Phoresis in cellular flows: from enhanced dispersion to blockage

Abstract

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, ${\mathbf{v}}_{\mathrm{dp}}=\alpha \nabla S$, 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 ${\mathbf{V}}_{\mathbf{m}}$ and effective diffusivity $D_{\mathrm{eff}}$ are influenced by the phoretic drift. We observe two regimes of colloids dynamics depending on a blockage criterion $R=\alpha GL/\sqrt{4D_c{D}_s}$, 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 $V_m\propto \alpha G\sqrt{P{e}_s}$, $P{e}_s$ 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.

References in corpus (2)

• Chaotic mixing in effective compressible flows
• On the terminal velocity of sedimenting particles in a flowing fluid