The Kenics static mixer was investigated numerically using Lagrangian methods to characterize mixer performance in laminar flow. Techniques from dynamical systems analysis (Poincare sections, tracking of fluid tracers, and the development of stretching histories for tracer elements) as well as a more traditional mixing measure (the variation coefficient) were used to compare mixing performance at various Reynolds numbers. For creeping flow conditions (Re less than or equal to 10), the Kenics flow is globally chaotic and mixing performance is independent of Re. For Re = 100, significant islands of regular motion develop. These islands do not exchange material with the remainder of the flow and act as a barrier to uniform mixing. For Re = 1000, the Row is predominantly chaotic again, but small islands remain, leading to less effective mixing than under creeping flow conditions.