The problem of thermocapillary convection in low-Prandtl-number liquid layers is studied. This convection is driven by variations of surface tension resulting from nonuniform temperature distributions imposed along the layer free surface. The analysis has been carried out using a model problem consisting of a liquid layer contained in a rectangular cavity with a free upper surface. This model provides a good approximation for a wide range of technological processes. Common examples of these processes include laser processing of materials, welding and coating processes, growth of metals and semiconductor crystals in open horizontal boats (e.g., Bridgman technique solidification), flame propagation in combustion chambers, etc. The study has covered both the steady and the unsteady flows.

A family of algorithms for the analysis of the dynamics of unsteady flow has been developed. The algorithms solve the unsteady free boundary problem for the Navier-Stokes and energy equations. The algorithms are based on a coordinate transformation method, streamfunction-vorticity formulation, and fully-implicit finite-difference discretization technique. All spatial discretization formulas are second-order accurate. Different treatments of the time derivatives lead to a one-step first-order implicit method, second-order Crank-Nicolson and trapezoidal methods, and a two-step second-order implicit method. The Crank-Nicolson and trapezoidal methods were found to be non-selfstarting (for practical applications) and subject to critical stability conditions, and thus are not recommended. The one-step and two-step implicit methods were found to work very well for a wide range of parameter values. The two-step method is not self-starting but is about 3 times faster (for the same absolute accuracy) than the one-step method. Various tests have shown that the algorithms deliver theoretically predicted accuracy even for very large interfacial distortions.

The steady response of the system has been studied through extensive numerical experiments. The effects of two different types of external heating and of the variations of transport parameters, such as capillary and Reynolds numbers, have been considered. The analysis also included the effect of changing the length of the cavity (i.e., changing the aspect ratio). Results have demonstrated that steady states corresponding to continuous interfaces do not exist beyond certain critical parameter values. This implies that steady thermocapillary flow may bifurcate to an unsteady flow when some limiting conditions have been exceeded.

Simulations of the unsteady problem showed that different factors affect the existence of the layers, depending on the type of external heating being applied. These factors include the interface approaching the bottom of the cavity (rupture of the layer;​ dryout of the bottom) and the interface becoming tangential to the side walls (dryout at the side walls). Also, depending on the external heating, the interface may begin to oscillate if the external-heating is applied too rapidly. A comprehensive insight into the physical phenomena leading to interface break up and dryout at the side walls has been provided through a detailed time history of the evolution of the interface deformation and the flow field.

The existence and characteristics of oscillatory thermocapillary flow have been investigated. Results suggest that the rate of heating has a strong effect on the development of the interface oscillations and that if the rate of heating is sufficiently reduced, the interface oscillations can be eliminated.