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• DC-induced transversal electroosmotic flow is super-imposed to pressure-driven axial flow. • Lagrangian chaos is created by periodically alternate electrode placement. • The convection enhanced branch of HETP curve is flattened as the degree of chaoticity increases. • Peclet-independent HETP at large flowrates is approached in globally chaotic conditions. Taylor-Aris dispersion represents an undesired phenomenon in pressure-driven liquid chromatography, often responsible for the unchecked increase of the Height Equivalent of the Theoretical Plate (HETP) when high throughput operating conditions are sought. Previous work on the subject showed how it is possible to contain the augmented dispersion in empty microchannels by inducing cross-sectional velocity components yielding an overall helical structure of the flow streamlines. Here, we explore the possibility of further reducing axial dispersion by devising flow conditions that give rise to chaotic streamlines. A three-dimensional steady flow generated by the combination of a pressure-driven Poiseuille flow and an electroosmotically-induced spatially periodic flow is used as a case study. Brenner's macrotransport approach is used to predict the axial dispersion coefficient of a diffusing solute in flows possessing regular, partially chaotic and globally chaotic kinematic features. Accurate Lagrangian-stochastic simulations of particle ensembles are used to validate the predictions obtained through Brenner's paradigm. Our findings suggest that the Taylor-Aris phenomenon can be altogether suppressed in the limit of globally chaotic kinematics. A theoretical interpretation of this outcome is developed by combining macrotransport theory with established results of the spectral approach to mixing in advecting-diffusing chaotic flows. [ABSTRACT FROM AUTHOR]