Droplet trapping in bendotaxis caused by contact angle hysteresis

Passive droplet transport mechanisms, in which continuous external energy input is not required for motion, have received significant attention in recent years. Experimental studies of such mechanisms often ignore, or use careful treatments to minimize, contact angle hysteresis, which can impede droplet motion, or even arrest it completely. Here, we consider the effect of contact angle hysteresis on bendotaxis, a mechanism in which droplets spontaneously deform an elastic channel via capillary pressure and thereby move. We seek to understand when contact angle hysteresis prevents bendotaxis. We supplement a previous mathematical model of the dynamics of bendotaxis with a simple model of contact angle hysteresis, and show that this model predicts droplet trapping when hysteresis is sufficiently strong. By identifying the equilibrium configurations adopted by these trapped droplets and assessing their linear stability, we uncover a sensitive dependence of bendotaxis on contact angle hysteresis and develop criteria to describe when droplets will be trapped.