Biochips are physically and/or electronically controllable miniaturized labs
(lab-on-a-chip) which are used for combinatorial chemical and biological ana-
lysis in environmental and medical studies, e.g., for high throughput screening,
hybridization and sequencing in genomics, protein pro¯ling in proteomics, and
cytometry in cell analysis. The precise transport of the samples (e.g., DNA or
proteins) in a lithographically produced network of channels and reservoirs on
top of the chip in picoliter to nanoliter volumes can be done either by means of
external forces (active devices) or by speci¯c geometric patterns (passive de-
vices). Here, we will consider active micro°uidic biochips where the core of the
technology are nanopumps featuring piezoelectrically agitated surface acous-
tic waves. These waves propagate like a miniaturized earthquake (nanoscale
earthquake), enter the °uid ¯lled channels and cause an acoustic streaming
in the °uid which provides the transport of the samples. The mathematical
model represents a multiphysics problem consisting of the piezoelectric equa-
tions coupled with multiscale compressible Navier-Stokes equations that have
to be treated by an appropriate homogenization. We discuss the modeling
approach, present algorithmic tools for the numerical simulation and address
optimal design issues as well. In particular, the optimal design of speci¯c
parts of the biochips leads to large-scale optimization problems whose compu-
tational complexity can be signi¯cantly reduced by a combination of domain
decomposition and balanced truncation model reduction.
The results are based on joint work with Harbir Antil, Roland Glowinski,
Matthias Heinkenschloss, Daniel KÄoster, Christopher Linsenmann, Danny So-
rensen, Tsorng-Whay Pan, and Achim Wixforth.
Copyright. All Rights Reserved.