Phoresis in cellular flows: from enhanced dispersion to blockage

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, vdp=α ∇ S , where α 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 Vₘ and effective diffusivity Deff are influenced by the phoretic drift. We observe two regimes of colloids dynamics depending on a blockage criterion R=α G L/√4 DcDₛ , where G is the mean salt gradient amplitude, L the length scale of the flow and Dc and Dₛ the molecular diffusivities of colloids and salt. When $R<1$ , the mean velocity is strongly enhanced with Vₘ ∝ α G √Peₛ , Peₛ 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.