An Asymptotic Analysis of a Falling Liquid Film on a Vertical Long Sine-Shaped Wavy Plane

Abstract

The flow of a freely falling liquid film of low Reynolds number down a vertical wavy plate with a small corrugation and a long period is researched theoretically. A model based on perturbation method and power series is presented. A dimensionless stream function is introduced into the Navier-Stokes equations. By perturbation expansion, two sets of equations describing the film flow separately at zeroth and first order are developed. The presented model is solved at leading approximation. Effects of parameters including Reynolds number Re, surface tension number M, nondimensional surface wavenumber λ, and surface amplitude ε on the film surface and on the shear stress at the wall surface are discussed.

Keywords:

• Liquid film
• Wavy plane
• Flow
• Perturbation

ACKNOWLEDGMENTS

The support of Natural Science Foundation of Tianjin, China (Grant No. 07JCYBJC01300) is greatly appreciated.