  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, $\mu/\mu_g \gg 1$. 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, $\delta$, and the local depth of the groove, $e(y,
\alpha)$. The latter varies in the direction $y$, orthogonal to the orientation
of stripes, and depends on the bevel angle of groove's edges, $\pi/2 - \alpha$,
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 $\mu/\mu_g$, $\delta$, and $\alpha$, but not on the depth. The
eigenvalues of the local slip length of shallow grooves depend on $\mu/\mu_g$
and $e(y, \alpha)$, 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.
