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

Abstract

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 $\varphi$. 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 $\varphi$. 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 $\varphi =0.5$.

9 pages, 7 figures

References in corpus (8)

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• A note on the effective slip properties for microchannel flows with ultra-hydrophobic surfaces
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• How micropatterns and air pressure affect splashing on surfaces
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Cited by in corpus (8)

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• Contact Angle Hysteresis on Superhydrophobic Stripes
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• Inertial migration of oblate spheroids in a plane channel
• Inhomogeneity-Induced Casimir Transport of Nanoparticles
• Quantum propulsion and trapping of nano-objects by inhomogeneity-induced lateral Casimir forces
• Instability of particle inertial migration in shear flow