The thin-film equation describes the evolution of a thin liquid film, typically on a solid substrate. This equation is important in fluid dynamics and materials science and is often used in contexts such as coatings, wetting, and thin-film flow dynamics. The thin-film equation can be derived from the Navier-Stokes equations under certain assumptions, specifically when considering a thin film with small thickness compared to its other dimensions.
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A thin-film equation combines a lubrication flux with mass conservation to evolve a free-surface thickness. Gravity, capillary pressure, wall motion, and intermolecular forces may contribute to the flux.