Long-Wave and Integral Boundary Layer Analysis of Falling Film Flow on Walls With Three-Dimensional Periodic Structures

Falling films exhibit very complex wavy patterns, which depend on the properties of the liquid, the Reynolds number, the wall inclination angle, and the distance from the film inlet. The film hydrodynamics governs the heat and mass transfer in the liquid films. Our vision is to control and enhance heat and mass transport by using walls with specific microscale topographies that influence the falling film flow, stability, and wavy pattern. In this work, long-wave theory and integral boundary layer approximation are used for modeling the falling film flow on walls with three-dimensional periodic microstructures. The wall topography is periodic both in the main flow direction and in the transverse direction. Examples of such microstructures are longitudinal grooves with sinusoidal path (or meandering grooves) and herringbone structures. The effects of the Reynolds number, the wall inclination angle, and the longitudinal and transverse periods of the structure on the shape of liquid–gas interface are investigated. It is shown that, as opposed to straight grooves in longitudinal direction, grooves with meandering paths may lead to significant interface deformations.