Evolution mechanism of solitary waves on the inviscid film flow under an electrostatic field

To investigate the nonlinear wave motion on an inviscid film flow under an electrostatic field a modified Korteweg-de Vries (KdV) equation has been derived by employing the long-wave and shallow-water approximations. A uniform or non-uniform electric potential on a charged electrode foil at some distance above the film is applied in the direction normal to the undisturbed free surface. The modified KdV equation is numerically solved with spatially periodic boundary conditions by using Crank-Nicholson scheme. Consequently, the uniform electrostatic field hinders the solitons from moving downward. In the non-uniform case where the electrostatic potential slowly varies with space, the wave energy changing rate has a maximum negative value as a new solitary wave is about to produce from the effective region of electrostatic field, and already-existed external solitons are getting accelerated if they pass through this region.