arXiv subjects

Alexander L. Dubov

Publications and source records attributed to Alexander L. Dubov.

5 recordsLinked to original sources

arXiv2018

Boundary conditions at the gas sectors of superhydrophobic grooves

The hydrodynamics of liquid flowing past gas sectors of unidirectional superhydrophobic surfaces is revisited. Attention is focussed on the local slip boundary condition at the liquid-gas interface, which is equivalent to the effect of a gas cavity on liquid flow. The system is characterized by a large viscosity contrast between liquid and gas, $μ/μ_g \gg 1$. We interpret earlier results, namely the dependence of the local slip length on the flow direction, in terms of a tensorial local slip boundary condition and relate the eigenvalues of the local slip length tensor to the texture parameters, such as the width of the groove, $δ$, and the local depth of the groove, $e(y, α)$. The latter varies in the direction $y$, orthogonal to the orientation of stripes, and depends on the bevel angle of groove's edges, $π/2 - α$, at the point, where three phases meet. Our theory demonstrates that when grooves are sufficiently deep their eigenvalues of the local slip length tensor depend only on $μ/μ_g$, $δ$, and $α$, but not on the depth. The eigenvalues of the local slip length of shallow grooves depend on $μ/μ_g$ and $e(y, α)$, although the contribution of the bevel angle is moderate. In order to assess the validity of our theory we propose a novel approach to solve the two-phase hydrodynamic problem, which significantly facilitates and accelerates calculations compared to conventional numerical schemes. The numerical results show that our simple analytical description obtained for limiting cases of deep and shallow grooves remains valid for various unidirectional textures.

physics.flu-dyn↗

arXiv2017

Inertial focusing of finite-size particles in microchannels

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.

physics.flu-dyn↗

arXiv2015

Regimes of Wetting Transitions on Superhydrophobic Textures Conditioned by Energy of Receding Contact Lines

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 effective contact angle, two different scenarios occur. For relatively dilute stripes the receding angle is above 90$^\circ$, 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 effective angle reaches 90$^\circ$ and represents the impregnation of the grooves from the triple contact line towards the drop center.

cond-mat.soft↗

arXiv2014

Contact Angle Hysteresis on Superhydrophobic Stripes

We study experimentally and discuss quantitatively the contact angle hysteresis on striped superhydrophobic surfaces as a function of a solid fraction, $ϕ_S$. It is shown that the receding regime is determined by a longitudinal sliding motion 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 $ϕ_S$, in contrast to predictions of the Cassie equation. To interpret this we develop a simple theoretical model, which shows that the value of the receding angle depends both on weak defects at smooth solid areas and on the elastic energy of strong defects at the borders of stripes, which scales as $ϕ_S^2 \ln ϕ_S$. The advancing contact angle was found to be anisotropic, except as in a dilute regime, and its value is determined by the rolling motion of the drop. The cosine of the longitudinal advancing angle depends linearly on $ϕ_S$, 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 $ϕ_S\simeq 0.5$. 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 proportional to $ϕ_S^2$. Finally, the contact angle hysteresis is found to be quite large and generally anisotropic, but it becomes isotropic when $ϕ_S\leq 0.2$.

cond-mat.soft↗

arXiv2014

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 $ϕ$. For very large values of h/R we recover the macroscopic formulae for a sphere moving towards a hydrophilic no-slip plane. For h/R=O(1) and smaller the drag force is smaller than predicted by classical theories for hydrophilic no-slip surfaces, but larger than expected for a sphere interacting with a uniform perfectly slipping wall. At a thinner gap, $h\ll R$ the force reduction compared to a classical result becomes more pronounced, and is maximized by increasing $ϕ$. In the limit of very small separations our simulation data are in quantitative agreement with an asymptotic equation, which relates a correction to a force for superhydrophobic slip to texture parameters. In addition, we examine the flow and pressure field and observe their oscillatory character in the transverse direction in the vicinity of the wall, which reflects the influence of the heterogeneity and anisotropy of the striped texture. Finally, we investigate the lateral force on the sphere, which is detectable in case of very small separations and is maximized by stripes with $ϕ=0.5$.

physics.flu-dyn↗