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IMPROVE MIXING BY GENERATING ELONGATIONAL FLOW
IMPROVE MIXING BY GENERATING ELONGATIONAL FLOW
By: Dr. Chris Rauwendaal
Rauwendaal Extrusion Engineering, Inc.
Los Altos Hills, California 94022 USA
www.rauwendaal.com
Introduction
Most dispersive mixers used in single screw extruders use geometries that
generate shear flow to disperse agglomerates or droplets. However, shear
flow is rather inefficient in dispersing agglomerates or droplets.
Elongational flow is much more efficient than shear flow in achieving
effective dispersion. As a result, if we want to achieve good dispersive
mixing in a single screw extruder we need to use mixer that create
elongational flow. A new class of mixing devices was developed with the
specific objective to achieve strong elongational flow. These CRD mixers
combine dispersive and distributive mixing capability.
Background
In polymer mixing we usually distinguish between distributive and
dispersive mixing. Distributive mixing aims to improve the spatial
distribution of the components without cohesive resistance playing a role; it
is also called simple or extensive mixing. In dispersive mixing cohesive
resistances have to be overcome to achieve finer levels of dispersion;
dispersive mixing is also called intensive mixing. The cohesive component
can consist of agglomerates where a certain minimum stress level is
necessary to rupture the agglomerate. It can also be droplets where
minimum stresses are required to overcome the interfacial stresses and
deform the droplet to cause break-up.
Dispersive mixing is usually more difficult to achieve than distributive
mixing. Single screw extruders are generally considered to be poor
dispersive mixers while twin screw compounding extruders have much
better dispersive mixing capability. However, when we analyze the mixing
process in co-rotating twin screw extruders (1), it is clear that the main
mixing action does not occur in the intermeshing region but in the region
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between the pushing flight flank and the barrel. This is particularly true
when the flight helix angle is large as it is in kneading disks.
Dispersive Mixing in Twin Screw Extruders
The reason that twin screw extruders make good dispersive mixers is that the
space between the pushing flight flank and the barrel is wedge shaped and
thus creates elongational flow as the material is force through the flight
clearance. Shear flow is not very efficient in achieving dispersive mixing
because particles in the fluid are not only sheared they are also rotated, see
figure 1. In elongational flow particles undergo a stretching type of
deformation without any rotation; rheologists call this “irrotational flow,”
see figure 1.
Dispersion in shear flow
Dispersion in elongational flow
Figure 1, dispersion in shear and elongational flow
Since there is no rotation in pure elongational flow the deformation of the
fluid is effectively transferred to the clusters in the fluid. This results in
tensile forces acting to pull apart the clusters into smaller clusters.
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Using Twin Screw Mixing Mechanism in Single Screw Extruders
In the past it was considered to be difficult to generate elongational flow in
single screw extruders. However, this is not the case at all. There are at
least two simple ways in which elongational flow can be achieved in single
screw extruders.
One is by using a slanted pushing flight flank so that the material is stretched
as it is forced through the flight clearance. The other way is by using
tapered slots in the flights. The tapered slot accelerates the fluid as it flows
through the slots and thus creates elongational deformation. The dashed
arrows in figure 2 indicate the screw velocity, the solid arrows indicate the
melt velocity relative to the screw.
Curved flight flank
barrel
Tapered flight slot
Figure 2, Two methods of creating elongational flow in the CRD mixer
The new dispersive (CRD) mixers developed by Chris Rauwendaal (2-4) use
both methods to create elongational flow. The tapered slots in the flights
serve to increase distributive mixing as well as dispersive mixing. If the
material is not randomized in its passage through the mixer, only the outer
shells of the fluid will be dispersed leaving the inner shells undispersed (5).
Therefore, it is critical to incorporate both distributive and dispersive mixing
ability within the mixer.
The initial design of the CRD mixer (2) was developed using the concept of
the passage distribution function (6), while the final geometry was
developed using a detailed three-dimensional flow analysis. The 3D flow
analysis was performed using BEMflow (7), a boundary element flow
analysis package originally developed at the University of Wisconsin,
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Madison by Professor Osswald and co-workers. The boundary element
analysis allows a complete description of flow, so that the stresses, the
number of passes over the mixing flights, the number of passes through the
tapered slots, residence time, etc. can be quantified for a large number of
particles. The CRD mixer may well be the first complex mixing device
developed solely based on engineering calculations and computer modeling.
With BEA many particles can be tracked as they flow through the mixer.
For each particle the flow number can be determined along its streamline.
The flow number is a measure of the strength of the elongational flow
relative to the shear flow; its value is between zero and one. A flow number
of one indicates pure elongational flow, a flow number of zero indicates pure
rotation. A flow number of 0.5 indicates simple shear flow. Figure 3 shows
the flow number of a particle traveling through a CRD mixer.
0
0.1
0.2
0.3
0.4
0
0.2
0.4
0.8
0.6
1.0
Time [seconds]
Flow
Nu
mb
er
Flow number vs. time for V4 configuration of points traveling through the nip
Figure 3, Flow number vs. time in CRD mixer
It is interesting to note that the highest flow number is about 0.95; this is
almost pure elongational flow. Similar analyses on twin screw extruders
indicate that the highest flow number is about 0.80. The reason that a good
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single screw mixer can achieve stronger elongational flow than a twin screw
extruder is that there are rather severe design constraints for the screw
geometry in intermeshing twin screw extruders (1). In single screw
extruders we more design freedom and we can actually create more effective
elongational flow as a result.
Experience from the Field
As of September 2000 over one hundred extruders are running with CRD
mixers. The current applications are color concentrates, foamed plastic,
post-consumer-reclaim with calcium carbonate, medical applications, heat
shrinkable tubing, wire coating, carbon black dispersion in polyolefins, and
blown film extrusion of low melt index metallocenes. All current
applications are on single screw extruders in sizes ranging from 19 to 200
mm (0.75 to 8.0 inch). CRD mixing screws are also used in injection
molding and even in twin screw extruders.
In the manufacture of color concentrates it was possible to produce even the
most difficult material, phthalate blue, with good quality using a single
screw extruder. The foamed plastic application polystyrene was foamed
with a physical blowing agent carbon dioxide, a demanding application
requiring very good dispersive and distributive mixing. The foamed product
was found to have uniform cell size and excellent surface quality, while the
extrusion process was very stable with respect to melt pressure and
temperature.
In the PCR application film scrap is extruded with relatively high levels of
calcium carbonate, up to thirty percent. The dispersion quality achieved in
this application is excellent. It should be noted that this is an application that
would normally use in twin screw extruder; single screw extruders are
generally considered not to be capable of handling these types of
compounding jobs. In the blown film application major problems were poor
film quality and the inability to feed more than three percent fluff with the
virgin plastic without generating gels in the film. The CRD mixing screw
was able to improve film quality and handle up to twelve percent fluff
without generating gels.
In all applications the CRD mixing screws have been able to achieve better
mixing at equal or higher levels of output at lower levels of power
consumption and lower melt temperatures. In most cases, the CRD mixing
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screws replaced barrier screws with mixing elements added after the barrier
section. Since barrier screws are based on shear mixing, while CRD mixing
screws are based in elongational mixing, the good results prove that
elongational mixing is more efficient than shear mixing.
The good results with respect to gels indicate that elongational mixing
devices can effectively disperse gels as opposed to shear mixing devices.
Luciani and Utracki found similar results in experiment using their
extensional flow mixer (8). The experience from the field was obtained with
a fifth generation mixing device, the CRD5, see figure 4. This mixer has
four parallel flights with tapered slots in the flights. Each wiping flight
segment is followed by three mixing flight segments. Tapered slots separate
the flight segments. The wiping segments are offset such that the mixer
wipes the entire barrel surface. Complete wiping of the barrel surface is
important to achieve efficient heat transfer between the plastic melt and the
extruder barrel.
Figure 4, Three dimensional rendering of a CRD5 mixer
Application to Injection Molding
Mixing is not only important in extrusion, it is equally important in injection
molding. CRD mixing elements can be added to an injection screw. Most
injection screws have a non-return valve (NRV) at the end of the screw to
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prevent the molten plastic flowing back into the screw during injection. It is
possible to incorporate mixing capability into the NRV to combine two
functions within one device.
Figure 5 shows an example of a CRD mixing element incorporated in a slide
ring NRV for injection molding (11).
Figure 5, CRD non-return valve for injection molding screws (open position)
The slide ring has multiple internal grooves that are tapered. The tapered
grooves are formed by elongational pins. The pins split and reorient the
fluid thus causing efficient distributive mixing. The tapered grooves
accelerate the fluid and cause elongational flow with efficient dispersive
mixing. The nosepiece of the valve has external pins that create a mixing
action similar to that of the internal pins of the slide ring. The CRDNRV
provides a convenient and cost efficient method to improve the mixing
capability of injection molding screws. Good mixing action can be obtained
simply by exchanging the conventional NRV with a CRDNRV.
Application to Static Mixers and Breaker Plates
The mixing mechanism of the CRD mixer has also been applied to static
mixers and breaker plates. The Madison Group in cooperation with
Rauwendaal Extrusion Engineering has developed the DDSM static mixer
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capable of distributive and dispersive mixing and the MBP, the mixing
breaker plate (12). Figure 6 shows two versions of the MBP. The first one
on the left has tapered circular channels to create elongational flow, the
second on the right has straight tapered channels. Different plates can be
stacked together to increase the mixing action.
Figure 6, Two examples of the mixing breaker plate
The mixing breaker plate provides a very convenient method to increase the
mixing action in an extruder. Another advantage of the MBP over
conventional breaker plates is that it is much more streamlined. As a result,
it has less chance of stagnation and it is easier to clean.
Conclusions
The CRD mixer allows the single screw extruder for the first time to be used
in applications that heretofore were only possible on twin screw extruders.
The high mixing efficiency of the CRD mixer is due to the generation of
strong elongational flow and the fact that all fluid elements make multiple
passes through the high stress regions. Elongational flow not only achieves
more effective dispersion, it also creates less viscous dissipation than shear
flow. As a result, the power consumption and temperature rise in the CRD
are less than in mixing devices that rely on shear flow.
The CRD mixer is easy to manufacture, can be mounted on existing extruder
screws, and fits in a normal extruder barrel, thus providing a cost effective
improvement in mixing capacity. Other mixers, such as the Cavity Transfer
Mixer (9) or the Crown Cup Mixer (10), require special barrel sections that
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increase the cost of the equipment and cost of operation. The use of the
CRD mixer is being extended to injection molding and twin screw mixers
and extruders. With the positive results obtained from the field it can be
expected that the CRD mixer will find widespread applications in extrusion,
compounding, and molding.
The CRDNRV provides a quick and convenient method to improve the
mixing action in injection molding machines. The CRDNRV simply
replaces an existing non-return valve. The mixing breaker plate provides a
fast and easy method to enhance mixing in extruders. The mixing breaker
plate also has a more streamlined design than conventional breaker plates
and is easier to clean.
References
1. “Polymer Mixing, A Self-Study Guide,” C. Rauwendaal, Carl Hanser
Verlag, Munich (1998)
2. “A New Dispersive Mixer for Single Screw Extruders,” 56
th
SPE
ANTEC, Atlanta, GA, 277-283, Chris Rauwendaal, Tim Osswald, Paul
Gramann, and Bruce Davis (1998)
3. “Experimental Study of a New Dispersive Mixer,” Chris Rauwendaal,
Tim Osswald, Paul Gramann, Bruce Davis, Maria del Pilar Noriega, and
O. A. Estrada, 57
th
SPE ANTEC, New York, 167-176 (1999)
4. “Design of Dispersive Mixing Sections,” Chris Rauwendaal, Tim
Osswald, Paul Gramann, and Bruce Davis, International Polymer
Processing, Volume 13, pp. 28-34 (1999)
5. “Kinematics and Deformation Characteristics as a Mixing Measure in the
Screw Extrusion Process,” T.H. Kwon, J.W. Joo, and S.J. Kim, Polym.
Eng. Sci., V. 34, N. 3, 174-189 (1994)
6. “The Distribution of Number of Passes Over the Flights in Single Screw
Melt Extruders,” Z. Tadmor and I. Manas-Zloczower, Advances in
Polymer Technology, V. 3, No. 3, 213-221 (1983)
7. BEMflow, Boundary Element Fluid and Heat Transfer Simulation
Program, ©1996 The Madison Group: PPRC
8. “The Extensional Flow Mixer”, A. Luciani and L. A. Utracki, Intern.
Polymer Processing XI, 4, 299-309 (1996)
9. “The Cavity Transfer Mixer: A Blender for all Seasonings,” R. S.
Hindmarch, Materials & Design, Vol. 8, No. 6, November/December
(1987)
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10. “Innovation Brings High Shear Mixing for Single Screw Extruder,” n.n.,
Plastics Additives & Compounding, April/May, 30-31 (1999)
11. “Non-Return Valve with Distributive and Dispersive Mixing Capability,”
C. Rauwendaal, 58
th
SPE ANTEC, Orlando, FL, 638-641, (2000)
12. “A New Dispersive and Distributive Static Mixer for the Compounding
of Highly Viscous Materials,” 57
th
SPE ANTEC, New York, 162-166, C.
Rauwendaal, P. Gramann, B. Davis, T. Osswald (1999)
