Enhanced slip properties of lubricant-infused grooves

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.