The flow of a thin conducting film over a spinning disc in the presence of an electric field

We consider the flow of a thin liquid film over a spinning disc in the presence of an electric field. This is imposed by applying a potential between the disc and an electrode above the film. The integral method and lubrication theory are used to derive a coupled set of evolution equations for the film thickness, radial and azimuthal flow rates and the surface charge density. These equations are parameterized by a modified Weber number, a modified Masuda number, dimensionless conductivities and a dimensionless electrode separation. We focus on the limit of large liquid conductivity and explore the influence of the applied electric field on the film dynamics via numerical simulations. The effects of spatially and temporally varying electric fields and electrode geometry on the formation of waves are also examined. Our results indicate that increasing the intensity of the electric field or decreasing the electrode separation exerts a destabilizing effect, leading to the formation of interfacial waves of larger amplitude. Spatial and temporal variations of the electric field also lead to complex film dynamics which, beyond a certain threshold of the relevant parameter values, give rise to sustained formation of waves over a large fraction of the spinning disc. These results suggest that electric fields have the potential to enhance the degree of wave-induced process intensification.