The Influence of Two-Dimensional Temperature Modulation on Floating Droplet Dynamics

We investigate the dynamics and instabilities of a droplet that floats on a liquid substrate. The substrate is cooled from below. In the framework of the slender droplet approximation and the precursor model, the problem is studied numerically. Oscillatory and stationary regimes of thermocapillary convection have been observed. The influence of a two-dimensional spatial inhomogeneity of temperature on the droplet dynamics is investigated. The two-dimensional spatial temperature inhomogeneity can suppress oscillations, changing the droplet's shape. In a definite region of parameters, the two-dimensional spatial modulation can lead to the excitation of periodic oscillations. The influence of the Biot number on the shape of the droplets is studied.