Antibubble Dynamics: The Drainage of an Air Film with Viscous Interfaces

An antibubble is a spherical air film that is immersed in a surfactant mixture and drains under the action of hydrostatic pressure. A dynamical model of this film is proposed that accounts for the surface shear viscosity effects in the case of purely viscous interfaces, which applies for surfactants whose adsorption rate is much larger than advection rate and at a concentration much above the critical micelle concentration. Our model shows that the lifetime of the antibubbles in this case increases with surface shear viscosity, denoted $\epsilon$, whose value is measured independently, all in agreement with experimental measurements. We also found that the critical thickness, $h_c$, at film rupture due to van der Waals interactions slightly depends on the surface shear viscosity, namely $h_c\propto {\epsilon }^{1/6}$.

Figure 1

Picture and sketch of the antibubble with $R\sim 1\mathrm{cm}$, $h\sim 1\mu \mathrm{m}$ (the large black stripe is due to total reflection).

Figure 2

Details of the flow in the air film with nearly parallel interfaces, the thickness $h$ increasing with $\theta$ due to drainage.

Figure 3

Time evolution of the antibubble film thickness with no-slip (${\overline{u}}_s=0$) and the first rupture scenario (RS1).

Figure 4

Antibubble lifetime versus the surface shear viscosity for the two rupture scenarios. The dotted line corresponds to Eq. (5).

Figure 5

Time evolution of the minimum film thickness for various surface shear viscosities, in the case of the RS2. The thick-dotted line separates the drainage period from the “instantaneous” rupture event. The numbers correspond to the slopes of the power-law behaviors.

Figure 6

Measurement of surface shear viscosity for varying shear rate $\dot{\gamma }$: (●) $\mathrm{CAPB}+\mathrm{SLES}+\mathrm{MAC}$, (▪) $\mathrm{CAPB}+\mathrm{SLES}$. The dotted and dashed lines are fits using the Cross model and where ${\epsilon }_0$ is the value of the Newtonian plateau as $\dot{\gamma }\to 0$.