Enhancement of heat and/or mass transfer via turbulence is often not feasible for highly viscous, non-Newtonian or shear sensitive fluids. One alternative to improve transport within such materials is chaotic advection, whereby Lagrangian chaos occurs within regular (non-turbulent) flows [J.M. Ottino, The Kinematics of Mixing: Stretching, Chaos and Transport, Cambridge University Press, Cambridge, 1989]. Complex interactions between chaotic advection and diffusion yields enhanced dispersion, and the topology of the Lagrangian dynamics is governed by the set of control parameters for the flow device. What parameter set maximises scalar dispersion for a given fluid rheology and diffusivity? Most studies to date have only considered a handful of points in the parameter space (sic), but as this space may be large and the solution distribution complex (fractal), robust optimisation requires detailed global resolution of (sic). By utilising a novel spectral method [D.R. Lester, G. Metcalfe, M. Rudman, H. Blackburn, Global parametric solutions of scalar transport, J. Comput. Phys. (2007). doi: doi: 10.1016/j.jcp.2007.10.015] which exploits the symmetries often present in chaotic flows, we can resolve the asymptotic transport dynamics over (sic), facilitating the identification of optima and elucidating the global structure of transport. We employ this method to optimize scalar transport for both Newtonian and non-Newtonian fluids in a chaotic mixing device, the Rotated Arc Mixer (RAM). Significant (up to sixfold) acceleration of scalar transfer is observed at Peclet number Pe = 10(3), which furthermore increases with Pe. Crown copyright (C) 2008 Published by Elsevier Ltd. All rights reserved.