Long wave thermocapillary convection in a liquid layer under a cover
Dinamika Sploshnoi Sredy, No 89, 1989, pp. 55 - 71.
Language russian [download]
A lubrication equation has been obtained that describes evolution of thickness for a liquid layer in a two-layer liquid-gas system located between parallel heater plates at different temperatures. Heat transfer in a gas layer is taken into account. The paper studies a linear stability of equilibrium states, stationary solutions of the equation for periodic flows, motions with an immovable interface such as "convex", "concave" or "bore". It is shown that the equation has now solutions in the form of stationary traveling waves. We consider an analogy between the derived two-side model of convection in a liquid layer and existing one-side model in which the "Biot heat exchange" condition is used.