Computational fluid dynamics (CFD) is very appealing to investigate mixing and reaction in microdevices, as it allows easily investigating different operating conditions as well as mixer geometries. This latter aspect is very important as the flow in microdevices is laminar so the mixing between reactants should be promoted by a clever mixer design, aimed at breaking the flow symmetries. Recently time periodic motions that improve mixing have been observed to take place in a T-junction at low Reynolds numbers. In this case the numerical modelling should be based on direct numerical simulations (DNS), thus involving high computational resources. In this work, two different CFD approaches, i.e., finite volume and spectral element methods, are applied and compared for the analysis of the mixing process in the well known T-shaped micromixer. Spectral elements methods are particularly suited for DNS; however, they have been scarcely applied to study micromixers, while plenty of works can be found with finite volume methods. The analysis is carried out using both ideal and non-ideal liquid binary mixtures, the latter presenting a negative fluidity of mixing (i.e., the viscosity of the mixture is higher than that of the pure components). Moreover the numerical results are validated with simple flow visualization experiments.