Drift without flux: Brownian walker with a space dependent diffusion   coefficient
  Space dependent diffusion of micrometer sized particles has been directly observed using digital video microscopy. The particles were trapped between two nearly parallel walls making their confinement position dependent. Consequently, not only did we measure a diffusion coefficient which depended on the particles' position, but also report and explain a new effect: a drift of the particles' individual positions in the direction of the diffusion coefficient gradient, in the absence of any external force or concentration gradient. 
P. Lancon, G. Batrouni, L. Lobry and N. Ostrowsky