Dynamics of floating droplets under the action of an inclined temperature gradient

The thermocapillary flows generated by an inclined temperature gradient in and around a floating droplet are studied in the framework of the lubrication approximation. Numerical simulations of nonlinear flow regimes are fulfilled. It is shown that under the action of Marangoni stresses, a droplet typically moves as a whole. It is found that an inclined temperature gradient can lead to the excitation of periodic oscillations. With an increase of the inclination of the temperature gradient, temporally quasi-periodic oscillations have been obtained. In a definite region of parameters, an inclined temperature gradient can suppress oscillations, changing the droplet's shape. The diagram of regimes in the plane of longitudinal and transverse Marangoni numbers has been constructed. Bistability has been found.