Dynamical Systems in Pin Mixers of
Single-Screw Extruders
W. R. Hwang, K. W. Kang and T. H. Kwon
Dept. of Mechanical Engineering, Pohang University of Science and Technology, San 31, Hyoja-dong, Pohang, Kyungbuk,
790-784, South Korea
DOI 10.1002/aic.10130
Published online in Wiley InterScience (www.interscience.wiley.com).
Dynamical systems generated by various types of pin mixers were studied for the
application to the single-screw extruders. A periodic unit of the pin mixer was modeled as
a dynamical system of the complex duct flow. It was found that the cross-sectional space
could be divided into two distinct regions: the inner and outer zones. The pin configu-
ration directly affects the motion of fluid particles in the inner region, while motion in the
outer region is governed by the resonance phenomena. The effects of the number of pins,
the pin height, the pin orientation, and the composition of two different pin units were
studied with the numerical results and explained in the language of the dynamical systems
theories. Finally, the validity of our modeling, and the numerical result was verified by
qualitative comparison with experimental results. © 2004 American Institute of Chemical
Engineers AIChE J, 50: 1372–1385, 2004
Keywords: dynamical systems, single-screw extruder, pin mixer, fluid mixing, flow visu-
alization.
Introduction
The pin mixer is a popular mixing device in the single-screw
extrusion industry. It is easy to operate and to manufacture, but the
mixing performance has been considered just moderate (Rau-
wendaal, 1991). Erwin and Mokhtarian (1980) studied the mixing
performance of the pin mixer via the quasi-three-dimensional
(3-D) analysis, and they explained that the reorientation of the
material line is the major mixing mechanism. Yao et al. (2001)
analyzed the mixing performance of the pin mixer, and their
modification through the 3-D numerical study. However, we still
have a few fundamental questions on the mixing mechanism of
the pin mixers: such as (a) the role of a single pin on the collective
motion of fluid particles over the whole domain, or (b) the effect
of the number of the pins and the pin configuration on the motion
of fluid particles and, thereby, on the mixing performance. In this
study, we attempted to resolve these questions with the help of the
classical dynamical systems theory and tools. Our objectives are to
analyze the dynamical systems structures in the pin mixer and to
understand mixing mechanisms, and finally to suggest an efficient
pin configuration for good mixing. The pin configuration of this
study includes the number of the pin, the height of the pin, the
alignment angle, and the composition of two different pin units.
Figure 1 shows the schematic description for the pin mixer in this
study.
Highly viscous flows in the metering section of the single-screw
extruder can be cast into the regular duct flow, and the flow in this
category can be decoupled into the cross-sectional and the longi-
tudinal flows, which play the roles of mixing and pumping,
respectively (Kusch and Ottino 1992). Suppose the flow preserves
the volume in 3-D, then the cross-sectional continuity is satisfied
as well in the regular duct flow, and the fluid particle motion can
be described with the stream function
x ˙ = u =
x , y
y
, y ˙ = v = -
x, y
x
, z ˙ = w x, y (1)
where (x, y, z) and (u, v, w) are the position of the fluid particle
and the fluid velocity, respectively. The flow satisfying Eq. 1 is
Current address of W.R. Hwang: Materials Technology, Eindhoven University of
Technology, Eindhoven, The Netherlands (Email: w.r.hwang@tue.nl).
Correspondence concerning this article should be addressed to T. H. Kwon at
thkwon@postech.ac.kr.
© 2004 American Institute of Chemical Engineers
1372 AIChE Journal July 2004 Vol. 50, No. 7