In this article, we study numerically the dispersion of colloids in a two-dimensional cellular flow in the presence of an imposed mean salt gradient. Owing to the additional scalar, the colloids do not follow exactly the Eulerian flow field, but have a (small) extra-velocity proportional to the salt gradient,
$\boldsymbol {v}_{dp}=\alpha \boldsymbol {\nabla } S$, where
$\alpha$ is the phoretic constant and
$S$ the salt concentration. We study the demixing of an homogenous distribution of colloids and how their long-term mean velocity
$\boldsymbol {V_m}$ and effective diffusivity
$D_{eff}$ are influenced by the phoretic drift. We observe two regimes of colloids dynamics depending on a blockage criterion
$R=\alpha G L/\sqrt {4 D_cD_s}$, where
$G$ is the mean salt gradient amplitude,
$L$ the length scale of the flow and
$D_c$ and
$D_s$ the molecular diffusivities of colloids and salt. When
$R<1$, the mean velocity is strongly enhanced with
$V_m \propto \alpha G \sqrt {Pe_s}$,
${Pe}_s$ being the salt Péclet number. When
$R > 1$, the compressibility effect due to the phoretic drift is so strong that a depletion of colloids occurs along the separatrices inhibiting cell-to-cell transport.