Modification of Taylor's law based on the Reynolds number effects on liquid film thickness

This study presents a new scaling law for evaluating the liquid film thickness of a Taylor bubble in capillary tubes. Numerous studies have investigated the estimation of the liquid film thickness and have expressed this thickness as a polynomial function of the capillary and Reynolds numbers. Herein, we assumed Reynolds number effects on enhancing viscous forces within the liquid film for accurately reproducing the film thickness compared with the conventional correlation and providing a clearer physical meaning. Moreover, the detailed inertial effects on Taylor bubbles were explored through numerical simulations. The liquid film thickness was calculated under turbulent conditions, revealing a correlation between the film thickness and turbulent viscosity. Correcting the capillary number with the turbulent viscosity unified the effects of inertia, viscosity, and surface tension on liquid film thickness. After modifying Taylor's law using the corrected capillary number and expressing the turbulent viscosity as a power function of Reynolds number, the inertia-induced increase in liquid film thickness was found to be represented by the original form of Taylor's law. The results of the modified model well matched the experimental results. Finally, the limiting effect of the velocity boundary layer on the liquid film thickness was investigated. Based on Prandtl's law, the transition Reynolds number at which the film thickness decreases was shown to be a function of the capillary number.