Factors controlling the pinning force of liquid droplets on liquid infused surfaces

Liquid infused surfaces with partially wetting lubricants have recently been exploited for numerous intriguing applications, such as for droplet manipulation, droplet collection and spontaneous motion. When partially wetting lubricants are used, the pinning force is a key factor that can strongly affect droplet mobility. Here, we derive an analytical prediction for contact angle hysteresis in the limit where the meniscus size is much smaller than the droplet, and numerically study how it is controlled by the solid fraction, the lubricant wetting angles, and the various fluid surface tensions. We further relate the contact angle hysteresis and the pinning force experienced by a droplet on a liquid infused surface, and our predictions for the critical sliding angles are consistent with existing experimental observations. Finally, we discuss why a droplet on a liquid infused surface with partially wetting lubricants typically experiences stronger pinning compared to a droplet on a classical superhydrophobic surface.