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At finite Reynolds numbers, Re, particles migrate across laminar flow streamlines to their equilibrium positions in microchannels. This migration is attributed to a lift force, and the balance between this lift and gravity determines the location of particles in channels. Here we demonstrate that velocity of finite-size particles located near a channel wall differs significantly from that of an undisturbed flow, and that their equilibrium position depends on this, referred to as slip velocity, difference. We then present theoretical arguments, which allow us to generalize expressions for a lift force, originally suggested for some limiting cases and Re ≪ 1, to finite-size particles in a channel flow at Re ≤ 20. Our theoretical model, validated by lattice Boltzmann simulations, provides considerable insight into inertial migration of finite-size particles in microchannel and suggests some novel microfluidic approaches to separate them by size or density at a moderate Re. † Email address for correspondence: aes50@yandex.ru ‡

We study experimentally and discuss quantitatively the contact angle hysteresis on striped superhydrophobic surfaces as a function of a solid fraction, ϕS. It is shown that the receding regime is determined by a longitudinal sliding motion of the deformed contact line. Despite an anisotropy of the texture the receding contact angle remains isotropic, i.e., is practically the same in the longitudinal and transverse directions. The cosine of the receding angle grows nonlinearly with ϕS. To interpret this we develop a theoretical model, which shows that the value of the receding angle depends both on weak defects at smooth solid areas and on the strong defects due to the elastic energy of the deformed contact line, which scales as ϕS(2)lnϕS. The advancing contact angle was found to be anisotropic, except in a dilute regime, and its value is shown to be determined by the rolling motion of the drop. The cosine of the longitudinal advancing angle depends linearly on ϕS, but a satisfactory fit to the data can only be provided if we generalize the Cassie equation to account for weak defects. The cosine of the transverse advancing angle is much smaller and is maximized at ϕS ≃ 0.5. An explanation of its value can be obtained if we invoke an additional energy due to strong defects in this direction, which is shown to be caused by the adhesion of the drop on solid sectors and is proportional to ϕS(2). Finally, the contact angle hysteresis is found to be quite large and generally anisotropic, but it becomes isotropic when ϕS ≤ 0.2.

Surface textures are used to impart advanced wetting properties to surfaces. However understanding the surface response in relation to the nature of the texture is still a challenge.Here we have measured advancing and receding contact angles on model hydrophobic surfaces with cylindrical pillars as a function of the pillar spacing. We show that the dependances of both advancing and receding contact angles upon spacing are well accounted for by a simple model of the instability of the triple line, following the line elasticity theory by Joanny and de Gennes (J. Chem. Phys. 81 (1984) 552). This result demonstrates the prominent role of the triple line elasticity in determining the wetting properties of textured surfaces.

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. We provide some theoretical arguments allowing us to quantify the transverse displacement of particles in the microfluidic channel, and confirm the validity of theoretical predictions in test experiments with monodisperse fractions of microparticles. Our results can guide the design of superhydrophobic microfluidic devices for efficient sorting of microparticles with a relatively small difference in size and density.

We discuss an evaporation-induced wetting transition on superhydrophobic stripes, and show that depending on the elastic energy of the deformed contact line, which determines the value of an instantaneous apparent contact angle, two different scenarios occur. For relatively dilute stripes the receding angle is above 90 • , and the sudden impalement transition happens due to an increase of a curvature of an evaporating drop. For dense stripes the slow impregnation transition commences when the apparent angle reaches 90 • and represents the impregnation of the grooves from the triple contact line towards the drop center.

We report a simple method to make hybrid or pure silica micropatterns at the surface of a substrate based on the combination of sol–gel process and nano-imprint lithography. The silica patterns can be easily designed during the photolithographic step and functionalized with a vapor phase deposition of fluorosilane molecules to obtain superhydrophobic surfaces. Benefiting from the properties of silica, our superhydrophobic patterns can withstand elevated temperatures and show interesting optical properties. These surfaces can be used for thermal transfer applications or microfluidic devices for example to limit noise in fluorescence measurements for biological applications. In connection to the fabrication of superhydrophobic surfaces, the organization of patterns (period of grating) and height of patterns were tested, and the stability of the Cassie–Baxter state studied. The transition can be described on a wide range of tested parameters by the sliding threshold where the control of side wall angle of patterns and chemistry of surface is essential.

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