Thermocapillary instability of a liquid sheet with centrifugal force

The thermocapillary instability of liquid sheets subjected to a temperature gradient that is perpendicular to the gas–liquid interface and moving in a gas medium is investigated in this paper. A linear instability analysis accounting for the weak form of the centrifugal force along the flow direction is proposed. The instability of liquid sheets with a temperature gradient is compared to that of isothermal liquid sheets, and the effect of the temperature difference is analyzed. The effect of the centrifugal force is also investigated. Furthermore, the effect of the density ratio, viscosity of liquid sheet and Weber number are also discussed by solving the dispersion equation. The results show that, when the thermocapillary effects are taken into account, the temporal growth rate of the varicose mode can become greater than that of the sinuous mode, in contrast to the condition of an isothermal liquid sheet. When the Marangoni number is relatively small, the swirl decreases the maximum growth rate for the sinuous mode. In other conditions, the swirl has only minor effects on the stability of the liquid sheets. The increase of the density ratio and Weber number enhances the instability of the sheets, while the increased Prandtl number has the opposite effect. The effect of the Ohnesorge number is relatively complicated.