Partition-induced vector chromatography in microfluidic devices

We investigate by means of macrotransport theory the transport of Brownian particles in a slit geometry in the presence of an arbitrary two-dimensional periodic energy landscape and driven by an external force or convected by a flow field. We obtained analytical expressions for the probability distribution and the average migration angle of the particles under the Fick-Jacobs approximation. The migration angle is shown to differ from the angle of the driving field and to strongly depend on the physical properties of the suspended species, thus providing the basis for vector chromatography, in which different species move in different directions and can be continuously fractionated. The potential of microfluidic devices as a platform for partition-induced vector chromatography is demonstrated by considering the particular case of a piece-wise constant, periodic potential that, in equilibrium, induces the spontaneous partition of different species into high and low concentration stripes, and which can be easily fabricated by patterning physically or chemically one of the surfaces of a channel. We show the feasibility to fractionate a mixture of particles for systems in which partition is induced via 1-g gravity and Van der Waals interactions in physically or chemically patterned channels.