Diffusiophoresis in Ionic Surfactant Gradients.

Surfactants play a ubiquitous role in many areas of science and technology, and gradients often form-either spontaneously or intentionally-in a variety of nonequilibrium situations and processes. We visualize and measure the diffusiophoretic migration of latex colloids in response to gradients of cationic and anionic surfactants, both below and above the critical micelle concentration (cmc). Below the cmc, colloidal migration can be described using classic theories for diffusiophoresis under electrolyte gradients, although subtleties and distinctions do appear. Cationic surfactants adsorb onto anionic colloids, changing the surface charge and thus reversing the direction of diffusiophoretic migration. Above the cmc, diffusiophoretic mobilties decrease by orders of magnitude. We argue this to occur because charged monomers (rather than micelles) dominate colloidal diffusiophoresis. Because monomer concentrations remain essentially constant above the cmc, surfactant gradients imposed above the cmc result in very small monomer gradients-and, therefore, very weak diffusiophoresis. Our findings suggest conceptual strategies to understand diffusiophoresis in the presence of surfactants, as well as strategies to predict and design systems that harness them.

Diffusiophoretic Focusing of Suspended Colloids.

Using a microfluidic system to impose and maintain controlled, steady-state multicomponent pH and electrolyte gradients, we present systems where the diffusiophoretic migration of suspended colloids leads them to focus at a particular position, even in steady-state gradients. We show that naively superpositing effects of each gradient may seem conceptually and qualitatively reasonable, yet is invalid due to the coupled transport of these multicomponent electrolytes. In fact, reformulating the classic theories in terms of the flux of each species (rather than local gradients) reveals rather stringent conditions that are necessary for diffusiophoretic focusing in steady gradients. Either particle surface properties must change as a function of local composition in solution (akin to isoelectric focusing in electrophoresis), or chemical reactions must occur between electrolyte species, for such focusing to be possible. The generality of these findings provides a conceptual picture for understanding, predicting, or designing diffusiophoretic systems.

Direct Measurements of Colloidal Solvophoresis under Imposed Solvent and Solute Gradients.

We describe a microfluidic system that enables direct visualization and measurement of diffusiophoretic migration of colloids in response to imposed solution gradients. Such measurements have proven difficult or impossible in macroscopic systems due to difficulties in establishing solution gradients that are sufficiently strong yet hydrodynamically stable. We validate the system with measurements of the concentration-dependent diffusiophoretic mobility of polystyrene colloids in NaCl gradients, confirming that diffusiophoretic migration velocities are proportional to gradients in the logarithm of electrolyte concentration. We then perform the first direct measurement of the concentration-dependent "solvophoretic" mobility of colloids in ethanol-water gradients, whose dependence on concentration and gradient strength was not known either theoretically or experimentally, but which our measurements reveal to be proportional to the gradient in the logarithm of ethanol mole fraction. Finally, we examine solvophoretic migration under a variety of qualitatively distinct chemical gradients, including solvents that are miscible or have finite solubility with water, an electrolyte for which diffusiophoresis proceeds down concentration gradients (unlike for most electrolytes), and a nonelectrolyte (sugar). Our technique enables the direct characterization of diffusiophoretic mobilities of various colloids under various solvent and solute gradients, analogous to the electrophoretic ζ-potential measurements that are routinely used to characterize suspensions. We anticipate that such measurements will provide the feedback required to test and develop theories for solvophoretic and diffusiophoretic migration and ultimately to the conceptual design and engineering of particles that respond in a desired way to their chemical environments.