A two-parameter model of wave regimes for viscous liquid film flows

Wavy flow regimes of viscous liquid films whose viscosity coefficients vary in a wide range are considered. An approximate model system of two differential equations with two external governing parameters for the layer thickness and local flow rate is derived. In this system, the viscous dissipation in the layer is taken into account more accurately than in the well-known one-parameter Shkadov model. New properties of linear and nonlinear waves caused by the hydrodynamic instability of strongly viscous liquid flow under gravity and surface tension are established.