INSTABILITIES INDUCED BY AN ELECTROSTATIC-FIELD OVER THE FILM FLOW DOWN AN INCLINED PLANE

A study of the instabilities in the interaction of an electrostatic field with a thin liquid film flowing under gravity down an inclined plane is presented. First, the long-wave stability conditions are studied by perturbing the evolution equation of film height about its steady-state solution. Three limits of flow systems are considered, i.e., static state, Reynolds number Re = O(1) and Re = O(1/xi). Here xi(much-less-than 1) is the ratio of the characteristic length scale parallel to the flow to the primary film thickness. Next, the long-wave behavior of the thin film flow is examined with the electrostatic potential of a Gaussian function in the two limits of Reynolds number, i.e., Re = O(1) and Re = O(1/xi). These results are also compared with those from a full-scale explicit calculation. Finally, wave-growth rates are calculated from the Orr-Sommerfeld equation to show the stability to wave number with and without the electric field. The effect of the electric field is to lessen the range of the wave number in which the thin film flow remains stable.