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We consider two-layers of immiscible liquids confined between an upper and alower rigid plate. The dynamics of the free liquid-liquid interface isdescribed for arbitrary amplitudes by a single evolution equation derived fromthe basic hydrodynamic equations using long-wave approximation. After givingthe evolution equation in a general way, we focus on interface instabilitiesdriven by gravity, thermocapillary and electrostatic fields. First, we studythe linear stability discussing especially the conditions for destabilizing thesystem by heating from above or below. Second, we use a variational formulationof the evolution equation based on an energy functional to predict metastablestates and the long-time pattern morphology (holes, drops or maze structures).Finally, fully nonlinear three-dimensional numerical integrations are performedto study the short- and long-time evolution of the evolving patterns. Differentcoarsening modes are discussed and long-time scaling exponents are extracted

Long-wave theory of bounded two-layer films with a free liquid–liquid interface: Short- and long-time evolution