Mixing and chaotic advection are studied in a liquid electrolyte set in motion by an electrical current passing through the fluid which is perpendicular to a magnetic field (Laplace force). Since the characteristic length in this system is very small, the inertia terms are negligible and the fluid motion is governed by the Stokes equations. Chaotic advection can occur in this flow if the potential between two electrodes is modulated time-periodically. Two tools have been implemented to characterize mixing in this flow. Poincare sections are plotted in order to distinguish between regular and chaotic regions and the advection of a blob of dye injected into the liquid is calculated and successfully compared to experiments. This very small device is shown to be an effective fluid mixer.