Spectral characterization of mixing properties of annular MHD micromixers

We develop a quantitative analysis of mixing regimes in an annular MHD-driven micromixer recently proposed by Gleeson et al. as a prototype for biomolecular applications. The analysis is based on the spectral properties of the advection-diffusion operator, with specific focus on the dependence of the dominant eigenvalue-eigenfunction on the Peclet number and on the system geometry. A theoretical prediction for the dominant eigenvalue encompassing all mixing regimes is developed and validated by comparison with numerical simulations. The theoretical prediction is extended to an open inflow-outflow version of the reactor, which shows the occurrence of new regimes associated with the existence of a nonuniform axial flow.