Thermocapillary instabilities of liquid layers on an inclined plane

The thermocapillary instabilities of the liquid layers on an inclined plane with zero heat flux are examined by linear stability analysis. There is an angle between the gravity and the thermocapillary force. The basic flow depends on the ratio of the gravity effect to thermocapillary effect. When the ratio is positive, the gravity always increases the velocity and destabilizes the flow. When the ratio is negative, the influence of gravity on the flow stability depends on the Prandtl (Pr) number. At high and moderate Pr, the critical Marangoni number always decreases with the ratio. The vertical convection is the key to the instability mechanism at high Pr, while the horizontal convection is dominant at moderate Pr. By contrast, at small Pr, the critical Marangoni number has a maximum and the energy from the basic flow is important for the perturbation energy. Published by AIP Publishing.