The Driving Force

In the particular case of fluid-borne colloidal particles, a uniform driving force might be exerted by viscous drag, by gravity, or through electrophoresis, magnetophoresis, or thermophoresis. Each of these plays a central role in practical fractionation techniques (8). More generally, analogous results should be expected for such related systems as electrons flowing through a periodically-gated low-mobility two-dimensional electron gas (9), magnetic flux quanta creeping through patterned type-II superconductors (10,11,12) or Josephson junction arrays (13), and atoms migrating across crystal surfaces (14).

In some instances of practical interest, the driving force itself can be modulated by the physical landscape, leading to additional interesting effects (15). These, however, are beyond the scope of the present discussion. Time-dependent driving forces also lead to exciting new phenomena, but are not required for the effects we describe. We consider the simplest case, where the driving force $\vec{F}_0$ is both uniform and constant and is oriented at a fixed angle $\theta$ with respect to the landscape symmetry axis, here denoted $\hat x$.

In the absence of other influences, particles would travel along the driving direction while dispersing diffusively in the transverse direction. Differential dispersion by transverse diffusion has proved useful for continuously fractionating heterogeneous samples across laminar flows in microfluidic channels (16). Adding a modulated substrate opens up new modes of separating particles according to their sizes, and can greatly improve the resolution of such separations.