Stick-slip to stick transition induced by contact angle hysteresis in U-shaped tubes: a projection method
Date:
A. Bongarzone (speaker) and F. Gallaire
The role of wetting properties in the damping of liquid oscillations is a long-standing problem in hydrodynamics. A series of lab-scale experiments have revealed that the damping of liquid natural oscillations varies nonlinearly with the oscillations amplitude, indicating a dependence on the contact line behaviour and hence on the solid substrate material. This effect has been attributed to a source of dissipation localized near the sliding triple line, which may exhibit a complex hysteretic behaviour due to solid-like wall friction. Consistently with previous observations, Dollet et al. (2020) have confirmed that contact angle hysteresis can explain and qualify this wall friction, responsible for the contact line finite-time arrest. In this work, assuming an experimentally inspired phenomenological contact line behaviour, we apply to U-shaped tubes the projection method formalized in Bongarzone et al. (2021) for idealized two-dimensional viscous capillary-gravity waves. This approach is based on successive linear eigenmode projections for solving numerically the nonlinear dynamics in the limit of small oscillation amplitudes. Each projection, corresponding to each stick-slip transition, eventually induces a rapid loss of total energy in the liquid motion and contributes to its nonlinear damping. In order to retain the viscous dissipation occurring at the sidewall boundary layers, the original formulation is amended with a wall-slip condition with a spatially variable slip length. Quantitative comparisons with experiments1 show that the projection method correctly captures the final stick-slip to stick transition, as well as the secondary fluid bulk motion following the associated arrest of the contact line, overlooked by previous asymptotic analyses.