Year: 2026
Type: preprint
Abstract: The fingering instability of thin-film flow is a significant obstacle to producing uniform and stable films in industrial processes. In the framework of lubrication theory, we investigate the linear stability of a gravity-driven thin film with an inclined contact line using numerical and asymptotic methods. The contact-line singularity is regularized by imposing the Greenspan slip model. As demonstrated by the results, although the contact-line inclination slightly enhances long-wavelength instability, it significantly suppresses the growth of spanwise finite-wavelength perturbations. Moreover, the most unstable wavenumber shifts toward the long-wave region as the inclination angle increases. The inclination of the contact line introduces complex eigenvalues, leading to traveling-wave modes, in contrast to the standing-wave modes observed for horizontal contact lines. We also performed asymptotic analysis in the limit of small wavenumbers, confirming the enhanced long-wave instability. The physical mechanisms underlying these stability characteristics are elucidated, revealing that the effects of contact-line inclination come from the eigenmode distortion and additional streamwise flux.
Source: arXiv (Cornell University)
Authors: Gao, Ze-Hui, Li, Er-Qiang, Gao, Peng
Institution: University of Science and Technology of China
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: G1429402685, G3150766826, G6913098797
OpenAlex ID: W7221777386