Figure 4

Initial drainage dynamics immediately after formation of the bubble in a capillary with 2 R = 1.58 mm ( Bo = 0.205 ). The minimum height corresponding to the bottom meniscus transition region (orange) and the mean height (blue) are plotted as a function of time after the bubble is inserted into the capillary. Initially the film is nonuniform, and not cylindrically symmetric, with a gravity biased dimple as can be seen in the interferogram and corresponding height map in (b) for t 0 . Over 2 h later, the dimple has drained on average, and the film has become flatter, as can be seen by the interferogram and the height map shown at t 1 . The film breaks azimuthal symmetry, perhaps due to residual submicron scale dirt on the glass surface remaining after the meticulous cleaning protocol. After over 8 h have elapsed, the film has reached an apparent steady state at a symmetric, uniform thickness of approximately 70 nm as shown in (b) at t 2 . The drainage dynamics are shown on a log-log scale (inset), suggesting that h min ∼ t − 0.5 ; this scaling may be self-similar, as shown by the collapse of the h − x profiles, as shown in the Supplemental Material [35]. The calculated drainage scaling for a 2D bubble h min ∼ t − 4 5 [19] using the experimentally observed initial value (gold) is shown for comparison. A scaling of film thickness to the power 1/2 is expected at the base of the bubble, however [19].