Stick-slip-to-stick transition of liquid oscillations in a U-shaped tube

In this work, we employ a physics-inspired mathematical model based on successive linear eigenmode projections to solve the relaxation dynamics of liquid oscillations in a U-shaped tube and subjected to a phenomenological nonlinear contact line model. Each projection induces a rapid loss of total energy in the motion and contributes to its nonlinear damping. The present approach not only describes well the transient stick-slip dynamics, but it also captures the global stick-slip-to-stick transition and the residual exponentially decaying bulk motion following the arrest of the contact line. This study offers a further contribution to rationalizing the impact of contact angle hysteresis.