Shear-driven drainage of lubricant in a spherical cavity of lubricant-infused surface

Abstract

Lubricant-infused surfaces (LISs), whose initial development was inspired by the slippery surface of Nepenthes pitcher plants, have been eliciting considerable attraction. LISs have been extensively investigated during the last decade due to their potential for various applications, including antifouling, self-cleaning, and drag reduction. However, they can lose slipperiness when the outermost lubricant layer is severely depleted by external forces, such as flow-induced shear force. In the current study, we examined the shear-induced depletion of a lubricant impregnated into a spherical cavity exposed to a laminar channel flow. When the depth of interfacial meniscus exceeds a critical value due to depletion of the infused lubricant, the rotational direction of the lubricant flow inside the cavity is changed. This conversion in the lubricant's rotational direction is attributed to the flow separation above the meniscus between the lubricant and the working fluid. The flow separation induces the formation of a vortex and largely increases the drag force, which is an undesirable situation for LISs to achieve a sustainable drag reduction. To identify the unfavorable drag increasing conditions, we examined the critical depth of meniscus, defined as the depth of meniscus at the onset of switch in the rotational direction of the lubricant flow, with varying cavity geometry, flow velocity, and dynamic viscosity of the working fluid. In addition, a simple scaling analysis was conducted by balancing the viscous pressure and capillary pressure to deduce a theoretical prediction of the critical meniscus depth. The experimentally measured results are matched well with the theoretical predictions.