  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.
