Boundary Value Problems (Jan 2022)

Solvability of a moving contact-line problem with interface formation for an incompressible viscous fluid

  • Yoshiaki Kusaka

DOI
https://doi.org/10.1186/s13661-021-01582-x
Journal volume & issue
Vol. 2022, no. 1
pp. 1 – 33

Abstract

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Abstract We investigate the free-boundary problem of a steadily advancing meniscus in a circular capillary tube. The problem is described using the “interface formation model,” which was originally introduced with the aim of avoiding the singularities that arise when classical hydrodynamics is applied to problems with a moving contact line. We prove the existence of an axially symmetric solution in weighted Hölder spaces for low meniscus speeds.

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