Electrohydrodynamic Ridge Instability of a Thin Film Flowing Down an Inclined Plate

Abstract

In the flow of a thin liquid film, ridge-type instability occurs in a wide variety of engineering systems. These are instability waves whose crests are parallel to the flow direction. Ridges have also been observed when a flowing film is stressed by an electric field applied normal to the interface. It is shown that in this case also the instability is essentially of a hydrodynamic nature and an analysis is presented explaining when and why ridges occur. In the analysis, the three-dimensional Orr-Sommerfeld equation is solved by the method of successive approximations in terms of small Reynolds numbers. The theory for ridge instability further takes into account the finite electrical conductivity of the liquid film, showing the limit of validity of the simplified theories in the literature for perfectly conducting interface and ideally polarized interface. Experimental results are presented supporting the theory.