a chucker with a constant force in our MC simulations, we find that indeed this system violates the FDT strongly, in a highly nontrivial way. The complex relationship between mobility and diffusion in this system is due to an interplay between crowding and osmotic effects which depends sensitively on the applied force and chucking rate. Finally, we have studied the behaviour of a chucker which sediments onto a planar surface which either absorbs the solute particles or behaves as a hard wall. When the surface is absorbing, a solute-mediated effective attraction (which increases with increasing k$_{c}$ ) pushes the chucker towards the surface. However, when we consider a hard surface, a solute- mediated effective repulsion exists. For small k$_{c}$ this simply results in a decrease in the gradient of the chucker probability density profile near the surface. For large k$_{c}$ , the repulsive interaction dominates the gravitational force near the surface, resulting in a peak in the probability density for the chucker position at some distance from the surface. This work was motivated by recent experimental, theoretical and simulation work on colloidal “swimmers” which catalyse a chemical reaction, or secrete some product, anisotrop- ically across their surface [8–15], by recent theoretical work on isotropic chuckers [11] and by the biological example of exopolysaccharide-secreting bacteria [16, 17]. However, the physical mechanisms explored here also have wider relevance in soft matter physics. As an example, Jiang et al [39] recently reported a system where migration of colloidal particles was mediated by inhomogeneities in polymer concentration, which were in turn induced by a temperature gradient. Dynamic depletion interactions between colloidal particles, in which one of the components of a phase separating binary fluid wets the colloid surface (creating a local depletion near the colloid), predicted in simulations by Araki and Tanaka [40], are also closely related to the phenomena studied here. We hope that the results reported here will make a useful contribution to ongoing dis- cussions concerning the effects of osmotic gradients on colloidal dynamics, as well as link- ing these discussions to the physics of biological systems (particularly exopolysaccharide- producing bacteria) and other nonequilibrium soft matter systems. Acknowledgements: We thank M. E. Cates, O. Croze, G. Dorken, G. Ferguson, D. Frenkel, W. C. K. Poon, E. Sanz, P. Visco and L. Wilson for discussions and advice, and the referee for comments that have significantly improved the paper. This work was supported by EPSRC under grant EP/E030173/1. CV acknowledges support from a Marie Curie Fellowship. RJA was funded by the Royal Society of Edinburgh and by the Royal Society. This work has 18