Marangoni flow is the motion induced by a surface tension gradient along a fluid–fluid interface. In this study, we report a Marangoni flow generated when a bath of surfactant contacts a pre-wetted film of deionized water on a vertical substrate. The thickness profile of the pre-wetted film is set by gravitational drainage and so varies with the drainage time. The surface tension is lower in the bath due to the surfactant, and thus a liquid film climbs upwards along the vertical substrate due to the surface tension difference. Particle tracking velocimetry is performed to measure the dynamics in the film, where the mean fluid velocity reverses direction as the draining film encounters the front of the climbing film. The effect of the surfactant concentration and the pre-wetted film thickness on the film climbing is then studied. High-speed interferometry is used to measure the front position of the climbing film and the film thickness profile. As a result, higher surfactant concentration induces a faster and thicker climbing film. Also, for high surfactant concentrations, where Marangoni driving dominates, increasing the film thickness increases the rise speed of the climbing front, since viscous resistance is less important. In contrast, for low surfactant concentrations, where Marangoni driving balances gravitational drainage, increasing the film thickness decreases the rise speed of the climbing front while enhancing gravitational drainage. We rationalize these observations by utilizing a dimensionless parameter that compares the magnitudes of the Marangoni stress and gravitational drainage. A model is established to analyse the climbing front, either in the Marangoni-driving-dominated region or in the Marangoni-balanced drainage region. Our work highlights the effects of the gravitational drainage on the Marangoni flow, both by setting the thickness of a pre-wetted film and by resisting the film climbing.
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Instability and symmetry breaking in binary evaporating thin films over a solid spherical dome
We examine the axisymmetric and non-axisymmetric flows of thin fluid films over a spherical glass dome. A thin film is formed by raising a submerged dome through a silicone oil mixture composed of a volatile, low surface tension species (1 cSt, solvent) and a non-volatile species at a higher surface tension (5 cSt, initial solute volume fraction $\phi _0$ ). Evaporation of the 1 cSt silicone oil establishes a concentration gradient and, thus, a surface tension gradient that drives a Marangoni flow that leads to the formation of an initially axisymmetric mound. Experimentally, when $\phi _0 \leqslant 0.3\,\%$ , the mound grows axisymmetrically for long times (Rodríguez-Hakim et al. , Phys. Rev. Fluids , vol. 4, 2019, pp. 1–22), whereas when $\phi _0 \geqslant 0.35\,\%$ , the mound discharges in a preferred direction, thereby breaking symmetry. Using lubrication theory and numerical solutions, we demonstrate that, under the right conditions, external disturbances can cause an imbalance between the Marangoni flow and the capillary flow, leading to symmetry breaking. In both experiments and simulations, we observe that (i) the apparent, most amplified disturbance has an azimuthal wavenumber of unity, and (ii) an enhanced Marangoni driving force (larger $\phi _0$ ) leads to an earlier onset of the instability. The linear stability analysis shows that capillarity and diffusion stabilize the system, while Marangoni driving forces contribute to the growth in the disturbances.
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- Award ID(s):
- 1952635
- NSF-PAR ID:
- 10223057
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 915
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2021.136
