Non-linear waves in electrified viscous film flow down a vertical cylinder

The non-linear dynamics of a viscous film falling under gravity on the outside surface of a vertical circular cylinder are investigated. An electric field is imposed radially and the non-linear deformations of the liquid–air interface are modelled using thin film asymptotic analysis. The resulting equation extends other thin film models found in the literature. The electrostatic terms are a result of both normal and tangential Maxwell stresses, the latter made possible when the fluid is a leaky dielectric. The normal stresses produce non-local terms that destabilize the flow, whereas the tangential stresses can be either stabilizing or destabilizing. Numerical computations show that the electric field can be used to either suppress or enhance the instability by producing travelling wave structures with relatively larger amplitudes.