Abstract
The flow of a thin film of a nonlinearly viscous fluid whose stress tensor is modeled by a power law, flowing down a vertical plane in the field of gravity, is considered. For the case of low flow rates, an equation that describes the evolution of surface disturbances is derived in the long-wave approximation. The domain of linear stability of the trivial solution is found, and weakly nonlinear, steady-state travelling solutions of this equation are obtained. The mechanism of branching of solution families at the singular point of the neutral curve is described.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 73–84, May–June, 2005.
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Tsvelodub, O.Y., Shushenachev, V.Y. Wave regimes on a nonlinearly viscous fluid film flowing down a vertical plane. J Appl Mech Tech Phys 46, 365–374 (2005). https://doi.org/10.1007/s10808-005-0086-5
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DOI: https://doi.org/10.1007/s10808-005-0086-5