  Understanding the mixing capability of mixing devices based on their
geometric shape is an important issue both for predicting mixing processes and
for designing new mixers. The flow patterns in mixers are directly connected
with the modes of the local strain rate, which is generally a combination of
elongational flow and planar shear flow. We develop a measure to characterize
the modes of the strain rate for general flow occurring in mixers. The spatial
distribution of the volumetric strain rate (or non-planar strain rate) in
connection with the flow pattern plays an essential role in understanding
distributive mixing. With our measure, flows with different types of screw
elements in a twin-screw extruder are numerically analyzed. The difference in
flow pattern structure between conveying screws and kneading disks is
successfully characterized by the distribution of the volumetric strain rate.
The results suggest that the distribution of the strain rate mode offers an
essential and convenient way for characterization of the relation between flow
pattern structure and the mixer geometry.
