On Shape Optimization of Acoustically Driven Microfluidic Biochips

The paper deals with the shape optimization of acoustically driven microfluidic biochips. This is a new type of nanotechnological devices with a wide range of applications in physics, pharmacology, clinical diagnostics, and medicine. The complex system of channels inside the chip can be optimized with regard to different objectives and various optimal criteria. To simplify the model, we solve Partial Differential Equations (PDEs) constraint optimization problem based on a stationary Stokes-like system as equality constraints and bilateral inequality constraints with upper and lower bounds for the design parameters coming from geometrical and technological restrictions. The shape of the domain is designed by control parameters determining certain parts of the boundary. Preliminary fixed segments of the lateral walls of the channel are approximated by Bézier-curves with design parameters taken as the Bézier control points. For the solution of the problem we use a path-following interior-point method with inexact Newton solvers.