Instabilities Induced by an Electrostatic Field over the Film Flow Down an Inclined Plane = Instabilities Induced by an Electrostatic Field over the Film Flow Down an Inclined Plane

다국어 초록 (Multilingual Abstract)

a study of the instabilities in the interactum of an electrostatic field with a thin liquid film flowing under gravity down an inclined plane is presented. First, the long-wave stability conditions arc studied by perturbing the evolution equaticm of film height about its steady-state solution. Three limits of film systems are considered, i.e., static state, Reynolds number Re=O(1) and Re=O(1/ξ). Here ξ($lt;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/ξ). 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 low remains stable.