Overflow cascades in liquid-infused substrates

Liquid-infused patterned surfaces offer a promising new platform for generating omniphobic surface coatings. However, the liquid infused in these surfaces is susceptible to shear-driven dewetting. Recent work [Wexler et al., "Shear-driven failure of liquidinfused surfaces," Phys. Rev. Lett. 114, 168301 (2015)] has shown how the substrate pattern in these surfaces can be designed to exploit capillary forces in order to retain infused lubricants against the action of an immiscible shear flow. In this study, we explore the behavior of the infused lubricant when external shear causes the lubricant to overflow finite or "dead-end" surface features, resulting in either temporary or permanent lubricant loss. Microfluidic experiments illustrate how both geometry and chemical Marangoni stresses within liquid-infused surfaces generate an overflow cascade in which the lubricant escapes from the substrate and forms droplets on the surface, after which the droplets depin and arewashed away by the external shear flow, allowing the overflowto repeat. General guidelines are developed to estimate the onset of the different stages of the cascade with the aim of providing additional robustness criteria for the design of future liquid-infused surfaces.