Rapid droplet leads the Liquid-Infused Slippery Surfaces more slippery

The introduction of lubricant between fluid and substrate endows the Liquid-Infused Slippery Surfaces with excellent wetting properties: low contact angle, various liquids repellency, ice-phobic and self-healing. Droplets moving on such surfaces have been widely demonstrated to obey a Landau-Levich-Derjaguin (LLD) friction. Here, we show that this power law is surprisingly decreased with the droplet accelerates: in the rapid droplet regime, the slippery surfaces seem more slippery than LLD friction. Combining experimental and numerical techniques, we find that the meniscus surrounding the droplet exhibits an incompletely developed state. The Incompletely Developed Meniscus possesses shorter shear length and thicker shear thickness than the prediction of Bretherton model and therefore is responsible for the more slippery regime. With an extended Bretherton model, we not only provide an analytical description to the IDM behavior but also the friction when the Capillary Number of the moving droplet is larger than the Critical Capillary Number