(221d) Diffusiophoretic Spreading Under Localized, Transient Solute Gradients: From Trapping to Super-Diffusion

Diffusiophoresis refers to the deterministic drift of one species induced by a concentration gradient of another species; recent microfluidic experiments have focused on the diffusiophoresis of micron-scale colloids in gradients of small ionic solutes. A solute concentration gradient results in a diffusiophoretic colloid velocity u_d = M∇logS, where M and S are the diffusiophoretic mobility and solute concentration, respectively. Here, we study the diffusiophoretic transport of an initially Gaussian distribution of colloids in an initially Gaussian distribution of solute. We derive an exact solution for spatio-temporal evolution of the colloidal distribution, which does not follow a Gaussian in general. While the centroid of the colloidal distribution remains stationary, its distribution depends critically on the ratio of the diffusiophoretic mobility to solute diffusivity, M/D_s. When M/D_s ≫ 1, diffusiophoresis drives colloids up the solute gradient. Thus, the strong diffusiophoresis inhibits the diffusive spread of colloids such that there is a sizable period of time over which the colloids are fixed temporally, suggesting a novel mechanism for particle trapping. When -1 ≤ M/D_s = O(1), the interference to the diffusive broadening of colloids by diffusiophoresis is negligible. When M/D_s < -1 the down-solute-gradient diffusiophoresis leads to super-diffusion of colloids at long times, with the peak of the colloid distribution decaying as t^M/2Ds. We discuss the generality of this three-class evolution in the context of different initial solute and colloid distributions, relevant to applications such as synthetic nano-motors, oil recovery, and sorting of biochemical species.