  The nonlinear decay of oscillations of a liquid column in a U-shaped tube is
investigated within the theoretical framework of the projection method
formalized by Bongarzone et al. (2021) [1]. Starting from the full hydrodynamic
system supplemented by a phenomenological contact line model, this
physics-inspired method uses successive linear eigenmode projections to
simulate the relaxation dynamics of liquid oscillations in the presence of
sliding triple lines. Each projection is shown to eventually induce a rapid
loss of total energy in the liquid motion, thus contributing to its nonlinear
damping. A thorough quantitative comparison with experiments by Dollet et al.
(2020) [2] demonstrates that, in contradistinction with their simplistic
one-degree-of-freedom model, the present approach not only describes well the
transient stick-slip dynamics, but it also correctly captures the global
stick-slip to stick transition, as well as the secondary bulk motion following
the arrest of the contact line, which has been so far overlooked by existing
theoretical analyses. This study offers a further contribution to rationalizing
the impact of contact angle hysteresis and its associated solidlike friction on
the decay of liquid oscillations in the presence of sliding triple lines.
