  A wide variety of tilted washboard potentials based on acoustic waves,
electric fields, optical patterns and so on have been applied to sort particles
in microchannels. In this paper, we present a theoretical analysis of the
particles trajectory in a washboard potential making a tilt angle $\theta$ with
the flow. Depending on the sorting to drag force ratio $\epsilon$, we
identified a transition threshold $\epsilon = \cos(\theta)$ between two
distinct regimes of particles motion: drift and locked modes. In drift mode,
the particles follow an oscillating trajectory which slope is given by
$\frac{\epsilon^2}{2}\tan(\theta)$, while in locked mode the trajectory slope
is given by $1/\tan(\theta)$. These theoretical predictions agree
quantitatively well with previously published experimental data and may help in
the design of high-performance microfluidic sorting devices.
