We investigate the stability of a thin two-dimensional liquid film when a uniform electric field is applied in a direction parallel to the initially flat bounding fluid interfaces. We consider the distinct physical effects of surface tension and electrically induced forces for an inviscid, incompressible nonconducting fluid. The film is assumed to be thin enough and the surface forces large enough that gravity can be ignored to leading order. Our aim is to analyze the nonlinear stability of the flow. We achieve this by deriving a set of nonlinear evolution equations for the local film thickness and local horizontal velocity. The equations are valid for waves which are long compared to the average film thickness and for symmetrical interfacial perturbations. The electric field effects enter nonlocally and the resulting system contains a combination of terms which are reminiscent of the Kortweg-de-Vries and the Benjamin-Ono equations. Periodic traveling waves are calculated and their behavior studied as the electric field increases. Classes of multimodal solutions of arbitrarily small period are constructed numerically and it is shown that these are unstable to long wave modulational instabilities. The instabilities are found to lead to film rupture. We present extensive simulations that show that the presence of the electric field causes a nonlinear stabilization of the flow in that it delays singularity (rupture) formation.
All Science Journal Classification (ASJC) codes
- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes