Size-Specific Transport of Colloidal Particles Using Magnetic Fields

Using computer simulations and experiments, we demonstrate a mechanism for simultaneous size-specific control over the trajectories of isotropic colloidal particles. Magnetic microparticles of different diameters suspended above a periodic magnetic film are driven by loops traced by the orientation of a uniform external magnetic field. The uniform time-dependent magnetic field couples to the inhomogeneous static magnetic field of the pattern, generating a complex energy landscape for the microparticles. The energy landscape varies with height above the pattern, acting on particles of different sizes in distinct ways, as their centers are located at different elevations. At a specific elevation, distinct modulation loops exist that transport the particles to a neighboring unit cell of the pattern. The transport is topologically protected because it is determined only by a set of winding numbers of the modulation loop, which act as topological invariants. The set of winding numbers depends on the elevation, and hence, on the particle size, allowing simultaneous and independent driving of different-sized particles along arbitrarily complex and distinct trajectories.