The F-function approach is a class of two-fluid phenomenological models which has been recently proposed to conceptualize two-phase flows through fractured porous media in connection with petroleum and nuclear engineering. This approach takes into account inertial effects during two-phase flow. It is based on the generalization of the single-phase Forchheimer equation by multiplying the superficial velocity of each fluid by a function F that depends only on the fluid saturation. In this study, we propose to extend the F-function concept to the chemical engineering circle, especially for high-pressure gas-liquid co-current downflow trickle-bed reactors. Reclassification of trickle flow regime is attempted by distinguishing viscous, transitional and inertial regimes. The approach is tested on experimental data and carried out in the pressure range 0.3-5.1 MPa using water/nitrogen, ethanol/nitrogen and ethylene glycol/nitrogen systems. Finally, the F-function concept performance is compared to most popular trickle-bed correlations.