Effective slip over partially filled microcavities and its possible failure

Abstract

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 nano-scale phase field simulations and then applied to micron-scale 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 $\tildeμ_2/\tildeμ_1$, the capillary number Ca, the static contact angle $θ_s$, and the filling fraction of the cavity $δ$, we find that the effective slip is most sensitive to the parameter $δ$. The effects of $\tildeμ_2/\tildeμ_1$ and $θ_s$ 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 $0.01 \tildeμ_1/\tildeμ_2$, we identify a possible failure mode, associated with lubricants draining from the LIS, for $\tildeμ_2/\tildeμ_1 \lesssim 0.1$. Very viscous lubricants (\eg $\tildeμ_2/\tildeμ_1 >1$), on the other hand, are immune to such failure due to their generally larger contact line velocity.