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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
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Experimental progression of the layering of colored resins in a Kenics static mixer
Entrance
Exit
Distributive Mixing
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Schematic diagram of a co-kneater
Distributive Mixing
10
Typical pin and slotted flight type single screw extruder distributive mixing sections.
Distributive Mixing
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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
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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
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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
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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
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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
42
