Fingering instability of thin films with an inclined contact line
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.
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BibTeX
@misc{gao2026fingering,
title = {{Fingering instability of thin films with an inclined contact line}},
author = {Ze-Hui Gao and Er-Qiang Li and Peng Gao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16380},
eprint = {2610.16380},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16380},
}
RIS
TY - UNPB
TI - Fingering instability of thin films with an inclined contact line
AU - Ze-Hui Gao
AU - Er-Qiang Li
AU - Peng Gao
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16380
UR - https://arxiv.org/abs/2610.16380
AB - 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.
ER -