No abstract

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.