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

## TL;DR

This paper critically examines the role of surface tension in the circular hydraulic jump in thin liquid films, correcting previous misconceptions and emphasizing the limited influence of surface tension when properly modeled.

## Contribution

It provides a corrected energy equation for thin film flows, clarifies the role of surface tension via Laplace pressure, and discusses the influence of viscosity and jump dynamics.

## Key findings

- Surface tension's effect is smaller than previously claimed when properly modeled.
- The corrected energy equation accounts for surface tension through Laplace pressure.
- Viscosity influences thin film flow behavior and hydraulic jump characteristics.

## 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.