DIMPLE FORMATION IN THE THIN-FILM BENEATH A DROP OR BUBBLE APPROACHING A PLANE SURFACE

The fourth-order differential equation governing the shape of the dimple as a function of time during the drainage of thin liquid film, derived by Hartland (1969, Chem. Engng Prog. Symp. Ser. No. 91, 65, 82 89), is solved numerically. The required four boundary conditions are obtained from the geometric symmetry of the system and the shape of the drop or bubble. The present theory applies to both large and small films, and predicts the drainage for any axisymmetric initial profile In particular, planar and parabolic initial profiles quickly predict identical development of the dimpled profile as do bell-shaped initial profiles. Similarly, the initial film thickness does not affect the subsequent development of the dimpled film. Comparison with the experimental profiles measured by Hartland (1969) for large drops and by Platikanov (1964, J. phys. Chem, 68, 3619-3624) for air bubbles shows good agreement.