Abstract
The problem of hydrodynamic instability of a very thin UCM liquid film flowing down on the outer surface of an inclined plane is investigated. In order to improve the accuracy of numerical results, the viscoelastic parameters and van der Waals forces have been included into the governing equations. Also, the analytical solutions are obtained by utilizing the long-wave perturbation method. The influence of some physical parameters is discussed in both linear and non-linear steps of the problem. It has been revealed that the instability of the film flow is weakened when Reynolds number, viscoelastic property and attractive van der Waals force are reduced. Further, the thin film flow can be stabilized by short-range Born repulsion. The results show that both supercritical stability and subcritical instability may take place within the film flow system. Moreover, the presence of non-linear terms leads to an obvious difference in the behavior of some physical parameters.
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