Giant amplification of interfacially driven transport by hydrodynamic slip: diffusio-osmosis and beyond

Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions

The venerable theory of electrokinetic phenomena rests on the hypothesis of a dilute solution of point-like ions in quasi-equilibrium with a weakly charged surface, whose potential relative to the bulk is of order the thermal voltage (kT/e approximately 25 mV at room temperature). In nonlinear electrokinetic phenomena, such as AC or induced-charge electro-osmosis (ACEO, ICEO) and induced-charge electrophoresis (ICEP), several V approximately 100 kT/e are applied to polarizable surfaces in microscopic geometries, and the resulting electric fields and induced surface charges are large enough to violate the assumptions of the classical theory. In this article, we review the experimental and theoretical literatures, highlight discrepancies between theory and experiment, introduce possible modifications of the theory, and analyze their consequences. We argue that, in response to a large applied voltage, the "compact layer" and "shear plane" effectively advance into the liquid, due to the crowding of counterions. Using simple continuum models, we predict two general trends at large voltages: (i) ionic crowding against a blocking surface expands the diffuse double layer and thus decreases its differential capacitance, and (ii) a charge-induced viscosity increase near the surface reduces the electro-osmotic mobility; each trend is enhanced by dielectric saturation. The first effect is able to predict high-frequency flow reversal in ACEO pumps, while the second may explain the decay of ICEO flow with increasing salt concentration. Through several colloidal examples, such as ICEP of an uncharged metal sphere in an asymmetric electrolyte, we show that nonlinear electrokinetic phenomena are generally ion-specific. Similar theoretical issues arise in nanofluidics (due to confinement) and ionic liquids (due to the lack of solvent), so the paper concludes with a general framework of modified electrokinetic equations for finite-sized ions.

Principles and applications of nanofluidic transport

The evolution from microfluidic to nanofluidic systems has been accompanied by the emergence of new fluid phenomena and the potential for new nanofluidic devices. This review provides an introduction to the theory of nanofluidic transport, focusing on the various forces that influence the movement of both solvents and solutes through nanochannels, and reviews the applications of nanofluidic devices in separation science and energy conversion.

Manipulation of colloids by a nonequilibrium depletion force in a temperature gradient

The nonequilibrium distribution of colloids in a polymer solution under a temperature gradient is studied experimentally. A slight increase of local temperature by a focused laser drives the colloids towards the hot region, resulting in the trapping of the colloids irrespective of their own thermophoretic properties. An amplification of the trapped colloid density with the polymer concentration is measured, and is quantitatively explained by hydrodynamic theory. The origin of the attraction is a migration of colloids driven by a nonuniform polymer distribution sustained by the polymer's thermophoresis. These results show how to control the thermophoretic properties of colloids.

Thermophoresis at a charged surface: the role of hydrodynamic slip

By matching boundary layer hydrodynamics with slippage to the force-free flow at larger distances, we obtain the thermophoretic mobility of charged particles as a function of the Navier slip length b. A moderate value of b augments Ruckenstein's result by a term 2b/λ, where λ is the Debye length. If b exceeds the particle size a, the enhancement coefficient a/λ is independent of b but proportional to the particle size. Similar effects occur for transport driven by a salinity gradient or by an electric field.

Effective slip over superhydrophobic surfaces in thin channels

Superhydrophobic surfaces reduce drag by combining hydrophobicity and roughness to trap gas bubbles in a microscopic texture. Recent work has focused on specific cases, such as arrays of pillars or grooves, with limited theoretical guidance. Here, we consider the experimentally relevant limit of thin channels and obtain rigorous bounds on the effective slip length for any two-component (e.g., low-slip and high-slip) texture with given area fractions. Among all anisotropic textures, parallel stripes attain the largest (or smallest) possible slip in a straight, thin channel for parallel (or perpendicular) orientation with respect to the mean flow. Tighter bounds for isotropic textures further constrain the effective slip. These results provide a framework for the rational design of superhydrophobic surfaces.

Boosting migration of large particles by solute contrasts

Brownian diffusion is a keystone concept in a large variety of domains, from physics, chemistry to biology. Diffusive transport controls situations as diverse as reaction-diffusion processes in biology and chemistry, Brownian ratchet processes, dispersion in microfluidic devices or even double-diffusive instability and salt-fingering phenomena in the context of ocean mixing. Although these examples span a broad range of length scales, diffusive transport becomes increasingly inefficient for larger particles. Applications, for example, in microfluidics, usually have recourse to alternative driving methods involving external sources to induce and control migration. Here, we demonstrate experimentally a strongly enhanced migration of large particles, achieved by slaving their dynamics to that of a fast carrier species, a dilute salt. The underlying fast salt diffusion leads to an apparent diffusive-like dynamics of the large particles, which is up to two orders of magnitude faster than their natural 'bare' diffusion. Moreover both spreading and focusing of the particle assembly can be achieved on demand. A model description shows a remarkable quantitative agreement with all measured data. Applications of this process are illustrated in microfluidics for filtering and concentrating operations, as well as in conjunction with standard hydrodynamic focusing. In a wider perspective, this mechanism can affect a broad range of scales and phenomena, from biological transport to the dispersion of sediments and pollutants in oceanographic situations.

Massive amplification of surface-induced transport at superhydrophobic surfaces

We study electro- and diffusio-osmosis of aqueous electrolytes at superhydrophobic surfaces by means of computer simulation and hydrodynamic theory. We demonstrate that the diffusio-osmotic flow at superhydrophobic surfaces can be amplified by more than 3 orders of magnitude relative to flow in channels with a zero interfacial slip. By contrast, little enhancement is observed at these surfaces for electro-osmotic flow. This amplification for diffusio-osmosis is due to the combined effects of enhanced slip and ion surface depletion or excess at the air-water interfaces on superhydrophobic surfaces. This effect is interpreted in terms of capillary driven Marangoni motion. A practical microfluidic pumping device is sketched on the basis of the slip-enhanced diffusio-osmosis at a superhydrophobic surface.

Slip-enhanced electrokinetic energy conversion in nanofluidic channels

We investigate theoretically the influence of hydrodynamic slip at the surface of a nanofluidic channel on the efficiency with which electrokinetic phenomena can be used to convert hydrostatic energy to electrical power. Slip is introduced by applying the Navier boundary condition to the pressure-driven and the electro-osmotic components of the fluid velocity. A strong enhancement in the efficiency is predicted for increasing slip length due to the resulting decrease in the fluidic impedance and increase in the streaming conductance. These effects are moderated by a decrease in the electrical impedance, which promotes dissipation. The maximum efficiency approaches 100% as the slip length diverges, and a potentially practical 40% efficiency is expected for a moderate 30 nm slip length in a 10 nm high channel. Recently reported slip lengths for carbon nanotube filters suggest that efficiencies above 70% and high power densities might be achieved in a graphitic system.

Does thermophoretic mobility depend on particle size?

Thermophoresis is particle drift induced by a temperature gradient. By measuring the full temperature dependence of this effect for polystyrene latex suspensions, we show that the thermophoretic mobility (or "thermal diffusion coefficient") D(T) is basically independent on particle size, in particular, when the interfacial properties of the colloidal particles are carefully standardized by adsorbing a surfactant layer on the particle surface. Even more, all investigated systems show values of D(T) which are very close to those measured for simple micellar solutions of the adsorbed surfactant. Our findings could be of relevance for downsizing microfluidics to the nanometric range.

Aqueous electrolytes near hydrophobic surfaces: dynamic effects of ion specificity and hydrodynamic slip

We demonstrate, using molecular-dynamics computer simulations, the strong influence of surface wettability on the equilibrium structure of the electrical double layer at solid interfaces and on electrokinetic transport in aqueous electrolytes due to the effects of interfacial ion specificity and hydrodynamic slip. In particular, we show that anomalous electrokinetic effects such as nonzero zeta potentials for uncharged surfaces are general features of electro-osmotic flow in hydrophobic channels for electrolytes with substantial cation/anion size asymmetry, as a result of the stronger attraction of the larger ion to the "vapor-liquid-like" interface induced by a hydrophobic surface. We establish that the simulated velocity profiles obey continuum hydrodynamics on the nanoscopic length scales studied and show that the anomalous flow profiles can be accurately predicted by using a modified Poisson-Boltzmann description for the ion density distributions that incorporates an ion-size-dependent hydrophobic solvation energy as a crucial component. We also demonstrate that, counterintuitively, the flow for a charge-neutral fluid is independent of the solid-fluid friction coefficient.

Nanohydrodynamics: the intrinsic flow boundary condition on smooth surfaces

A dynamic surface force apparatus is used to determine the intrinsic flow boundary condition of two simple liquids, water and dodecane, on various smooth surfaces. We demonstrate the impact of experimental errors and data analysis on the accuracy of slip length determination. In all systems investigated, the dissipation is described by a well-defined boundary condition accounting for a whole range of separation, film thickness, and shear rate. A no-slip boundary condition is found in all wetting situations. On strongly hydrophobic surfaces, water undergoes finite slippage that increases with hydrophobicity. We also compare the relative influence of hydrophobicity and liquid viscosity on boundary flow by using water-glycerol mixtures with similar wetting properties.

Diffusioosmotic flows in slit nanochannels

Diffusioosmotic flows of electrolyte solutions in slit nanochannels with homogeneous surface charges induced by electrolyte concentration gradients in the absence of externally applied pressure gradients and potential differences are investigated theoretically. A continuum mathematical model consisting of the strongly coupled Nernst-Planck equations for the ionic species' concentrations, the Poisson equation for the electric potential in the electrolyte solution, and the Navier-Stokes equations for the flow field is numerically solved simultaneously. The induced diffusioosmotic flow through the nanochannel is computed as functions of the externally imposed concentration gradient, the concentration of the electrolyte solution, and the surface charge density along the walls of the nanochannel. With the externally applied electrolyte concentration gradient, a strongly spatially dependent electric field and pressure gradient are induced within the nanochannel that, in turn, generate a spatially dependent diffusioosmotic flow. The diffusioosmotic flow is opposite to the applied concentration gradient for a relatively low bulk electrolyte concentration. However, the electrolyte solution flows from one end of the nanochannel with a higher electrolyte concentration to the other end with a lower electrolyte concentration when the bulk electrolyte concentration is relatively high. There is an optimal concentration gradient under which the flow rate attains the maximum. The induced flow is enhanced with the increase in the fixed surface charge along the wall of the nanochannel for a relatively low bulk electrolyte concentration.

Catalytically Induced Electrokinetics for Motors and Micropumps

We have explored the role of electrokinetics in the spontaneous motion of platinum-gold nanorods suspended in hydrogen peroxide (H2O2) solutions that may arise from the bimetallic electrochemical decomposition of H2O2. The electrochemical decomposition pathway was confirmed by measuring the steady-state short-circuit current between platinum and gold interdigitated microelectrodes (IMEs) in the presence of H2O2. The resulting ion flux from platinum to gold implies an electric field in the surrounding solution that can be estimated from Ohm's Law. This catalytically generated electric field could in principle bring about electrokinetic effects that scale with the Helmholtz-Smoluchowski equation. Accordingly, we observed a linear relationship between bimetallic rod speed and the resistivity of the bulk solution. Previous observations relating a decrease in speed to an increase in ethanol concentration can be explained in terms of a decrease in current density caused by the presence of ethanol. Furthermore, we found that the catalytically generated electric field in the solution near a Pt/Au IME in the presence of H2O2 is capable of inducing electroosmotic fluid flow that can be switched on and off externally. We demonstrate that the velocity of the fluid flow in the plane of the IME is a function of the electric field, whether catalytically generated or applied from an external current source. Our findings indicate that the motion of PtAu nanorods in H2O2 is primarily due to a catalytically induced electrokinetic phenomenon and that other mechanisms, such as those related to interfacial tension gradients, play at best a minor role.