  We investigate a real 3D stationary flow characterized by chaotic advection
generated by a magnetic field created by permanent magnets acting on a weakly
conductive fluid subjected to a weak constant current. The model under
consideration involves the Stokes equations for viscous incompressible fluid at
low Reynolds number in which the density forces correspond to the Lorentz force
generated by the magnetic field of the magnets and the electric current through
the fluid. An innovative numerical approach based on a mixed finite element
method has been developed and implemented for computing the flow velocity
fields with the electromagnetic force. This ensures highly accurate numerical
results, allowing a detailed analysis of the chaotic behavior of fluid
trajectories through the computations of associated Poincar\'e sections and
Lyapunov exponents. Subsequently, an examination of mixing efficiency is
conducted, employing computations of contamination and homogeneity rates, as
well as mixing time. The obtained results underscore the relevance of the
modeling and computational tools employed, as well as the design of the
magnetohydrodynamic device used.
