ON A NONLINEAR THERMOCAPILLARY EFFECT IN THIN LIQUID LAYERS

Dilute aqueous solutions of long alcohol chains were recently found to cause a quadratic dependence of surface tension on the temperature without affecting other bulk properties of the liquid: sigma = sigma0 + alpha(Q)(T-T0)2, alpha(Q) > 0. The impact of such Marangoni instability on the behaviour of a thin liquid layer is studied in this work. We derive an equation describing a nonlinear spatiotemporal evolution of a thin film. The behaviour of the perturbed film in the absence of gravity, critically depends on whether the temperature T0, yielding a minimal surface tension, is attained on the surface of the film. When this is the case, a qualitatively new behaviour is observed: perturbations of the film interface may evolve into continuous steady patterns that do not rupture. Otherwise, the observed patterns due to the linear and quadratic Marangoni effects are qualitatively similar and result in the rupture of the film into separate drops.