor (1980)23

PA6 ThreadPS Matrix

Dispersive Mixing (Grace Diagram)Incompatible liquids (Polymer Blends)

Dispersive mixing of incompatible liquids

0 sec 1 sec 2 sec 3 sec 4 sec

Meijer24

Dispersive Mixing (Grace Diagram)Incompatible liquids (Polymer Blends)

Ca ≈ 0

Ca < CacritCa = Cacrit

Ca =τR

σs

τ = ηγ̇SHEAR FLOW

25

SHEAR FLOW

Cacrit

100

101

102

10−6 10310010−1.......................

3.8

Dispersive Mixing (Grace Diagram)Incompatible liquids (Polymer Blends)

µdrop

µmatrix

26

Dispersive Mixing (Grace Diagram)Incompatible liquids (Polymer Blends)

Ca ≈ 0

Ca =τR

σs

τ = ηγ̇

Ca < CacritCa = Cacrit

ELONGATIONAL FLOW

27

SHEAR FLOW

Cacrit

100

101

102

10−6 10310010−1.......................

3.8

Dispersive Mixing (Grace Diagram)Incompatible liquids (Polymer Blends)

µdrop

µmatrix

ELONGATIONAL FLOW

28

Typical single screw extruder distributive mixing sections with dispersive capabilities

Dispersive Mixing

29

Commonly used single screw extruder dispersive mixing section

Dispersive Mixing

30

Twin screw extruders

Dispersive Mixing

31

Dispersive Mixing (Blends)Co-Rotating Twin screw extruder (Commonly used today)

32

Dispersive Mixing (Blends)Counter-Rotating Twin screw extruder (Not commonly used today)

33

Schiffer/Osswald(2003)

Schiffer/Osswald(2003)

Schiffer/Osswald(2003)

Schiffer/Osswald(2003)

Schiffer/Osswald(2003)

Krawinkel/Osswald(2003)

Krawinkel/Osswald(2002)

Schiffer/Osswald(2003)

• Distributive mixing governed by deformation and orientation• Dispersive mixing governed by stresses• Elongational flows are preferred for both distributive and dispersive mixing• Elongational flows lead to lower energy consumption and consequently lower viscous heating

CONCLUSIONS

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