Abstract
Marangoni convection plays an important role in hydrodynamics of evaporating liquid films and sessile drops. Evaporation of liquid films induces unsteady nonuniform temperature distribution across the liquid layer and in a substrate. If the substrate is composed of parts with different thermal properties, the interface temperature distribution becomes non-uniform, leading to appearance of Marangoni stresses, convective vortices, and film deformation. In this article, a model describing evaporation, Marangoni effect and interface dynamics of liquid films on composite substrates is developed. The film dynamics is described in the framework of long-wave theory. The unsteady heat conduction in the substrate is described using the Laplace transform method for semi-infinite substrates and using the separation of variables technique for substrates of finite thickness. The non-uniformity of substrate thermal properties has a pronounced effect on film dynamics.
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