TY - JOUR

T1 - Lattice-Boltzmann simulations of the drag force on a sphere approaching a superhydrophobic striped plane

AU - Dubov, A.L.

AU - Schmieschek, S.M.P.

AU - Asmolov, E.S.

AU - Harting, J.D.R.

AU - Vinogradova, O.I.

PY - 2014

Y1 - 2014

N2 - 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 ¿. 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), 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 « R the force reduction compared to a classical result becomes more pronounced, and is maximized by increasing ¿. 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 ¿ = 0.5.

AB - 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 ¿. 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), 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 « R the force reduction compared to a classical result becomes more pronounced, and is maximized by increasing ¿. 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 ¿ = 0.5.

U2 - 10.1063/1.4861896

DO - 10.1063/1.4861896

M3 - Article

C2 - 25669407

SN - 0021-9606

VL - 140

SP - 034707-1/8

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

M1 - 034707

ER -