Osmotic traps for colloids and macromolecules based on logarithmic sensing in salt taxis† J er emie Palacci,‡ * C ecile Cottin-Bizonne, Christophe Ybert and Lyd eric Bocquet Received 21st July 2011, Accepted 23rd September 2011 DOI: 10.1039/c1sm06395b 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 ¼ D DP Vlogc. 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 Vc/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. At equilibrium, small particles like colloids and macromolecules are subjected to thermal Brownian motion, leading to an unavoidable diffusive exploration of their spatial environment. On the other hand, it is possible to overcome Brownian motion and induce directed motion of colloids under the application of gradients of thermodynamic variables. Classical examples involve electro-phoresis—transport under an applied electric field—, thermophoresis—transport under a temperature gradient—, and diffusiophoresis—transport under a solute gradient—, as well as variations of these phenomena, such as dielectrophoresis 1 or induced charge electrophoresis. 2 These phenomena have been extensively studied over the years, but new opportunities were offered by recent experimental developments in microfluidic technologies, which have led to some important progress in their understanding and allowed to explore novel applications. 3–12,14–16 In particular phoretic transport provides interesting tools to manipulate colloidal populations, proposing new ways to separate, concentrate or screen particles. 6,10,12,14,15 In this paper, we focus on the formation of patterns of colloidal population, which originate in the non-linear behavior of diffusiophoretic (DP) transport. Diffusiophoresis is the osmotically induced motion of particles—colloids or macro- molecules—under a gradient of solute, here salts. We show that under certain conditions, this phoretic directed motion may be used to create osmotic colloidal traps of various geometries, thereby overcoming Brownian motion to confine the particles. We will follow two different strategies, both of which rely upon the non-linearities of DP motion as a function of salt concen- tration: (i) traps created by the rectification of time-dependent salt gradients; (ii) traps created by an ‘osmotic’ shock resulting from a step change of the salt concentration at the boundaries. Diffusiophoresis is an interfacially driven transport phenom- enon. It results from an unbalanced osmotic pressure gradient occurring within the diffuse layer in the close vicinity of the solid (typically of the order of a few nanometres), this interface thereby playing the role of the semi-permeable membrane in classical osmosis. 17 This induces an interfacial flow along the surface leading to the motion of the colloidal particle in the surrounding medium. 1,18–20 While this mechanism has been known for some time, 1 it was recently re-investigated experi- mentally, by using the benefits of microfluidics technology to study the diffusiophoretic migration of particles in well-defined solute gradients. 3,11,12 In ref. 3,12, diffusiophoresis under small salt contrasts was e.g. shown to boost a diffusive-like migration of colloidal particles in a co-flow geometry. For salts as a solute, the DP velocity of particles is expected to exhibit a log-sensing migration, in the form: V DP ¼ D DP Vlogc. (1) This log dependence originates in the specific electrostatic interaction between the ionic salt solute and the charged surface. 1,3 Such a behavior was shown to be in quantitative LPMCN, Universit e de Lyon, Universit e Lyon 1 and CNRS, UMR5586 † Electronic supplementary information (ESI) available. See DOI: 10.1039/c1sm06395b ‡ Present address: CSMR, Department of Physics, New York University, 4 Washington Place, New York, New York 10003, USA 980 | Soft Matter , 2012, 8, 980–994 This journal is ª The Royal Society of Chemistry 2012 Dynamic Article Links C < Soft Matter Cite this: Soft Matter , 2012, 8, 980 www.rsc.org/softmatter PAPER Downloaded by Ecole Normale Superieure de Lyon on 03 January 2012 Published on 16 November 2011 on http://pubs.rsc.org | doi:10.1039/C1SM06395B View Online / Journal Homepage / Table of Contents for this issue