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 ratioμ 2 /μ 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 ofμ 2 /μ 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 0.01μ 1 /μ 2 , we identify a possible failure mode, associated with lubricants draining from the LIS, forμ 2 /μ 1 0.1. Very viscous lubricants (e.g.μ 2 /μ 1 > 1), on the other hand, are immune to such failure due to their generally larger contact line velocity.

Flow-driven collapse of lubricant-infused surfaces

“…We have already mentioned the prior numerical work of Ge et al (2018) who studied deep transverse grooves, filled by a lubricant only partly (implying the mobility of the contact line), and found that the meniscus deformation decreases with . One important difference of our results for shallow transverse grooves with pinned contact lines is that the deformation decreases upon reducing , likewise in the case of deep longitudinal grooves (Wexler et al 2015; Liu et al 2016).…”

“…As a result, the curvature of the static meniscus is largest near the channel inlet, and the failure of deep LI grooves occurs when the dynamic contact angle becomes large, while the failure of shallow grooves takes place when the meniscus contacts the groove bottom. The collapse of partially filled deep SH and LI grooves induced by an external transverse shear has been studied numerically by Ge et al (2018). These authors concluded that the meniscus deformation induced by such a flow decreases with the lubricant/outer liquid viscosity ratio and that the collapse of lubricant-infused grooves is possible only when this ratio is smaller than unity.…”

Slip length formulas for longitudinal shear flow over a superhydrophobic grating with partially filled cavities

“…Several authors have carried out numerical studies quantifying slip for partially filled cavities (Ng & Wang 2009; Teo & Khoo 2010; Ge et al. 2018), and the author has previously given some analytical formulas quantifying slip in which a small set of parameters must be found numerically (Crowdy 2011 a ), but the extant literature contains no explicit formulas akin to Philip's that have proven so useful in the field. The present paper contributes in this direction.…”

Turbulent drag reduction by rotating rings and wall-distributed actuation

“…A spanwise wall slip instead promotes the growth of streamwise rolls leading to drag increase due to an enhanced lift-up effect. Both constant (Min and Kim, 2004) and shear-dependent (Aghdam and Ricco, 2016) slip-length wall boundary conditions have been proposed to describe the effect of different types of hydrophobic surfaces, modeling lotus-leaf-type surfaces, where air pockets are trapped in small cavities (Ling et al, 2017;Seo et al, 2018;Reholon and Ghaemi, 2018), and pitcher-plant-type surfaces, where oil is imbibed in the porous surface (Wong et al, 2011) or in transverse microcavities (Ge et al, 2018). In the present work we follow the approach of Min and Kim (2004) where the no-slip boundary condition on the streamwise velocity is replaced by the following constantslip-length condition:…”