Effective slip over partially filled microcavities and its possible failure

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 ̃μ2/ ̃μ1, the capillary number Ca, the static contact angle θs, and the filling fraction of the cavity δ, we find that the effective slip is most sensitive to the parameter δ. The effects of ̃μ2/ ̃μ1 and θs are generally intertwined but weakened if δ<1. Moreover, for an initial filling fraction δ=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⁢ ̃μ1/ ̃μ2, we identify a possible failure mode, associated with lubricants draining from the LIS, for ̃μ2/ ̃μ1≲0.1. Very viscous lubricants (e.g., ̃μ2/ ̃μ1>1), however, are immune to such failure due to their generally larger contact line velocity.