1. Xiaofei Sun, Mark A. Spalding
Optimization of Maddock-Style Mixers for Single-Screw Extrusion Feb, 2019
Xiaofei Sun, Mark A. Spalding
The Dow Chemical Company, Midland, MI
Timothy W. Womer
TWWomer and Associates, LLC, Edinburg, PA
Ned Uzelac
Performance Feed Screw Inc., Mississauga, ON, Canada

2. INTRODUCTION

3. Goals
Develop guidelines for the flute geometry with the goal of mitigating resin degradation and undispersed gels
Investigated three major design factors of a Maddock mixer using 3D finite element numerical simulation
Flute channel depth
Mixing flight undercut
Flute lead length

4. Maddock Mixer
Invented by Gene LeRoy at the Union Carbide Corporation (UCC) Research Center, and was perfected by Bruce Maddock in 1973
Used to trap, melt, and disperse solid polymer fragments
Constructed by placing flute pairs with an undercut positioned between them.

5. Flute Channel Depth---Resin Degradation
Mixer with excessive channel depth – flutes are too deep causing long residence time and resin degradation.
Well designed mixer – flute depth is half the width of the flute. Short residence times and no resin degradation.

6. Mixing Flight Undercut – Entangled Gels
(stress smeared)
Entangled gels are due to entangled molecular chains that solidify first when cooled, appearing like unmelted resin.
Stress disentangles the chains. A stress of 200 kPa or above is needed for PE
A undercut of 1% of barrel diameter may not provide sufficient shear stress in many circumstances
Shear stress can be increased by reducing mixing flight undercut
𝝉M is the stress for flow over the mixing flight.
Page 6

7. MIXER DESIGNS & SIMULATION SETUP

8. Mixer Designs Mixer 1 Mixer 2 Mixer 3 Mixer 4 Flute lead length (mm)
straight
345
Mixing undercut (mm)
0.46
0.76
Flute depth (mm)
12.3
11.0
12.8
Flute width (mm)
24.6
22.2
Depth/width ratio
0.5
0.6
Mixer 1
Mixer 2

9. Extrusion Conditions
Simulated the polymer flow from the mixing section toward the end of the screw tip in a 63.5 mm barrel diameter single-screw extruder
Screw speed: 70 rpm
Rate: 50.8 kg/h
Specific rate: 0.73 kg/(h·rpm)
Barrel temperature: 220°C
Entry condition: 220°C, 19.3 MPa

10. Simulation Setup
Mass, momentum, and energy balance equations were solved by StarCCM+ using screw rotation physics
Resin layer discretized to 5.5 to 6 million elements
Assumptions:
non-isothermal laminar flow
Incompressible polymer melt
the influences of inertia, gravity, and elasticity of the melt are small and neglected

11. Material
Material used in the simulation and experiments is a LLDPE resin with a melt index (MI) of 1 dg/min (190oC, 2.16 kg)

12. RESULTS & DISCUSSION

13. Pressure Profiles
Spiral flute design enhances the conveying capability of the mixer
Mixing undercut is the major flow restriction, and a larger undercut help increase the conveying capability
Deeper flute channels only lead to slight increase in the conveying capability
Mixer 1: straight flute
Mixer 2: spiral flute
Mixer 3: spiral flute, larger undercut
Mixer 4: spiral flute, deeper flute

14. Temperature Profiles
Temperature at discharge almost identical regardless the mixer design

15. Residence Time Distribution
Excessively deep flute channels lead to long residence time at the root of the trailing side of the flutes
Mixer 1
(straight flute)
Mixer 2
(spiral flute)
Mixer 3
(spiral flute, larger undercut)
Mixer 4
(spiral flute, deeper flute)

16. Mixing Quality
Mixing quality was evaluated by using a passive scalar tracing method
Assuming 50/50 black and white tracer at the entry with no mixing
Entry Plane
Discharge Plane
Larger mixing flight undercut leads to reduced mixing performance
0.76 mm undercut
0.46 mm undercut

17. Mixing Quality
PE requires a shear stress of 200+ kPa to ensure mitigation of entangled gels
With a undercut of 1% of the barrel diameter, even at 70 rpm, the stress level is still below 200 kPa
As a general guideline, a undercut of about 0.5% of barrel diameter is more appropriate for high-shear applications
Smaller undercut will also mitigate solid polymer fragments in the extrudate

18. Summary
Three major design factors of Maddock mixer were investigated using numerical simulation
Larger mixing flight undercut enhances the conveying capability but leads to poor mixing quality
Excessively deep flute channels lead to long residence time
Spiral flute channel design improves the conveying capability

19. Recommendations
Keep the flute depth at or slightly below half the flute width to avoid excessive residence time and resin degradation
Use a spiral flute design when additional conveying capability is desired
As a general guideline, mixing flight undercut around 0.5% of the barrel diameter is recommended for applications requiring high shear stress levels
Need to be evaluated on a case-by-case basis depending on the specific resin type, machine size, and application

20. BACKUP SLIDES

21. Experimental Validation of Simulation Results
Simulated and experimental pressure data exhibit consistent trend

22. Experimental Validation of Simulation Results
Satisfactory agreement between simulation and experimental data

23. Mixing Flight Undercut
Undispersed gel content exhibits negative trend with shear stress
Gel count v.s. shear stress experimental data generated using a shear refiner for a PS-elastomer blend
A undercut of 1% of barrel diameter may not provide sufficient shear stress in many circumstances
As a general guideline, satisfactory dispersive mixing can be usually achieved at an undercut around 0.5% of barrel diameter
The optimal undercut size needs to determined with various other factors taken into consideration such as resin type, barrel size, and the applications