Evolution of solitary three- dimensional waves on vertically falling liquid films S. Alekseenko, V. Antipin, V. Guzanov, S. Kharlamov, D. Markovich Institute. - презентация

1 Evolution of solitary three- dimensional waves on vertically falling liquid films S. Alekseenko, V. Antipin, V. Guzanov, S. Kharlamov, D. Markovich Institute of Thermophysics Russian Academy of Sciences Siberian Branch

2 Introduction The first theoretical solution: Petviashvili V. I., Tsvelodub O. Yu., Horseshoe-shaped solitons on an inclined viscous liquid film, Dokl. Acad. Nauk. SSSR (in Rusian), V. 238, pp (1978) Problems: slow natural evolution, chaotic interaction. Solution: short impact by working liquid in upper part of waveless region

3 The case 2 gives low level of optical distortion Laser beam makes easy calibration procedure Laser Induced Fluorescence technique

4 Experimental setup Doubled Nd:YaG laser (3 – 10 ms, 7.5 Hz) 532 nm Rhodamine 6G (~0.01%) Low-pass filter (>550 nm) Water-alcohol solution: ρ=931 kg/m 3, ν =2.72·10 -6 m 2 /s, σ=0.03 kg/s 2 Water-glycerol solution: ρ=1070 kg/m 3, ν =2.15·10 -6 m 2 /s, σ=0.065 kg/s 2 Mass of drops: 0.3 – 10 mg, velocity: 0.4 – 1.5 m/s Re=1 – 25 (Re=q/v, where q – volumetric flow rate per unit area, v – kinematic viscosity)

5 Experimental errors Main errors: spatial redistribution of intensity of laser beam from flash to flash and CCD matrix noise (2 – 3% under experimental condition) Additional errors: spatial intensity redistribution under free curvilinear boundary (in presented later cases these errors are sufficiently less then 1%)

6 Preliminary results Fast formation of wave train occurs when excitation energy is low Evolution as one-humped solitary wave occurs for higher excitation energy

7 Evolution. Wave train Water-glycerol solution. Re=12.

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10 Evolution. Solitary wave Water-alcohol solution. Re=25.

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13 Parameters Section is passed via center of main peak in downstream direction mm Dy Velocity C is defined by cross-correlation function

14 Evolution Re=10 water- glycerol solution Two energy of excitation: E < E

15 Evolution Re=5 water- alcohol solution Two energy of excitation: E < E

16 Parameters of stationary solitary waves Water-alcohol solution Re=2.5 C, cm/s X, mm A, mm X, mm Dy, mm X, mm Dx, mm X, mm

17 Parameters of stationary solitary waves Water-glycerol solution Re=10 X, mm A, mm X, mm Dx, mm X, mm Dy, mm X, mm C, cm/s

18 Shape of stationary solitary waves Water-alcohol solution Re=2.2

19 Shape of stationary solitary waves Water-alcohol solution Re=2.5 mm Re ~ 1 KS Petviashvili, Tsvelodub, 1978

20 Shape of stationary solitary waves Water-alcohol solution Re=3.9

21 Shape of stationary solitary waves Water-alcohol solution Re=4.7 mm

22 Shape of stationary solitary waves Water-glycerol solution Re=10

23 Theory mm Demekhin E. A., Kalaydin E. N., Shapar S. M., Shelistov V. S., Stability of three-dimensional solitons in vertically falling liquid films, Dokl. Akad. Nauk, 2007, vol. 413, 2, pp. 193 – 197. Comparison with theory (gKS) Experiment Water-alcohol solution Re=3.9

24 Experiment Comparison with theory (gKS) Theory Water-alcohol solution Re=3.9 mm

25 Comparison with theory (KS) Petviashvili V. I., Tsvelodub O. Yu., Horseshoe-shaped solitons on an inclined viscous liquid film, Dokl. Acad. Nauk. SSSR (in Rusian), V. 238, pp (1978) - undisturbed film thickness - mean flow rate velocity

26 Conclusions Experimental results on evolution of 3-D solitary waves on falling liquid films for Reynolds numbers of film flow Re < 25 are presented. LIF method is applied to measure the shape and instant velocity of the waves. Generation of the wave train as well as evolution in the form of one- humped solitary wave are main scenarios of the wave evolution. Stationary 3-D solitary waves were registered for several experimental conditions. For Re<5 their amplitudes and velocities agree well with theoretically predicted values based both on KS and gKS equation. The shape of registered stationary 3-D waves agree well with the shape of stationary KS wave for Re<3 and with stationary gKS waves for 3