Surfactant stabilization of film rupture

Outward interfacial flow from a thinning region dilutes surfactant there and raises its surface tension. The resulting Marangoni stress pulls fluid back toward the thinning region, opposes further stretching, and slows rupture.

Table of contents
- Strong-surfactant long-wave rupture maximum Surfactant stabilization of film rupture

Strong-surfactant long-wave rupture maximum ( $K_{m}^{2} \sim 1/ (2Γ), s_{m a x} \sim 3 V^{2} / (4 μ γ h_{0}^{5})$ )

 0  0

For strong Marangoni stress and large

Γ = γ h_{0}^{2} / (3 V)

, the unstable band has

K ≪ 1

. Its rate is asymptotically

[3 V / (μ h_{0}^{3})] K^{2} (1 - Γ K^{2}) /3

. Maximizing this quadratic in

K^{2}

gives the displayed finite-wavelength maximum. The growth timescale is not alone a bubble lifetime: initial disturbance size and thickness evolution also enter.