(108g) Solitary Waves in a High Reynolds Number Falling Film Under An Electrostatic Field

The stability problems of solitary waves in a high Reynolds number falling film have been investigated with the effect of an electrostatic field. For this purpose, the evolving finite-amplitude surface wave has been described by the dimensionless partial differential equation based on Karman-Polhausen integral boundary layer theory. This evolution equation contains Reynolds number (Re) of order x^-1. Linear stability theory shows the destabilizing effect of an applied electrostatic field on a long wave in the inception region. Far away from that region the linear stability theory can approximately predict the motion of the surface wave, fully developed solitary waves have been pursued by taking advantage of moving coordinates at the same velocity as the wave. Following the global and the structural stability theory, the existence of solitary waves has been mathematically approached: fixed points in the phase space which means Nusselt film thickness should be found, then the characteristics of the sink and the source of each point has been confirmed by the linearized system near the point. By integrating the ordinary differential equation with Nusselt film boundary conditions, solitary wave with its homoclinic phase portrait in the 3 dimensional phase space have been obtained. From this solution, the existence and the characteristics of pulse-like solitary wave can be acquired either qualitatively or quantitatively. For these works, the momentum integral and energy integral methods have been compared each other.