  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
$\phi$. 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 $\phi$. 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
$\phi=0.5$.
