Instabilities of dynamic thermocapillary liquid layers. Part 1. Convective instabilities

A planar liquid layer is bounded below by a rigid plate and above by an interface with a passive gas. A steady shear flow is set up by imposing a temperature gradient along the layer and driving the motion by thermocapillarity. This dynamic state is susceptible to two types of thermal-convective instabilities: (i) stationary longitudinal rolls, which involve the classical Marangoni instability studied by Pearson; and (ii) unsteady hydrothermal waves, which involve a new mechanism of instability deriving its energy from the horizontal temperature gradients. Thermal stability characteristics for liquid layers with and without return-flow profiles are presented as functions of the Prandtl number of the liquid and the Biot number of the interface. Comparisons are made with available experimental observations.