When a monolayer of Lennard-Jones atoms is driven by an external force over an atomically spaced lattice, the atoms do not move in the direction of the force. By considering monolayers containing a solvent and two different solutes, we show that the different atomic species follow distinct directions and so partition from one another and from the solvent. The strength of the driving force is chosen so that at any instant, most atoms are stationary while only a small fraction propagates as solitary waves. In this regime, the mean velocity of the layer is due to the nonzero contribution from merely a few atoms. We also present a simple theory, based on the probability that an atom in the monolayer will hop from one equilibrium location to the next, that explains the distinct directions of atomic migration.