  We study the effective slippage on superhydrophobic grooves with trapezoidal
cross-sections of various geometries (including the limiting cases of triangles
and rectangular stripes), by using two complementary approaches. First,
dissipative particle dynamics (DPD) simulations of a flow past such surfaces
have been performed to validate an expression [E.S.Asmolov and O.I.Vinogradova,
J. Fluid Mech. \textbf{706}, 108 (2012)] that relates the eigenvalues of the
effective slip-length tensor for one-dimensional textures. Second, we propose
theoretical estimates for the effective slip length and calculate it
numerically by solving the Stokes equation based on a collocation method. The
comparison between the two approaches shows that they are in excellent
agreement. Our results demonstrate that the effective slippage depends strongly
on the area-averaged slip, the amplitude of the roughness, and on the fraction
of solid in contact with the liquid. To interpret these results, we analyze
flow singularities near slipping heterogeneities, and demonstrate that they
inhibit the effective slip and enhance the anisotropy of the flow. Finally, we
propose some guidelines to design optimal one-dimensional superhydrophobic
surfaces, motivated by potential applications in microfluidics.
