Viscous Equations of Fluid Film Dynamics
Pavel Grinfeld

Source CMC: Computers, Materials & Continua, Vol. 19, No. 3, pp. 239-254, 2010
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Abstract We model viscosity in the framework of the exact nonlinear equations of fluid film dynamics. The proposed approach yields monotonic dissipation of energy and guarantees that viscous forces are not engaged when the film undergoes rigid motion. With the addition of viscosity, the governing system has all the essential elements - inertia, surface tension, interaction with the ambient medium, influence of external fields and, now, viscosity - for accurate prediction and interpretation of experimental observations.
The fluid film is modelled as a two-dimensional manifold. The film's thickness is represented by a surface density function. The resulting system is the fluid film equivalent of the classical Navier-Stokes equations. The domain of definition of the fluid film equations is a deforming manifold which makes computer simulation the mostly likely course for obtaining solutions.
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