Technical Paper: PIM International, Vol.3 No. 2 June 2009, pages 59-62, 1959 words

Author: Tae Gon Kang [1], Seokyoung Ahn [2], Seong Jin Park [3], Sundar V Atre [4] and Randall M German [5]

[1] School of Aerospace and Mechanical Engineering, Korea Aerospace University, 100 Hanggongdae-gil Hwajeon-dong, Goyang-City, Gyeonggi-do 412-791, South Korea
[2] Mechanical Engineering Department, The University of Texas-Pan American, 1201 W. University Drive Edinburg, TX 78539, USA
[3] Oregon Nanoscience & Microtechnologies Institute, Oregon State University, Covell 118, Corvallis, OR 97331, USA
[4] College of Engineering, San Diego State University, 5500 Campanile Drive, San Diego CA 92182-1326, USA
[5] Center for Advanced Vehicular Systems, Mississippi State University, 200 Research Blvd., Starkville, MS 39759, USA

Abstract

Micro-powder injection moulding (microPIM, µPIM) is accepted as a means to mass-produce various metal or ceramic three-dimensional micro devices. There are several technological barriers for micro-PIM, such as the production of nano-size powders, mixing of nano-size powders with a binder system, injection moulding, debinding, and sintering.

One of the key technologies in the early stage of the process is a mixing of nano-size powders with a polymer-based binder. In this regard, we examined chaotic mixing in a continuous mixer using a finite element method and a particle tracking method.

Using the particle size distributions along the down-channel direction, information entropy was used as a measure of the mixing progress. The final mixing performance as affected by varying processing conditions was investigated in detail using the numerical scheme. The influence of processing conditions on mixing was studied via sensitivity analysis for the parameters.

Introduction

With the increasing interests in miniaturised devices made of ceramic and metallic materials, micro-powder injection moulding is an important means to mass produce complex micro-devices [1, 2]. To successfully achieve the final goal, the mass-production of ceramic or metallic micro-devices, we need to overcome several technical barriers. In this paper, we address the mixing of nano particles with a polymer-based binder system as an underlying issue necessary to ensure uniform products with the desired properties [3].

Chaotic mixing of viscous liquids in laminar flow is usually based on the baker’s transformation [4], a continuous repetition of stretching and folding. This principle is exploited in static industrial mixing devices. In this study, we selected a static mixer called a Kenics mixer, as a mixing device for powder injection moulding feedstock preparation. It operates in the Stokes flow regime where inertia is negligible. Fig. 1 depicts a representative geometry of a 6-element static mixer (Fig. 1(a)) with mixing elements twisted by 180o in alternating directions (Fig. 1(b)) that is used in our simulations.

The flow problem in this mixer is solved using the finite element method. For the mixing analysis, we employed a particle tracking method [5], where the kinematics of fluid-particle interactions was taken into account while neglecting the effect of molecular diffusion. A distribution of particles at a down-channel location is used to characterise the progress of mixing both qualitatively and quantitatively. A measure of mixing, called the information entropy [6], based on the particle distribution is introduced to quantify mixing.

Further sections of this article include:

- Modelling
- Numerical methods
- Conclusion
- References

Figures and Tables:

Fig. 1 Kenics static mixer. (a) Shaded image of a mixer with 6 helical elements, (b) two mixing elements twisted by 180o in alternating directions, called LR-180 elements

Fig. 2 Measured viscosity of the feedstock of carbonyl iron 63 vol.%

Fig. 3 Axial velocity contours at a down-channel position for different values of the exponent, (a) n=0.3, (b) n=0.4, and (c) n=1 (Newtonian fluid).

Fig. 4 Working principle of the Kenics mixer. The progress of mixing is illustrated by the two colors representing fluid-particles mixtures for the first half period (length of one mixing element)

Fig. 5 Evolution of the interface between two fluids with the exponent n=0.4 in time at several down-channel positions, (a) z=0, (b) z=0.5L, (c) z=L, (d) z=2L, (e) z=3L, and (f) z=4L. Here L is the length of a mixing unit with a blade twisting 180o in left or right direction

Fig. 6 The progress of mixing characterised by the normalised entropy increase S* along the normalised axial direction z/L depending on the exponent n in the viscosity model (see Eq. (2))

Table 1 Coefficients of the Cross-WLF model