Thermocapillary flow of droplets on axisymmetric heated surfaces: A stability analysis*

This research examines the stability of a droplet situated at the center of a horizontal disk, which is subject to an axisymmetric thermal gradient that induces a stress at the liquid-air interface. We numerically the unsteady base flow and perturbations together as they evolve over time. The base state axisymetrically spreads, but its thickness transitions from a droplet to a ring, the front position and the maximum thickness following power law trends with time. We find that the perturbations travel at the same speed as the advancing front and develop their maxima near the contact line. Interestingly, the dominant wavenumber increases with time after a brief transient where all of the perturbations are stable, aligning with recent experimental observations on contact line motion in axial thermocapillary outward flow (Journal of Fluid Mechanics, 892, A8, 2020).