APPLICATION OF TOPOLOGY OPTIMIZATION IN LAB-ON-A-CHIP DESIGN

Fridolin Okkels1 and Henrik Bruus1

1DTU Nanotech, Technical University of Denmark, DENMARK

ABSTRACT A free-form structural optimization of microfluidic devices may greatly improve

their functionality. This approach is illustrated by numerical examples, where the change in geometry should easily be implemented in existing manufacture proc-esses. KEYWORDS: Free-form optimization, microfluidics, reactors, numerical analysis

INTRODUCTION

Most microfluidic systems are fabricated using a lithographic process which en-ables a free planar design, but still the true potential of this capability is seldom ac-knowledged, as almost all channel-geometries are very regular. With the emerging of structural optimization methods [1], the optimal geometrical channel-design of many devices can now be found numerically, and this literally utilizes the fabrica-tion process in the most efficient way.

When computing optimal design using the method of topology optimization, the channel-structure is initially not known, but gradually forms through an iterative process, guided by the optimization of the problem. The great advantage of topology optimization is that the complexity of the final solution is unconstrained, and there-fore not burdened by our preconceived expectations. Recently this method has been successfully applied to design optimal catalytic micro-reactors [2], and bio-reactors [3], which have resulted in more than a 10-fold increase of the related reaction rates.

Some possible applications of the method on Lab-on-a-chip systems are pre-sented in the following:

OPTIMAL HOMOGENIZATION OF PERFUSION FLOWS IN MICROFLU-IDIC BIO-REACTORS

We have developed a general design of a continuously feed bio-reactor using to-pology optimization, which homogenizes the perfusion flow at minimal pressure drop [4]. The resulting homogeneous flow reduces the effect of shear-stress on im-mobilized biological organisms, and may also ensure full control of e.g. concentra-tion gradients introduced at the reactor inlet. A typical optimized design of the ex-pansion-region is shown in Figure 1, where the broad channel to the right extends through the reaction-region. The channel-height in the white area is four times deeper than the gray area. The contour-lines of the pressure show that the design produces a homogeneous pressure-field, and thereby a homogeneous velocity-field, at the reactor-entrance to the right.

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Twelfth International Conference on Miniaturized Systems for Chemistry and Life SciencesOctober 12 - 16, 2008, San Diego, California, USA

OPTIMAL MICROFLUID CATALYTIC REACTORS The method has also been applied to study the optimal distribution of catalytic

material in chemical microfluidic reactors [2]. As a starting-point, the simplest reac-tor-model has been chosen, having a single first order reaction. The objective is to maximize the reaction rate inside the reaction-chamber, where a pressure-driven flow transports the reactant and the product to and from the reactor, as illustrated in Figure 2. For a specific set of physical parameters, Figure 3 shows the optimal struc-turing of active material in black together with the corresponding flow, colored by the flowspeed. In Figure 4 the reactant concentration is shown in colors-grading to-gether with the activity of the catalyst in grayscale.

DESIGN OF ARTIFICIAL GLAND

In this bio-oriented application, the objective is to drain a collection of fluid-producing cells most efficiently.

The dense regions of cells are assumed to be porous, and placed inside a closed region, with a single outlet channel. The fluid-production is modeled by letting the cells be fluid sources, and thereby introducing a divergence in the flow i.e. “·u > 0. The cell distribution is determined as to minimize the viscous energy-dissipation of the produced fluid, and in the example in Figure 5 the drain-channels must occupy at most 40% of the gland region.

Figure 1. Optimal fluid-expansion design, seen from the top, with the flow visu-

alized by arrows. The channel-height is much smaller than the remaining length-scales, and the height of the dark-gray area is 4 times smaller than in the white

area.

Figure 2. Illustration of microfluidic catalytic reactor setup, where reactant A

enters the reactor from the left, driven by a fixed pressure-difference Δp between the

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inlet and outlet. The catalyst C is optimally distributed to maximize the reaction-rate of the product B.

Figure 3. One example of an optimized microfluidic reactor design, with inlet to

the left. Left is shown the active material in black and a color-coding of the flow speed. Right is shown the reactant concentration at top and reaction rate below.

Figure 4. Optimal design of an artificial gland, where fluid is produced in the

gray areas, and has to leave with the least energy-dissipation. CONCLUSIONS

Free-form structural optimization seems to be a promising tool for improving the efficiency of a whole range of microfluidic devices. REFERENCES [1] 1. M. P. Bendsøe, O. Sigmund, Topology Optimization - Theory, Methods

and Applications, Springer, Berlin (2003) [2] F. Okkels and H. Bruus Phys. Rev. E 75, 016301 (2007). [3] F. Okkels and H. Bruus, J. Comput. Theor. Nanosci. 4, 814-816 (2007). [4] F. Okkels and H. Bruus. Submitted to J. Micromech. Microingine (2008).

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