# Thin films flowing down inverted substrates: two dimensional flow - Physics > Fluid Dynamics

Abstract: We consider free surface instabilities of films flowing on invertedsubstrates within the framework of lubrication approximation. We allow for thepresence of fronts and related contact lines, and explore the role which theyplay in instability development. It is found that a contact line, modeled by acommonly used precursor film model, leads to free surface instabilities withoutany additional natural or excited perturbations. A single parameterD=3Ca^{1-3}\cot\alpha$, where$Ca$is the capillary number and$\alpha$isthe inclination angle, is identified as a governing parameter in the problem.This parameter may be interpreted to reflect the combined effect of inclinationangle, film thickness, Reynolds number and the fluid flux. Variation of$D\$leads to change of the wave-like properties of the instabilities, allowing usto observe traveling wave behavior, mixed waves, and the waves resemblingsolitary ones.

Author: Te-sheng Lin, Lou Kondic

Source: https://arxiv.org/