The rapidly advancing contact line Part-1: Navier slip and microscale inertial effects
Abstract
Curtain coating, in which a moving plate is coated by a falling liquid sheet, sustains rapidly advancing contact lines at large capillary numbers Ca ~ 1. Steady-state solutions exist up to a critical capillary number, beyond which wetting failure occurs through the entrainment of air bubbles. In the steady regime, experiments report an acceleration of the velocity along the fluid-fluid interface as the contact line is approached, down to a few tens of micrometres, and this observation has been interpreted as evidence against the Navier slip model. Here we show that the observed acceleration is compatible with slip models. We perform two-phase Navier--Stokes Volume-of-Fluid simulations with quadtree adaptive mesh refinement use Navier slip and a fixed contact angle. Although the velocity vanishes at the contact line in the contact-line frame, the experimentally accessible microscale region lies outside the slip region. The local Reynolds number based on the distance from the contact line is order unity in this region, and therefore local inertial effects cannot be neglected. The scaled interfacial velocity is well described by an inertially corrected wedge flow solution whose wedge angle can be chosen as the interfacial angle at the inflection point, with agreement improving as the slip length is reduced. Reducing the slip length also recovers a non-monotonic dependence of the critical capillary number on the feed-flow Reynolds number, beyond which wetting failure occurs. At larger scales, a local Young--Laplace arc describes a finite sessile-drop-like region of the outer heel; this region contracts as the heel is suppressed.
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BibTeX
@misc{kulkarni2026rapidly,
title = {{The rapidly advancing contact line Part-1: Navier slip and microscale inertial effects}},
author = {Yash Kulkarni and Tomas Fullana and Stephane Popinet and Stephane Zaleski},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.00303},
eprint = {2605.00303},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.00303},
}
RIS
TY - UNPB
TI - The rapidly advancing contact line Part-1: Navier slip and microscale inertial effects
AU - Yash Kulkarni
AU - Tomas Fullana
AU - Stephane Popinet
AU - Stephane Zaleski
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2605.00303
UR - https://arxiv.org/abs/2605.00303
AB - Curtain coating, in which a moving plate is coated by a falling liquid sheet, sustains rapidly advancing contact lines at large capillary numbers Ca ~ 1. Steady-state solutions exist up to a critical capillary number, beyond which wetting failure occurs through the entrainment of air bubbles. In the steady regime, experiments report an acceleration of the velocity along the fluid-fluid interface as the contact line is approached, down to a few tens of micrometres, and this observation has been interpreted as evidence against the Navier slip model. Here we show that the observed acceleration is compatible with slip models. We perform two-phase Navier--Stokes Volume-of-Fluid simulations with quadtree adaptive mesh refinement use Navier slip and a fixed contact angle. Although the velocity vanishes at the contact line in the contact-line frame, the experimentally accessible microscale region lies outside the slip region. The local Reynolds number based on the distance from the contact line is order unity in this region, and therefore local inertial effects cannot be neglected. The scaled interfacial velocity is well described by an inertially corrected wedge flow solution whose wedge angle can be chosen as the interfacial angle at the inflection point, with agreement improving as the slip length is reduced. Reducing the slip length also recovers a non-monotonic dependence of the critical capillary number on the feed-flow Reynolds number, beyond which wetting failure occurs. At larger scales, a local Young--Laplace arc describes a finite sessile-drop-like region of the outer heel; this region contracts as the heel is suppressed.
ER -