(171s) Spontaneous Climbing of Thin Films Due to Drainage-Induced Surfactant Marangoni Effect

Marangoni flows, driven by gradients in surface tension appear in different forms including thermal, solutal, and surfactant Marangoni flows. While numerous factors can influence the Marangoni flows, previous studies show that three main physical features govern their dynamics: adsorption, advection, and diffusion. The interplay of these effects dictates the prevailing dynamics of interfacial transport.

Thin film formation in capillaries is observed in various applications from coating for corrosion protection to biomedical and environmental engineering. Additionally, surfactants are widely employed across diverse fields of industry. However, despite their widespread usage, there is a lack of study on the impact of surfactants on the dynamics of thin films inside capillaries. In this regard, this study investigates the surface tension gradients induced by the drainage of surfactant-laden liquid slugs inside circular capillaries. As the liquid drains, a thin film forms on the tube walls, initiating a Marangoni effect which results in a climbing film against gravity, constrained by both capillary force and gravity. The conditions in which these climbing films occur, as well as the interplay of mechanisms influencing their behavior including diffusion, adsorption, and advection, are examined. Furthermore, the study explores the effects of the surfactant concentration and the liquid slug release height on the climbing film characteristics.

The experimental setup includes previously cleaned glass tubes placed vertically and connected to a vacuum pump. Surfactant-laden (Sodium dodecyl sulfate (SDS)) aqueous Methylene blue solution with different SDS concentrations below the critical micelle concentration (CMC 8 mM) was suctioned inside the capillary tubes at specific heights. A valve was used to control the connection of the capillaries to the vacuum pump. By closing the valve, the suction stops, and the liquid slug inside the tube drains. The thin film formed near the tube walls due to the sudden drainage of the liquid slug imparts a surface tension gradient which results in a self-climbing liquid film induced by Marangoni forces near the capillary tip.

The dynamics of the falling meniscus, draining thin film, and the Marangoni-induced climbing film were recorded by digital single-lens reflex (DSLR) and High-speed (HS) cameras. The interferometry method was utilized for estimating the draining film thickness. The obtained data from the videos were processed using custom-built MATLAB codes.

The results show that at low SDS concentrations, increasing the SDS concentration results in a faster climbing film due to an increased gradient in surface tension. However, past a certain concentration (3 mM), even though the concentration is well below the CMC limit, no climbing film occurs. A simple calculation of the governing time scales shows that at lower SDS concentrations, the advection time scale is significantly smaller than the diffusion and adsorption time scales which signifies an advection-dominant regime. However, for the 3 mM solution, the diffusion time scale becomes the smallest time scale which means the problem is not advection dominant anymore. This shift in the dominant effects causes the fast diffusion of the surfactant particles to cancel any gradient in surface tension caused by the drainage. Moreover, it was observed that by even further increasing the SDS concentration (7 mM) not only no climbing film is observed, but also the high surfactant concentration causes a dewetting effect on the tube walls preventing the drainage thin films from forming.

Comparing the climbing films that occurred at different liquid slug release heights reveals that raising the release height causes an increase in the climbing film velocity which is mainly due to the amplified surface tension gradient caused by a larger draining film. The results for the temporal variations of the climbing film front are non-dimensionalized and compared with the model proposed by Xue et al¹. The results show a good agreement with the model.

The findings of this study aim to elucidate the dynamics of interfacial phenomena in surfactant-laden flows within capillaries, as well as the governing effects on thin films. These results are anticipated to be of interest to designers of devices utilizing such flows, providing insight into the formation of climbing films and how they can be leveraged for practical benefits.

¹ Xue, N., Pack, M.Y. and Stone, H.A., 2020. Marangoni-driven film climbing on a draining pre-wetted film. Journal of Fluid Mechanics, 886, p.A24.