  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 is investigated by means of macrotransport
theory. Analytical expressions for the probability distribution and the average
migration angle of the particles are obtained under the Fick-Jackobs
approximation. The migration angle is shown to differ from the orientation
angle of the driving field and to strongly depend on the physical properties of
the suspended species, thus providing the basis for vector chormatography, 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. The feasibility to
separate different particles of the same and different size is shown for
systems in which partition is induced via 1g-gravity and Van der Waals
interactions in physically and chemically patterned channels, respectively.
