Soap Film Drainage Under Tunable Gravity Using a Centrifugal Thin Film Balance

TL;DR

The study investigates soap-film drainage under tunable effective gravity using a centrifugal thin-film balance, paired with time-resolved interferometry to map film thickness. It identifies two gravity-dependent drainage regimes and demonstrates that marginal regeneration controls thinning while capillary suction governs the flux, with a universal TFE-to-film thickness ratio of $h_{\rm TFE}/h \approx 0.87$ across conditions. The thinning dynamics scale as $|\mathrm{d}h_{\rm R}/\mathrm{d}t| \propto h_{\rm R}^{5/2}$ and exhibit an $\omega^{3/2}$ dependence, consistent with the flux law and a gravity-modulated meniscus radius $r_{\rm m}$. Overall, the results show the robustness of capillary-driven drainage and marginal regeneration for surface bubbles under extreme gravity and offer insight into how other body forces might influence drainage processes.

Abstract

Surface bubbles are an abundant source of aerosols, with important implications for climate processes. In this context, we investigate the stability and thinning dynamics of soap films under effective gravity fields. Experiments are performed using a centrifugal thin-film balance capable of generating accelerations from 0.2 up to 100 times standard gravity, combined with thin-film interferometry to obtain time-resolved thickness maps. Across all experimental conditions, the drainage dynamics are shown to be governed by capillary suction and marginal regeneration-a mechanism in which thick regions of the film are continuously replaced by thin film elements (TFEs) formed at the meniscus. We consistently recover a thickness ratio of 0.8 - 0.9 between the TFEs and the adjacent film, in agreement with previous observations under standard gravity. The measured thinning rates also follow the predicted scaling laws. We identified that gravity has three distinct effects: (i) it induces a strong stretching of the initial film, extending well beyond the linear-elastic regime; (ii) it controls the meniscus size, and thereby the amplitude of the capillary suction and the drainage rate; and (iii) it reveals an inertia-to-viscous transition in the motion of TFEs within the film. These results are supported by theoretical modeling and highlight the robustness of marginal regeneration and capillary-driven drainage under extreme gravity conditions.

Figures (7)

• Figure 1: (a) Schematic of the experimental setup. (b) Time sequence showing the evolution of a film initially exhibiting two distinct regions (Regime 1). Thin film elements (TFEs) progressively invade the film—first up to the boundary at radius $r_{\rm b}$ (dashed white line), and eventually to the center once $r_{\rm b} = 0$. Note that the central region remains unchanged in thickness but is gradually eroded over time until it vanishes at $r_{\rm b}=0$. The final panel shows the formation and opening of a common black film. The inward migration of TFEs is indicated by wavy magenta arrows. (c) Magnified view of the white dashed rectangular area in (b), highlighting the nucleation of TFEs along the edge and their inward migration. $\ell_{\rm TFE}$ denotes the TFE diameter.
• Figure 2: Two drainage Regimes. Regime 1: (a) Typical image and (b) space–time diagram constructed along a radius. Isothickness fringes are tracked using color-coded markers that correspond to film thickness. The dashed line indicates $r_{\rm b}(t)$, separating the central smooth region ($0 < r < r_{\rm b}$) from the peripheral zone containing TFEs ($r_{\rm b} < r < R$). After a characteristic time $t^{\star}$, the central region vanishes and TFEs invade the entire film. Regime 2: (c) Typical image and (d) space–time diagram showing a single region fully populated by TFEs. (e) Regime diagram as a function of $\tilde{g}$ and $\eta$. symbols correspond to Regime 1, $\blacktriangle$ to Regime 2, and $\blacklozenge$ to undetermined cases.
• Figure 3: (a) Initial thickness profiles for various rotation speeds at constant viscosity. Inset: corresponding interface elasticity $\tilde{E}(r)$ inferred from the same dataset. (b) Initial thickness profiles for various viscosities at constant rotation speed. Inset: corresponding interface elasticity $\tilde{E}(r)$ inferred from the same dataset.
• Figure 4: Thickness profiles for the experiment shown in Fig. \ref{['fig:setup']}. (a) Profiles at different times with min and max fringe intensities. Circles denote the central region, which maintains a steady thickness (mean $\pm$ standard deviation over time), while squares correspond to the peripheral region. Dashed lines are guides to the eye. (b) Temporal evolution of $h_{\rm R}(t)$, $h_{\rm 0}(t)$, and $h_{\rm b}(t)$ on a log–log scale. Data are shown for every other interference fringe for clarity. The time $t^\star$ marks the full erosion of the central zone, defined by $h_{\rm b}(t^\star)=h_{\rm 0}(t^\star)$. (c) $h_{\rm b}(t)$ as a function of $h_{\rm R}(t)$, with open and closed symbols corresponding to times before and after $t^\star$, respectively. The dashed line shows a proportionality of 0.87.
• Figure 5: (a) $h_{\rm b}$ as a function of $h_{\rm R}$ for various times and rotation speeds, showing an initial deviation from proportionality at the highest rotation speeds. The dashed line indicates a proportional relationship with a coefficient of 0.87. (b) Deviation diagram as a function of $\tilde{g}$ and $\eta$. symbols correspond to cases with no deviation from proportionality, $\blacktriangle$ to cases with deviation, and $\blacklozenge$ to undetermined cases.