Surface potentials of conductors in electrolyte solutions.

When we place conducting bodies in electrolyte solutions, their surface potential Φs appears to be much smaller in magnitude than the applied one Φ0 and normally does not obey the classical electrostatic boundary condition of a constant potential expected for conductors. In this paper, we demonstrate that an explanation of these observations can be obtained by postulating that diffuse ions condense at the "wall" due to the reduced permittivity of a solvent. For small values of Φ0, the surface potential responds linearly.

Enhanced transport of ions by tuning surface properties of the nanochannel.

Motivated by recent observations of anomalously large deviations of the conductivity currents in confined systems from the bulk behavior, we revisit the theory of ion transport in parallel-plate channels and also discuss how the wettability of a solid and the mobility of adsorbed surface charges impact the transport of ions. It is shown that depending on the ratio of the electrostatic disjoining pressure to the excess osmotic pressure at the walls two different regimes occur. In the thick channel regime this ratio is small and the channel effectively behaves as thick, even when the diffuse layers strongly overlap.

Electro-osmotic flow in hydrophobic nanochannels.

Hydrophobic surfaces with large slip lengths have the potential to enhance electro-osmotic flows. Existing theories of electroosmosis in hydrophobic channels postulate immobile surface charges and/or make a number of simplifying assumptions by considering mostly weakly charged surfaces and thin diffuse layers compared to channel dimension. In this paper, we extend prior models by focusing on planar and cylindrical nanochannels.

Advective superdiffusion in superhydrophobic microchannels.

We consider pressure-driven flows in wide microchannels, and discuss how a transverse shear, generated by misaligned superhydrophobic walls, impacts cross-sectional spreading of Brownian particles. We show that such a transverse shear can induce an advective superdiffusion, which strongly enhances dispersion of particles compared to a normal diffusion, and that maximal cross-sectional spreading corresponds to a crossover between its subballistic and superballistic regimes. This allows us to argue that an advective superdiffusion can be used for boosting dispersion of particles at smaller Péclet numbers compared to known concepts of passive microfluidic mixing.

Principles of transverse flow fractionation of microparticles in superhydrophobic channels.

We propose a concept of fractionation of micron-sized particles in a microfluidic device with a bottom wall decorated by superhydrophobic stripes. The stripes are oriented at an angle α to the direction of a driving force, G, which generally includes an applied pressure gradient and gravity. Separation relies on the initial sedimentation of particles under gravity in the main forward flow, and their subsequent lateral deflection near a superhydrophobic wall due to generation of a secondary flow transverse to G.

Flows and mixing in channels with misaligned superhydrophobic walls.

Aligned superhydrophobic surfaces with the same texture orientation reduce drag in the channel and generate secondary flows transverse to the direction of the applied pressure gradient. Here we show that a transverse shear can be easily generated by using superhydrophobic channels with misaligned textured surfaces. We propose a general theoretical approach to quantify this transverse flow by introducing the concept of an effective shear tensor.

Lattice-Boltzmann simulations of the drag force on a sphere approaching a superhydrophobic striped plane.

By means of lattice-Boltzmann simulations the drag force on a sphere of radius R approaching a superhydrophobic striped wall has been investigated as a function of arbitrary separation h. Superhydrophobic (perfect-slip vs. no-slip) stripes are characterized by a texture period L and a fraction of the gas area ϕ.

Gas cushion model and hydrodynamic boundary conditions for superhydrophobic textures.

Superhydrophobic Cassie textures with trapped gas bubbles reduce drag, by generating large effective slip, which is important for a variety of applications that involve a manipulation of liquids at the small scale. Here we discuss how the dissipation in the gas phase of textures modifies their friction properties. We propose an operator method, which allows us to map the flow in the gas subphase to a local slip boundary condition at the liquid-gas interface.

Effective slippage on superhydrophobic trapezoidal grooves.

We study the effective slippage on superhydrophobic grooves with trapezoidal cross-sections of various geometries (including the limiting cases of triangles and rectangular stripes), by using two complementary approaches. First, dissipative particle dynamics (DPD) simulations of a flow past such surfaces have been performed to validate an expression [E. S.

Effective slip-length tensor for a flow over weakly slipping stripes.

We discuss the flow past a flat heterogeneous solid surface decorated by slipping stripes. The spatially varying slip length, b(y), is assumed to be small compared to the scale of the heterogeneities, L, but finite. For such weakly slipping surfaces, earlier analyses have predicted that the effective slip length is simply given by the surface-averaged slip length, which implies that the effective slip-length tensor becomes isotropic.

Flow past superhydrophobic surfaces with cosine variation in local slip length.

Anisotropic superhydrophobic surfaces have the potential to greatly reduce drag and enhance mixing phenomena in microfluidic devices. Recent work has focused mostly on cases of superhydrophobic stripes. Here, we analyze a relevant situation of cosine variation of the local slip length.

Effective hydrodynamic boundary conditions for microtextured surfaces.

Understanding the influence of topographic heterogeneities on liquid flows has become an important issue with the development of microfluidic systems, and more generally for the manipulation of liquids at the small scale. Most studies of the boundary flow past such surfaces have concerned poorly wetting liquids for which the topography acts to generate superhydrophobic slip. Here we focus on topographically patterned but chemically homogeneous surfaces, and measure a drag force on a sphere approaching a plane decorated with lyophilic microscopic grooves.

Drag force on a sphere moving toward an anisotropic superhydrophobic plane.

We analyze theoretically a high-speed drainage of liquid films squeezed between a hydrophilic sphere and a textured superhydrophobic plane that contains trapped gas bubbles. A superhydrophobic wall is characterized by parameters L (texture characteristic length), b1 and b2 (local slip lengths at solid and gas areas), and φ1 and φ2 (fractions of solid and gas areas). Hydrodynamic properties of the plane are fully expressed in terms of the effective slip-length tensor with eigenvalues that depend on texture parameters and H (local separation).

Shear-induced self-diffusion in a wall-bounded dilute suspension.

Random migrations of non-Brownian neutrally buoyant particles in the flow of a dilute suspension in a periodic Couette cell is simulated on the basis of a dipole model. A diffusivity is due to far-field collective hydrodynamic interactions. Large-scale fluctuations of particle concentration induce fluid velocity disturbances with a length scale comparable to the cell size.

Fluctuating interface in a dilute sedimenting suspension.

The evolution of large-scale fluctuations in a monodisperse dilute suspension sedimenting in a wall-bounded container is considered on the basis of a continuum model. The case when the velocity fluctuations are comparable with the Stokes settling velocity is studied. Small deformations of the sedimentation front is replaced by a flat interface with a surface force distribution.