  We ascertain the enhanced slip properties for a liquid flow over
lubricant-infused unidirectional surfaces. This situation reflects many
practical settings involving liquid flows past superhydrophobic grooves filled
with gas, or past grooves infused with another, immiscible, liquid of smaller
or equal viscosity, i.e. where the ratio of lubricant and liquid viscosities,
$\mu \leq 1$. To maximize the slippage, we consider deep grooves aligned with
the flow. The (normalized by a texture period $L$) effective slip length,
$b_{\mathrm{eff}}$, is found as an expansion to first order in protrusion angle
$\theta$ about a solution for a flat liquid-lubricant interface. Our results
show a significant increase in $b_{\mathrm{eff}}$ with the area fraction of
lubricant, $\phi$, and a strong decrease with $\mu$. By contrast, only little
influence of $\theta$ on $b_{\mathrm{eff}}$ is observed. Convex meniscus
slightly enhances, and concave - slightly reduces $b_{\mathrm{eff}}$ relative
the case of a flat liquid-lubricant interface. The largest correction for
$\theta$ is found when $\mu = 0$, it decreases with $\mu$, and disappears at
$\mu = 1$. Finally, we show that lubricant-infused surfaces of small $\theta$
can be modeled as flat with patterns of local slip boundary conditions, and
that the (scaled with $L$) local slip length at the liquid-lubricant interface
is an universal function of $\phi$ and $\mu$ only.
