How Topological Rearrangements and Liquid Fraction Control Liquid Foam Stability

The stability of foam is investigated experimentally through coalescence events. Instability (coalescence) occurs when the system is submitted to external perturbations (T1) and when the liquid amount in the film network is below a critical value. Microscopically, transient thick films are observed during film rearrangements. Film rupture, with coalescence and eventual collapse of the foam, occurs when the available local liquid amount is too small for transient films to be formed. Similar experiments and results are shown in the two-bubble case.

Figure 1

(1) Image sequence showing one T1 event in a 3D foam made of TTAB solution (A) at a liquid fraction $ϵ>{ϵ}_{\mathrm{crit}}$. Images (a), (b) and (c) correspond to situations, respectively, before, just after, and long after bubble rearrangement. Color pattern in (b) reveals the thickening of the new film formed by T1. The size of images is approximately 1.5 mm. (2) Scheme of the corresponding T1 rearrangement.

Figure 2

Diagram showing stability behavior of foam bubbles during T1 events as a function of foam liquid fraction ($ϵ$) and bubble radius $R$: unstable events (filled squares), stable events (open squares). Liquid fraction range for transition between stable and unstable events is marked by the grey area and the critical liquid fraction is defined as the median value in this range (dashed line).

Figure 3

(1) Picture of two bubbles before contact (a), in contact (b), after a coalescence (c). Scalebar is 3 mm. (2) Scheme of the Plateau border linking bubbles in the two-bubble cluster encircled in (1b).

Figure 4

Radius of curvature of the Plateau border $r$ linking two bubbles versus the number of contact $N$ in a semilog plot. The solution used is solution D. Bubble radius is 3 mm. The line fits $r=1.75e^{-0.39N}$. Inset: bubbles 1 ms after separation. ($R=2.3\mathrm{mm}$).

Figure 5

Radius of curvature of the Plateau border $r$ at the last contact before coalescence versus bubble radius $R$. Solution A (●), solution B (□), solution C (×), solution D (△). The red lines correspond to linear fit $r=pR$ with $p=0.056$ (●) and $p=0.019$ (□).