Three-dimensional mathematical model of the liquid film downflow on a vertical surface

Film downflow from captured liquid without wave formation and its destruction is one of the most important aspects in the development of separation equipment. Consequently, it is necessary to create well-organized liquid draining in areas of captured liquid. Thus, the proposed 3D mathematical model of film downflow allows for the determination of the hydrodynamic parameters of the liquid film flow and the interfacial surface. As a result, it was discovered that the interfacial surface depends on the proposed dimensionless criterion, which includes internal friction stress, channel length, and fluid density. Additionally, equations for determining the averaged film thickness, the averaged velocity vectors over the film thickness, the longitudinal and vertical velocity components, and the initial angle of streamline deviation from the vertical axis were analytically obtained.