Laser-induced thermocapillary flows on a flowing soap film

Letter

Laser-induced thermocapillary flows on a flowing soap film

Yu Zhao and Haitao Xu

Phys. Rev. Fluids 9, L022001 – Published 8 February 2024

Abstract

For a flowing soap film with added surfactants, theoretically there exists symmetric elastic waves due to the elasticity of the soap film that originates from the surface tension change with the film surface area change. However, the symmetric elastic waves remain elusive from experimental observations due to the lack of approaches to stimulate such waves. Here, we propose a focused laser heating method to study the properties of liquid films under symmetric disturbances. The thermocapillary flows caused by the laser-induced Marangoni effect lead to symmetric disturbances in the film thickness without causing antisymmetric disturbances in the film shape. Thus, on flowing soap films with low surfactant concentrations, i.e., with appreciable elasticities, the laser-induced disturbances in the film thickness are propagated by the symmetric elastic waves, and the envelope of the wave fronts forms a shock wave starting from the laser heating point. Interestingly, on flowing soap films with high surfactant concentrations, i.e., vanishingly small elasticities, the laser-induced disturbances in the film thickness remain unchanged and flow with the film without propagating, similar to “laser engraving” on free liquid films.

Received 18 September 2023
Accepted 16 January 2024

DOI:https://doi.org/10.1103/PhysRevFluids.9.L022001

Physics Subject Headings (PhySH)

Capillary waves Elastic waves Instability of free-surface flows Interfacial flows Thin fluid films Waves and free surface flows

Fluid Dynamics

Authors & Affiliations

Yu Zhao and Haitao Xu ^*

Center for Combustion Energy and School of Aerospace Engineering, Tsinghua University, Beijing 100084, China

^*hxu@tsinghua.edu.cn

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Issue

Vol. 9, Iss. 2 — February 2024

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Images

Figure 1
(a) Schematics of waves on liquid films: (i) antisymmetric Taylor waves, (ii) symmetric Taylor waves, and (iii) symmetric elastic waves. (b) Sketch of the gravity-driven flowing soap film setup. The soap-film flow was confined by two nylon wires held by weights and four hooks. The peristaltic pump circulated the soap solution and set its volume flow rate. (c) Top view of the optical setup of the interferometry imaging (left) and an example interference image (right) of the undisturbed high-concentration ( $c = 2 %$ ) flowing soap film. (d) Schematics of the optical setup of the Schlieren imaging and an example Schlieren image (right) taken simultaneously with the interference image shown in (c).
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Figure 2
(a) Interference (left) and Schlieren (right) images of the soap film shown in Fig. 1 perturbed by laser heating at a pulsing frequency of $f_{laser} = 3500 Hz$ . (b) Interference (left) and Schlieren (right) images of the same soap film when the laser beam was vibrating horizontally at 115 Hz. (c) A sketch showing how the flowing soap film records the motion of the laser focusing point. (d) Interference (left) and Schlieren (right) images of the von Kármán vortex street behind a rod inserted in the soap film, on which dots printed by a stationary pulsed laser formed a streak line in this complex 2D flow.
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Figure 3
Schlieren images of shock waves stimulated by pulsed laser heating with a duty cyle of 50% and an average power of $P_{ave} = 3.38 W$ on a flowing soap film with a low concentration of detergent ( $c = 0.057 %$ ). (a) For laser pulsing frequencies in the range $100 Hz < f_{laser} < 10 000 Hz$ , shock waves formed and their Mach angles were measured to be $α = 26^{\circ}$ , independent of $f_{laser}$ . (b) The growth process (within $4 ms$ ) of the shock wave stimulated by the laser heating at the pulse frequency $4000 Hz$ .
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Figure 4
Effects of detergent concentration on the behavior of flowing soap films. (a) Schlieren images of the soap films with $c = 0.042 %$ , $0.057 %$ , and $0.078 %$ , respectively, at the same flow rate of $Q = 35 ml / \min$ and the same laser pulsing frequency of $f_{laser} = 4000 Hz$ with a duty cyle of 50% and an average laser power of $P_{ave} = 3.38 W$ . (b) Variations of the surface tension $σ$ and film elasticity $E$ with detergent concentrations $c$ . The surface tension data (purple triangles and red circles) are measured by Wan et al. [39]. The film elasticities (green symbols) are calculated from the measured Mach angles, together with the result from the semiempirical formula $E = - 0.25 d σ / d (ln c)$ (green curve). The inset shows the Schlieren image of the comparative experiment, in which a rod was inserted in the soap film with a detergent concentration $c = 0.057 %$ and at the same time a laser heating with $f_{laser} = 5000 Hz$ was applied on the soap film at the same height as the rod.
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