On the origin of the hydraulic jump in a thin liquid film

TL;DR

This paper reveals that thin-film hydraulic jumps are primarily caused by surface tension and viscous forces rather than gravity, challenging long-held beliefs and highlighting the role of capillary waves in flow transitions.

Contribution

The study demonstrates that surface tension and viscous forces, not gravity, induce thin-film hydraulic jumps, introducing a new theoretical framework emphasizing capillary waves as the key mechanism.

Findings

Surface tension and viscous forces balance momentum in thin-film jumps.

Gravity has negligible influence on circular thin-film jumps.

Capillary waves act as gravity waves in flow transition.

Abstract

For more than a century, it has been believed that all hydraulic jumps are created due to gravity. However, we found that thin-film hydraulic jumps are not induced by gravity. This study explores the initiation of thin-film hydraulic jumps. For circular jumps produced by the normal impingement of a jet onto a solid surface, we found that the jump is formed when surface tension and viscous forces balance the momentum in the film and gravity plays no significant role. Experiments show no dependence on the orientation of the surface and a scaling relation balancing viscous forces and surface tension collapses the experimental data. Experiments on thin film planar jumps in a channel also show that the predominant balance is with surface tension, although for the thickness of the films we studied gravity also played a role in the jump formation. A theoretical analysis shows that the downstream transport of surface tension energy is the previously neglected, critical ingredient in these flows and that capillary waves play the role of gravity waves in a traditional jump in demarcating the transition from the supercritical to subcritical flow associated with these jumps.