THESIS FOR THE DEGREE OF LICENTIATE OF ENGINEERING From Eulerian to Lagrangian Viewpoints in Fluid Flows Convective Chaotic Mixing in Microfluidics

Fluid mixing in small systems is difficult when the diffusion is a slow process compared to other relevant processes, and when the fluid dynamics is laminar, i.e., dominated by viscous forces. This is the prevailing situation in microfluidic systems. However, mixing is enhanced in chaotic flows. In this work we estimate and compute the mixing time in chaotic channel flows as tm = 1/(2σ) ln (Pe), where σ is related to a stability factor for the flow and Pe is the Péclet number. We compute the flow in a number of realistic microfluidic mixers by solving the stationary three-dimensional Navier-Stokes equations and Stokes equations by the finite element method. Stability factors are obtained by computing and analyzing flow trajectories. The procedure is motivated by maximum norm a priori error estimates quoted from the literature. A major part of this work has been to choose, evaluate, and implement algorithms. The implemented Navier-Stokes/Stokes solver, written in C++ code, combines a Krylov method with multigrid. Our results indicate that the solver is optimal.