STATIONARY STABILITY OF TWO LIQUID LAYERS COATING BOTH SIDES OF A THICKWALL UNDER THE SMALL BIOT NUMBERS APPROXIMATION

In this paper the linear stability of two liquid layers with flat free-surface coating of both sides of a wall of finite thickness and thermal conductivity is investigated under the assumption that the liquid/gas Biot numbers are very small. It is supposed that gravity is negligible and that the atmospheres at both sides of the system have different temperatures. These conditions allow for the formation of very large thermocapillary convection cells. Thus, the small wave-number approximation is done up to fourth order to calculate the marginalMarangoni number. From this result, the criticalMarangoni number (Mac) and its corresponding wave number (k(c)) have been calculated numerically. The wave number corresponding to the maximum growth rate (k(max)) is also calculated for a Marangoni number slightly above criticality. It is shown that, under these conditions, the flow is stationary. It is found that Mac may have two magnitudes, one positive and another one negative, depending on the magnitude of some particular parameters of the problem. It is shown that k(c) may be zero or different from zero with small but finite magnitude. Some parameters are fixed and the numerical results are presented by means of plots of Ma(c), k(c), and k(max) against different important parameters of the problem.