We present new passive microfluidic mixing structures based on 2D and 3D geometries. The primary mechanism of mixing in these devices is based on chaotic advection. The mixers which incorporate 3D structures introduce transverse flow rotation greatly enhancing performance. Simulations and experimental tests were performed over a Reynolds number (Re) range from 0.1 to 20 and showed good agreement. At an Re of 0.1, 90% mixing was achieved in a path length of 32 and 7 mm, for the 2D and 3D geometrical mixers, respectively. This represents an improvement in performance over a standard T-mixer of 20% for the 2D mixer and 82.5% for the 3D mixer. An inflection point in the mixing efficiency was observed for both mixer types around an Re of 1. The devices were fabricated on a polymethylmethacrylate (PMMA) substrate, using an excimer laser beam incorporating an intelligent pinhole mask. Initially, structures were developed off-line using a laser simulation tool. A design-of- experiments (DOE) approach along with computational fluid dynamic (CFD) analysis was used to optimise mixing element geometry. This precursor to the fabrication step greatly reduces the time between the design stage and device realisation.