Abstract
The design of MEMS devices have benefitted from the topology
optimization tool and complicated layout problems have been solved,
see [1] for an overview. This research is aimed at micro fluidic
devices known as micro-Total-Analysis-Systems (muTAS) where the main
physical phenomena originate from fluid mechanics. In future
practice a muTAS could be used by doctors, engineers etc. as a hand
held device with short reaction time that provides on-site analysis
of a flowing substance such as blood, polluted water or similar.
Borrvall and Petersson [2] paved the road for using the topology
optimization tool for micro fluidic design problems by considering
design of energy efficient devices subjected to Stokes flow. Several
researchers have elaborated on [2], however, this research has
focused on 2D fluid modelling which limits the practical impact of
the computed designs. This limitation is caused by the finite size
domain used in topology optimization problems which ensures that the
velocity components couples, even for Stokes flow [3]. Physically
Stokes flow is an exotic inertia free flow, which in practice
complicates mixing by passive devices. Passive mixing devices are
relevant particular at micro scales since they are easily
manufacturable and maintenance free.
Here we consider topology optimization of 3D Stokes flow problems
which is a reasonable fluid model to use at small scales. The
presentation elaborates on effects caused by 3D fluid modelling on
the design. Numerical examples relevant for optimal micro fluidic
mixer design are shown where the design is planar - compliant with
micro fabrication techniques - and where the designs are 3D. In
addition issues related to the parallel solution of the linear
algebra problems are discussed. The implementation uses the
commercial COMSOL multiphysics programme which is sufficiently
flexible to provide semi--automated analytical sensitivities.
1. M. P. Bendsoe and O. Sigmund, "Topology Optimization - Theory,
Methods and Applications", Springer Verlag, Berlin Heidelberg, 2003.
2. T. Borrvall and J. Petersson, "Topology optimization of fluids in
Stokes flow", Int. J. Num. Meth. Fluids v. 41, p. 77-107, 2003.
DOI:10.1002/fld.426
3 E. Lauga, A. D. Stroock, and H. A. Stone, "Three-dimensional flows
in slowly varying planar geometries", Physics of fluids v. 16(8), p.
3051-3062, 2004. DOI: 10.1063/1.1760105
| Original language | English |
|---|---|
| Publication date | 2006 |
| Publication status | Published - 2006 |
| Event | Seventh World Congress on Computational Mechanics - Century City, United States Duration: 16 Jul 2006 → 22 Jul 2006 Conference number: 7 |
Conference
| Conference | Seventh World Congress on Computational Mechanics |
|---|---|
| Number | 7 |
| Country/Territory | United States |
| City | Century City |
| Period | 16/07/2006 → 22/07/2006 |