Planar hydraulic jumps in thin films: a regular solution against experiments

TL;DR

This paper analyzes planar hydraulic jumps in thin films using a full depth-averaged model, demonstrating that surface tension effects are negligible in relevant experimental conditions and providing a methodology for laminar flow analysis.

Contribution

It introduces a regular solution framework for the full depth-averaged thin film model including surface tension effects and assesses their significance in hydraulic jump phenomena.

Findings

Surface tension effects are negligible in relevant parameter ranges.

Regular weak solutions of the full DAM are demonstrated.

Methodology serves as a benchmark for hydrodynamic models.

Abstract

The formation of a planar hydraulic jump has been analysed in the framework of a full depth-averaged thin film model (DAM) with surface tension effects included. We have demonstrated regular weak solutions of the full DAM and analysed surface tension effects. It has been shown that surface tension effects within the parameter range relevant to the recent experiments are expected to be very weak and practically negligible. The developed methodology can be used in the analysis of laminar flow regimes and as a benchmark in developing full scale hydrodynamic models.