We present a numerical study of chaotic advection and mixing in a spatially periodic, three-dimensional flow. The flow inside a cylindrical tube, into which one or more Kenics KM static mixer elements are inserted to promote mixing, is studied by solving the momentum equations numerically and then applying tools for analysis of mixing in time-periodic two-dimensional and three-dimensional chaotic flows. It is found that for this particular static mixer geometry, the initial location of a blob of dye is important for its spreading over the cross section of the tube only in the first few mixing elements, its influence decreases afterwards. The influence of the Reynolds number on mixing is mainly a finer grain of the resulting mixture, this is visible after several elements. A symmetry breaking modification of the standard Kenics KM static mixer geometry is suggested and subject to the same analysis as the original geometry. A slight improvement in the mixing efficiency is obtained with the modified geometry: it increases the extensional efficiency and gives a more homogeneous distribution of the stretching rates. (C) 2012 Elsevier B.V. All rights reserved.