Linear stability analysis of a droplet under an axisymmetric thermal gradient

Abstract

We study the linear stability of a droplet placed at the center of a horizontal disk under the effect of surface stress promoted by an axisymmetric thermal gradient. Since the fluid volume is constant, we solve the non-steady base flow and the perturbation simultaneously as they evolve over time. The numerical results show that the base state migrates from a droplet to a ring shape, with the front position and maximum thickness following power laws with time. The perturbations travel with the same velocity as the advancing front and develop their maxima close to the contact line. All of them initially decrease their amplitudes, later showing an increment with the growth rates depending on the wavenumber and time. The dominant wavenumber increases with time, in agreement with recent experimental work.