This article extends the analysis of laminar mixing driven by a chaotic flow in the presence of diffusion to three-dimensional open-flow devices by means of the mapping-matrix method. The extended formulation of the mapping matrix recently proposed by Gorodetskyi et al. (2012) allows inclusion of the molecular diffusion in the mixing process. This provides an efficient numerical tool for understanding the interplay between a chaotic advective field and diffusion, especially for high Peclet numbers. As a prototypical open-flow device we consider the partitioned-pipe mixer. Results deriving from the application of the extended mapping method are compared with Galerkin simulations, and a close agreement is found. Short-term properties in the evolution of the concentration and the effect of axial diffusion are also addressed. (c) 2013 American Institute of Chemical Engineers