Multiple equilibria enables tunable wetting of droplets on patterned liquid surfaces

Patterning solid surfaces with varying wettability is important to manage droplets in microfluidics, heat transfer, and printing. Solid surface roughness poses fundamental limitations including contact-line pinning and solid friction. Here, we report an experimental strategy and theoretical design principles for patterned liquid surfaces (PaLS) that combine the controlled wettability from patterning with the ultrasmoothness of a lubricant-infused surface. In contrast to a solid, on PaLS, a droplet can be in 10 different wetting states. This richness arises from the adaptation of the liquid lubricants and can be harnessed to control the apparent contact angle of the droplet over the full range of wettability while removing contact-line pinning effects induced by the solid surface. In the limit of thin liquid films, we derive surface-averaged laws for the apparent contact angle for each wetting state, which capture both experimental and simulation data. Our results provide a distinct approach to surface patterning that exploits the interaction of fluids with lubricant-impregnated surfaces.