Structural Optimization of non-Newtonian Microfluidics

Many of the biological fluids analyzed in Lab-on-a-Chip systems contain elastic components, which gives the fluids elastic character. Such fluids are said to be non-Newtonian or, more precisely, viscoelastic. They can give rise to exotic effects on the macroscale, which are never seen for fluids consisting of small molecules, such as water. These viscoelastic effects become increasingly important as devices are scaled down, in particular relative to inertial effects. Experimental researchers have thus investigated the possibility of replacing Lab-on-a-Chip components relying on inertial effects with components relying on viscoelastic effects, but the non-intuitive nature of these fluids complicates the design process.
This thesis combines the method of topology optimization with differential constitutive equations, which govern the flow of viscoelastic fluids. The optimization method iteratively improves a material layout based on a mathematical analysis, and this technique therefore has the potential to identify excellent designs without user intervention. We have applied the combination to the problem of a valve without moving parts, and found a novel design [P2]. We characterized this design experimentally, and compared the results with the established hyperbolic designs. We found superior performance in the parameter regime of the optimization as well as similar optimal performance [P3].
The cross-slot geometry is known to exhibit bistability for viscoelastic fluids. We studied this geometry, and applied the optimization to ideas related to the bistability using a heuristic approach [P4]. This is successful for the most simple ideas, but the most advanced idea seems to call for a stricter methodology. Finally the thesis contains numerical code specific to COMSOL Multiphysics [P1], a commercial finite element package. The code is capable of calculating the viscoelastic flow in a benchmark geometry, and we hope that it will help newcomers as well as experienced researchers in the field of differential constitutive equations.