  Motivated by recent studies of colloidal particles in optical tweezer arrays,
we study a two-dimensional model of a colloidal suspension in a periodic
potential. The particles tend to stay near potential minima, approximating a
lattice gas. The interparticle interaction, a sum of Yukawa terms, features
short-range repulsion and attraction at somewhat larger separations, such that
two particles cannot occupy the same potential well, but occupation of adjacent
cells is energetically favored. Monte Carlo simulation reveals that the
equilibrium system exhibits condensation, as in the Ising model/lattice gas
with conserved magnetization; the transition appears to be continuous at a half
occupancy. We study the effect of biased hopping probabilities favoring motion
along one lattice direction, as might be generated by a steady flow relative to
the potential array. This system is found to exhibit features of the driven
lattice gas: the interface is oriented along the drive, and appears to be
smooth. A weak drive facilitates ordering of the particles into high- and
low-density regions, while stronger bias tends to destroy order, and leads to
very large energy fluctuations. Our results suggest possible realizations of
equilibrium and driven lattice gases in a colloidal suspension subject to an
optical tweezer array.
