A new device containing three circular electrodes and where very small quantities of a weakly electrically conductive liquid are propelled and mixed by chaotic advection is designed and constructed. The liquid, a copper sulfate solution, is propelled by the Lorentz body force, i.e., a magnetic field perpendicular to an electrical current. When the potentials of the electrodes are constant and the Lorentz force is small enough so that at the free surface the vertical velocity is practically zero, the flow field exhibits there a saddle point when the three circular electrodes are not in a concentric position. By modulating the electrical potential between the electrodes, the position of the saddle point changes. This slowly varying system is far from integrable and exhibits large-scale chaos, the non-integrability is due to the slow continuous modulation of the position of the saddle stagnation point and the two streamlines stagnating on it. Dye advection experiments are compared successfully to a numerical solution of the 3D equations of motion under these assumptions. We have also defined a potential mixing zone to predict the location of the chaotic region and calculated Poincare sections. These two tools give results which are in excellent agreement, they are used, with others, to adjust the mixing protocol parameters and the geometry in order to improve mixing.