Modeling, simulation, and optimization of surface acoustic wave driven microfluidic biochips *

TLDR: For shape optimization of pressure driven capillary barriers between microchannels and reservoirs, a multilevel interior point method relying on a predictor-corrector strategy with an adaptive choice of the continuation steplength along the barrier path is presented.

Abstract: We will be concerned with the mathematical modeling, numerical simulation, and shape optimization of micro∞uidic biochips that are used for various biomedical applications. A particular feature is that the ∞uid ∞ow in the ∞uidic network on top of the biochips is induced by surface acoustic waves generated by interdigital transducers. We are thus faced with a multiphysics problem that will be modeled by coupling the equations of piezoelectricity with the compressible Navier-Stokes equations. Moreover, the ∞uid ∞ow exhibits a multiscale character that will be taken care of by a homogenization approach. We will discuss and analyze the mathematical models and deal with their numerical solution by space-time discretizations featuring appropriate flnite element approximations with respect to hierarchies of simplicial triangulations of the underlying computational domains. Simulation results will be given for the propagation of the surface acoustic waves on top of the piezoelectric substrate and for the induced ∞uid ∞ow in the microchannels of the ∞uidic network. The performance of the operational behavior of the biochips can be signiflcantly improved by shape optimization. In particular, for such purposes we present a multilevel interior point method relying on a predictor-corrector strategy with an adaptive choice of the continuation steplength along the barrier path. As a speciflc example, we will consider the shape optimization of pressure driven capillary barriers between microchannels and reservoirs.