The inertial migration of a small rigid sphere translating parallel to the walls within channel flow at large Reynolds numbers is investigated. method matched asymptotic expansions used solve equations governing disturbance past particle number and evaluate lift. Both neutrally non-neutrally buoyant particles are considered. wall-induced inertia significant in thin layers near where lift close that calculated for linear shear flow, bounded by single wall. In major portion excluding near-wall...

In many applications it is advantageous to construct effective slip boundary conditions, which could fully characterize flow over patterned surfaces. Here we focus on laminar shear flows smooth anisotropic surfaces with arbitrary scalar $b(y)$, varying in only one direction. We derive general expressions for eigenvalues of the slip-length tensor, and show that transverse component equal a half longitudinal twice larger local slip, $2b(y)$. A remarkable corollary this relation along any...

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

An analytical theory of electroosmosis in hydrophobic nanochannels large surface potential/charge density incorporates a mobility adsorbed charges and hydrodynamic slip, is valid both for thin strongly overlapping diffuse layers.

At finite Reynolds numbers, $Re$ , particles migrate across laminar flow streamlines to their equilibrium positions in microchannels. This migration is attributed a lift force, and the balance between this gravity determines location of channels. Here we demonstrate that velocity finite-size located near channel wall differs significantly from an undisturbed flow, position depends on this, referred as slip velocity, difference. We then present theoretical arguments, which allow us generalize...

We ascertain the enhanced slip properties for a liquid flow over lubricant-infused unidirectional surfaces. This situation reflects many practical settings involving flows past superhydrophobic grooves filled with gas, or infused another, immiscible, of smaller equal viscosity, i.e., where ratio lubricant and viscosities, $\ensuremath{\mu}\ensuremath{\le}1$. To maximize slippage, we consider deep aligned flow. The (normalized by texture period $L$) effective length, ${b}_{\mathrm{eff}}$, is...

The theory of electrokinetic ion transport in cylindrical channels a fixed surface charge density is revisited. Attention focused on impact the hydrophobic slippage and mobility adsorbed charges. We formulate generalised Onsager relations for cylinder an arbitrary radius then derive exact expressions mean electro-osmotic conductivity. To employ these we perform additional electrostatic calculations, with special focus non-linear effects. Our provides simple explanation giant enhancement...

Catalytic Janus swimmers demonstrate a diffusiophoretic motion by self-generating the gradients of concentrations and electric potential. Recent work has focused on simplified cases, such as release solely one type ions or low surface fluxes ions, with limited theoretical guidance. Here, we consider experimentally relevant case particles that both types obtain simple expression for particle velocity in limit thin electrostatic diffuse layer. Our approximate is very accurate even when ion...

We analyze theoretically a high-speed drainage of liquid films squeezed between hydrophilic sphere and textured superhydrophobic plane that contains trapped gas bubbles. A wall is characterized by parameters $L$ (texture characteristic length), ${b}_{1}$ ${b}_{2}$ (local slip lengths at solid areas), ${\ensuremath{\varphi}}_{1}$ ${\ensuremath{\varphi}}_{2}$ (fractions areas). Hydrodynamic properties the are fully expressed in terms effective slip-length tensor with eigenvalues depend on...

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 scale of heterogeneities, $L$, but finite. For such "weakly" surfaces, earlier analyses have predicted that effective length simply given surface-averaged which implies slip-length tensor becomes isotropic. Here we show different scenario expected if local has step-like jumps at edges heterogeneities. In this case,...

We propose a concept of fractionation micron-sized particles in microfluidic device with bottom wall decorated by superhydrophobic stripes.

Anisotropic super-hydrophobic surfaces have the potential to greatly reduce drag and enhance mixing phenomena in microfluidic devices. Recent work has focused mostly on cases of stripes. Here, we analyze a relevant situation cosine variation local slip length. We derive approximate formulae for maximal (longitudinal) minimal (transverse) directional effective lengths that are good agreement with exact numerical solution lattice-Bolzmann simulations any surface fraction. The texture can...

Aligned superhydrophobic surfaces with the same texture orientation reduce drag in channel and generate secondary flows transverse to direction of applied pressure gradient. Here we show that a shear can be easily generated by using channels misaligned textured surfaces. We propose general theoretical approach quantify this flow introducing concept an effective tensor. To illustrate its use, present approximate solutions Dissipative Particle Dynamics simulations for striped channels. Our...

We discuss an electro-osmotic flow near charged porous coatings of a finite hydrodynamic permeability, impregnated with outer electrolyte solution. It is shown that their electrokinetic (zeta) potential generally augmented compared to the surface electrostatic potential, thanks large liquid slip at emerging due in enriched by counter-ions films. The inner shows very rich behavior controlled volume charge density coating, its Brinkman length, and concentration added salt. Interestingly, even...

Abstract We consider sedimented at a solid wall particles that are immersed in water containing small additives of photosensitive ionic surfactants. It is shown illumination with an appropriate wavelength, beam intensity profile, shape and size could lead to variety dynamic, both unsteady steady state, configurations particles. These well-controlled switchable particle patterns the due emerging diffusio-osmotic flow takes its origin adjacent electrostatic diffuse layer, where concentration...

We report measurements of the hydrodynamic drag force acting on a smooth sphere falling down under gravity to plane decorated with microscopic periodic grooves. Both surfaces are lyophilic, so that liquid (silicone oil) invades surface texture being in Wenzel state. A significant decrease resistance as compared predicted for two is observed. To quantify effect roughness we use effective no-slip boundary condition, which applied at imaginary homogeneous isotropic located an intermediate...

We discuss an inertial migration of oblate spheroids in a plane channel, where the steady laminar flow is generated by pressure gradient. Our lattice Boltzmann simulations show that orient flow, so their minor axis coincides with vorticity direction (a log-rolling motion). Interestingly, for moderate aspect ratios, equilibrium positions relative to channel walls depend only on equatorial radius a. By analyzing lift force, we argue this force proportional a3b, b polar radius, and conclude...

Lubricant-infused surfaces in an outer liquid flow generally reduce viscous drag. However, owing to the meniscus deformation, infused state could collapse. Here we discuss transition between and collapsed states of transverse shallow grooves, considering capillary number, liquid/lubricant viscosity ratio aspect groove as parameters for inducing this transition. It is found that depending on depth two different scenarios occur. A collapse lubricant-infused happen due a depinning from front...

The linear stability of incompressible boundary-layer flow dusty gas on a semi-infinite flat plate is considered. particles are assumed to be under the action Stokes drag only. problem reduced solution modified Orr–Sommerfeld equation (Saffman 1962). This solved numerically using two approaches: directly by orthonormalization method, and perturbation method at small particle mass content. characteristics calculated for both mono- polydisperse particles.The dust suppresses instability waves...

Superhydrophobic one-dimensional surfaces reduce drag and generate transverse hydrodynamic phenomena by combining hydrophobicity roughness to trap gas bubbles in microscopic textures. Recent studies this area have focused on specific cases of superhydrophobic stripes. Here we provide some theoretical results guide the optimization forward flow a parallel-plate channel with trapezoidal texture, varying scales larger than thickness. The permeability such thin is shown be equivalent that...

We study the effective slippage on superhydrophobic grooves with trapezoidal cross-sections of various geometries (including limiting cases triangles and rectangular stripes), by using two complementary approaches. First, dissipative particle dynamics (DPD) simulations a flow past such surfaces have been performed to validate an expression [E.S.Asmolov O.I.Vinogradova, J. Fluid Mech. \textbf{706}, 108 (2012)] that relates eigenvalues slip-length tensor for one-dimensional textures. Second,...