Observation of nonlinear sloshing induced by wetting dynamics

Abstract

Back-and-forth oscillations of a container filled with fluid often result in spilling as the gravest mode gets excited, a well-known phenomenon experienced in everyday life and of particular importance in industry. Our understanding of sloshing is largely restricted to linear response, and existing extensions mostly focus on nonlinear coupling between modes. Linear theory is expected to correctly model the dynamics of the system as long as the amplitude of the mode remains small compared to another length scale, so far unknown. Using a fluid in the vicinity of its critical point, we demonstrate that in perfect wetting this length scale is neither the wavelength nor the capillary length but a much shorter one, the thickness of the boundary layer. Above this crossover length scale, the resonance frequency remains roughly constant while dissipation significantly increases. We also show that dynamical wetting is involved in both linear and nonlinear dissipative processes.

Three-wave interactions among surface gravity waves in a cylindrical container

“…Although the study of sloshing is almost two centuries old [1], it is still extremely challenging to predict the surface deformation of a container undergoing back-and-forth oscillations. The main source of difficulties is nonlinearities, which must be taken into account starting from very small amplitudes: The experiments of Cocciaro et al [2,3] have proved that the first nonlinearity to occur corrects the dissipation, and it has been recently demonstrated that, in perfect wetting, this effect becomes sizable when the sloshing amplitude compares to the thickness of the boundary layers (a fraction of millimetre in everyday life containers) [4]. This explains why, whereas natural frequencies are experimentally found in good agreement with linear sloshing theory [2,3,[5][6][7], damping rates involve larger discrepancies [2,[5][6][7].…”

Axisymmetric gravity-capillary standing waves on the surface of a fluid

“…Axisymmetric surface waves have been routinely studied in the past. Indeed, the behavior of standing waves in a circular basin is of primary interest, in particular to the study of sloshing in cylindrical tanks or harbor oscillations [14,15]. Experiments in large-scale basins were also reported in which converging axisymmetric gravity waves are generated by several wavemakers, driven in unison, surrounding the tank [16][17][18].…”

Slamming Liquid Impact and the Mediating Role of Air

“…The free surface instabilities can be either be intensified or reduced, depending on a number of ambient conditions. Some experimental work on sloshing of a liquid close to its critical point has been done [275]. However, how the impact loads would be affected in such a situation, remains to be experimentally investigated.…”