Sorting on periodic surfaces

Particles moving on crystalline surfaces and driven by external forces or flow fields can acquire velocities along directions that deviate from that of the external force. This effect depends upon the characteristics of the particles, most notably particle size or particle index of refraction, and can therefore be (and has been) used to sort different particles. We introduce a simple model for particles subject to thermal fluctuations and moving in appropriate potential landscapes. Numerical results are compared to recent experiments on landscapes produced with holographic optical tweezers and microfabricated technology. Our approach clarifies the relevance of different parameters, the direction and magnitude of the external force, particle size, and temperature.