Motivated by the emerging applications of liquid-infused surfaces (LIS), we study the drag reduction and robustness of transverse flows over two-dimensional microcavities partially filled with an oily lubricant. Using separate simulations at different scales, characteristic contact line velocities at the fluid-solid intersection are first extracted from nanoscale phase field simulations and then applied to micronscale two-phase flows, thus introducing a multiscale numerical framework to model the interface displacement and deformation within the cavities. As we explore the various effects of the lubricant-to-outer-fluid viscosity ratio ${\tilde{\mu }}_2/{\tilde{\mu }}_1$, the capillary number Ca, the static contact angle ${\theta }_s$, and the filling fraction of the cavity $\delta$, we find that the effective slip is most sensitive to the parameter $\delta$. The effects of ${\tilde{\mu }}_2/{\tilde{\mu }}_1$ and ${\theta }_s$ are generally intertwined but weakened if $\delta <1$. Moreover, for an initial filling fraction $\delta =0.94$, our results show that the effective slip is nearly independent of the capillary number when it is small. Further increasing Ca to about $0.01{\tilde{\mu }}_1/{\tilde{\mu }}_2$, we identify a possible failure mode, associated with lubricants draining from the LIS, for ${\tilde{\mu }}_2/{\tilde{\mu }}_1\lesssim 0.1$. Very viscous lubricants (e.g., ${\tilde{\mu }}_2/{\tilde{\mu }}_1>1$), however, are immune to such failure due to their generally larger contact line velocity.

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• Microfluidics
• Nanofluidics
• Surface tension effects