Onset of solitary wave in a high Reynolds number falling film under an electrostatic field

Document Type

Conference Proceeding

Publication Date

12-1-2007

Abstract

The stability of solitary wave in a high Reynolds number falling film has been investigated with the effect of an electrostatic field. The evolving finite-amplitude surface wave is described by dimensionless partial differential equation based on Karman-Polhausen integral boundary layer theory. This evolution equation contains Reynolds number (Re) of order ξ-1, Capillary number (Ca) of order ξ-2 which measures the surface tension, and dimensionless constant of electric strength (K) of order unity. Froude number (Fr) which is implicitly included should have same order of magnitude as that of Reynolds number. Linear stability theory shows the destabilizing effect of an applied electrostatic field on a long wave in the inception region. Far away from the 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 a moving coordinate at the same velocity as the wave. Plugging the new coordinate, z = x - vt in which v is a velocity of a solitary wave, into the evolution equation produces ordinary differential equation describing a stationary wave with respect to z. Following the global and the structural stability theory, the existence of solitary waves has been mathematically approached. 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 momemtum integral and energy integral methods have been compared each other.

Identifier

56349115533 (Scopus)

ISBN

[9780816910229]

Publication Title

Aiche Annual Meeting Conference Proceedings

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