When does contact angle hysteresis prevent bendotaxis?

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. Here, we
seek to understand when contact angle hysteresis prevents bendotaxis. We
supplement a previous mathematical model of the dynamics of bendotaxis with a
simple, experimentally-verified 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.