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Encyclopedia of Physical Science and Technology EN012c-593 July 26, 2001 15:56

624 Polymer Processing

depends on how well the flight of one screw closes the a maximum as the configuration becomes random. Mixing
opposing channel of the other screw. Closely intermesh- is considered to be one of the most widespread industrial
ing counterrotating twin screw extruders provide the most unit operations, and it is found in the core of many areas
positive displacement. However, some leakage will occur, in the general industry. This unit operation might be a
which will reduce the degree of positive conveying that process in itself or it might be part of a more extended
can be achieved. Counterrotating self-wiping twin-screw sequence of processes.
extruders actually operate in a mode similar to that of a In this article we will restrict ourselves to the study of
single-screw extruder. However, because elements can be the mixing of two-component systems. The two compo-
easily interchanged in a twin-screw extruder, it is possible nents are defined as either major or minor components by
to change the channel depth profile and add more mixing the level of their total concentration. The goal of the mix-
elements. ing process is usually to achieve a homogeneous disper-
The flow of material in twin-screw extruders is very sion of the minor component into the major one obtaining
complex,andtheflowpatternsaredifficulttopredictmath- the ultimate particle or subdivision (or volume element)
ematically. For this reason the simulation of processes in level of the minor component. The above term is used in
twin-screw extruders is not as well developed as it is for a restricted sense, because in its general form the ultimate
single-screw extruders. It is, therefore, difficult to pre- particle is the molecule and ultimate mixing is molec-
dict the performance of a twin-screw extruder based on ular mixing. However, in typical mixing operations the
geometrical features, polymer properties, and processing two parameters that define the size and form of the ulti-
conditions. Hence, it is difficult to carry out accurate de- mate particle are the form of the component and the level
sign calculations. For this reason twin-screw extruders are of satisfaction of the final dispersion. For example, in the
constructed in modules in which the screw and barrel ele- mixing of carbon black agglomerates in polyethylene (PE)
ments can be changed. The screw design can be changed the ultimate particle is one particle of carbon black defined
by changing the sequence of the screw elements. Hence, by the form of the initial agglomerates (many particles to-
much of the design of twin-screw extruders is done on gether)aswellasbythesatisfactorydispersionlevelofone
an empirical basis. One can use a combination of screw carbon black particle. In general, typical ultimate particles
elements and kneading blocks to accomplish a given op- are molecules and colloidal and microscopic particles.
eration. Mixing is accomplished by movement of material from
The sizes of twin-screw extruders range from 25 to various parts by the flow field. This movement occurs by a
244 mm (this is the diameter of one of the barrels). The combination of the following mechanisms, two of which
barrel length to diameter ratio, L/D, ranges from 39 to 48. are hydrodynamic and one is molecular. The first is con-
The length can be altered as required for most twin-screw vective transport. It is present in both laminar and turbu-
extruders because of their modular construction. lent regimes, and it can also be called “bulk diffusion.”
Generally speaking, a colored pigment being dispersed in
a bucket of paint is an example of laminar mixing. In this
V. COMPOUNDING case, layers of pigment are thinned, lumps are flattened,
and threads are elongated by laminar convective flow. Stir-
Polymers are rarely used in neat form but usually in the ring of cream in a cup of coffee is an example of turbulent
presence of other additives. These additives may be in mixing, in which the mechanism of turbulent bulk flow
the form of other polymers, processing aids, stabilizers, predominates at the first stages.
colarants, fillers, etc. The process by which additives are The second mechanism is eddy diffusion which is pro-
combined with polymers is called compounding. Funda- duced by local turbulent mixing. This mechanism prevails
mental principles of mixing are described briefly followed at the later stages in the example of the stirring of cream
by commercial techniques used for compounding, and into a cup of coffee mentioned above. The turbulent ed-
then a description is given of some types of additives that dies in the flow field create small-scale mixing, which is
influence processibility and to some degree properties. sometimes thought to be analogous to molecular diffusion.
However, eddy diffusivity is much higher than molecular
diffusivity, and it occurs over longer length scales. For
A. Principles of Mixing
gases and low-viscosity liquid systems eddy diffusion be-
The term mixing refers to operations that have a tendency comes the usual mode of mixing.
to reduce nonuniformities or gradients in concentration, Finally, there is molecular diffusion or interpenetration
temperature, size of a dispersed phase, or other properties of molecular species. It is responsible for the ultimate ho-
of materials. Equivalently, a mixing operation increases mogenization on a molecular scale (the ultimate particles
the configurational entropy of the system, which reaches are the molecules), and it is considered to be true