Surface tension and the origin of the circular hydraulic jump in a thin liquid film (1903.11495v3)

Abstract: It was recently claimed by Bhagat et al. (J. Fluid Mech. vol. 851 (2018), R5) 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 {\em 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 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.