Shapes of floating droplets under non-uniform heating from below

Floating droplets (liquid lenses) are widely used in engineering applications. A typical way of droplet manipulation is the non-uniform heating. In the present work, the influence of two-dimensional spatial inhomogeneity of temperature on the dynamics and instabilities of a droplet floating on a heated liquid substrate is investigated. The problem is studied numerically in the framework of the slender droplet approximation and the precursor model. It is shown that spatial temperature inhomogeneity leads to the liquid redistribution in the substrate toward the region of lower temperature, which is accompanied by the change in the droplet shape. Heating from below can lead to the substrate layer's rupture due to its monotonic instability. Symmetric and asymmetric droplets under the action of spatial temperature inhomogeneity have been obtained.