Surface tension and the origin of the circular hydraulic jump in a thin liquid film

It was recently claimed by Bhagat et al. [J. Fluid Mech. 851, R5 (2018)] that the scientific literature on the circular hydraulic jump in a thin liquid film is flawed by improper treatment and severe underestimation of the influence of surface tension. Bhagat et al. use an energy equation with a new surface energy term that is introduced without reference, and they conclude that the location of the hydraulic jump is determined by surface tension alone. We show that this approach is incorrect, and we derive a corrected energy equation. Proper treatment of surface tension in thin film flows is of general interest beyond hydraulic jumps, and we show that the effect of surface tension is fully contained in the Laplace pressure due to the curvature of the surface. Following the same approach as Bhagat et al., i.e., keeping only the first derivative of the surface velocity, the influence of surface tension is, for thin films, much smaller than claimed by them. We further describe the influence of viscosity in thin film flows, and we conclude by discussing the distinction between time-dependent and stationary hydraulic jumps.

Figure 1

Schematic illustration of the circular hydraulic jump appearing when a liquid (blue) impinges in a jet on a horizontal plate (gray). (a) Side view of a cut through the liquid layer in a vertical plane containing the axis of symmetry. The positions of the jump and the expanding liquid front (contact line) are indicated. (b) Top view that shows the finite extent of the circular bottom plate and the irregular shape of the expanding liquid front. Both views show the fixed annular control volume (red) inside the jump region.