The performance of a coaxial mixer in the laminar-transitional flow regime was numerically investigated with Newtonian and non-Newtonian fluids. These mixers comprised two shafts: a central fast speed shaft mounted with an open turbine, and a slow speed shaft fitted with a wall scraping anchor arm. To model the complex hydrodynamics inside the vessel, the virtual finite element method (POLY3D (TM) software) coupled with a Lagrange multiplier approach to cope with the non-linearity coming from the rheological model was employed. Co-rotation and counter-rotation mode were compared, based on several numerical criteria, namely, mixing time, power consumption and pumping rate. It was found that co-rotating mode is more efficient than counter-rotating mode in terms of energy, pumping rate and homogenization time. (c) 2005 Elsevier Ltd. All rights reserved.