Arrested Dynamics of Droplet Spreading on Ice

Abstract

We investigate the arrested spreading of room temperature droplets impacting flat ice. The use of an icy substrate eliminates the nucleation energy barrier, such that a freeze front can initiate as soon as the droplet's temperature cools down to 0 °C. We employ scaling analysis to rationalize distinct regimes of arrested hydrodynamics. For gently deposited droplets, capillary-inertial spreading is halted at the onset of contact line freezing, yielding a 1/7 scaling law for the arrested diameter. At low impact velocities (We≲100), inertial effects result in a 1/2 scaling law. At higher impact velocities (We>100), inertio-viscous spreading can spill over the frozen base of the droplet until its velocity matches that of a kinetic freeze front caused by local undercooling, resulting in a 1/5 scaling law.