  Colloidal particles of two types, driven in opposite directions, can
segregate into lanes [Vissers et al. Soft Matter 7, 2352 (2011)]. This
phenomenon can be reproduced by two-dimensional Brownian dynamics simulations
of model particles [Dzubiella et al. Phys. Rev. E 65, 021402 (2002)]. Here we
use computer simulation to assess the generality of lane formation with respect
to variation of particle type and dynamical protocol. We find that laning
results from rectification of diffusion on the scale of a particle diameter:
oppositely-driven particles must, in the time taken to encounter each other in
the direction of the drive, diffuse in the perpendicular direction by about one
particle diameter. This geometric constraint implies that the diffusion
constant of a particle, in the presence of those of the opposite type, grows
approximately linearly with Peclet number, a prediction confirmed by our
numerics over a range of model parameters. Such environment-dependent diffusion
is statistically similar to an effective interparticle attraction; consistent
with this observation, we find that oppositely-driven non-attractive colloids
display features characteristic of the simplest model system possessing both
interparticle attractions and persistent motion, the driven Ising lattice gas
[Katz, Leibowitz, Spohn, J. Stat. Phys. 34, 497 (1984)]. These features include
long-ranged correlations in the disordered regime, and a critical regime
characterized by a change in slope of the particle current with Peclet number
and by fluctuations that grow with system size. By analogy, we suggest that
lane formation in the driven colloid system is in the macroscopic limit a phase
transition, but that macroscopic phase separation would not occur in finite
time upon starting from disordered initial conditions.
