Damping the jump of coalescing droplets through substrate compliance

Sessile droplets coalescing on superhydrophobic surfaces result in spontaneous droplet jumping. Here, through coalescence experiments and fluid-structure interaction simulations for microliter droplets, we demonstrate that such droplet jumping can be damped if the underlying substrate is designed to be compliant. We show that a compliant superhydrophobic substrate with synergistic combinations of low stiffness and inertia deforms rapidly during the coalescence process to minimize the substrate reaction, thus diminishing the jumping velocity. A spring-mass system model for coalescing water droplets is proposed that successfully captures droplet motion and substrate deformation for a wide range of compliant superhydrophobic substrates. These insights can be leveraged to improve the process efficiency in multiple applications, such as designing compliant superhydrophobic substrates for minimizing the scattering of small, nanoliter-sized droplets during atmospheric water harvesting. Lastly, experiments on an exemplar butterfly wing show that droplet jumping velocity reduction can also manifest on natural superhydrophobic substrates due to their inherent compliance.