Osmotic traps for colloids and macromolecules based on logarithmic sensing in salt taxis

Diffusiophoretic motion of colloids and macromolecules under salt gradients exhibits a logarithmic-sensing, i.e. the particle velocity is proportional to the spatial gradient of the logarithm of the salt concentration, as V_DP = D_DP∇logc. Here we explore experimentally the implications of this log-sensing behavior, on the basis of a hydrogel microfluidic device allowing to build spatially and temporally controlled gradients. We first demonstrate that the non-linearity of the salt-taxis leads to a trapping of particles under concentration gradient oscillations via a rectification of the motion. As an alternative, we make use of the high sensitivity of diffusiophoretic migration to vanishing salt concentration due to the log-sensing: in a counter-intuitive way, a vanishing gradient can lead to measurable velocity provided that the solute concentration is low enough, thus keeping ∇c/c finite. We show that this leads to a strong segregation of particles in osmotic shock configuration, resulting from a step change of the salt concentration at the boundaries. These various phenomena are rationalized on the basis of a theoretical description for the time-dependent Smoluchowski equation for the colloidal density.