Round splashes of a viscous liquid

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The splashes of a highly viscous fluid (glycerol) resulting from its pulsed displacement from a gap between two rapidly approaching disks are studied. It is found that, outside the disks, the splash has the form of a thin film bounded by an annular rim. A physical model of the splash is formulated, and analytical solutions describing its trajectory are given. The calculation results are compared with experimental data. The effects of fluid viscosity, surface tension, and film breakdown are analyzed. It is shown that the key influence on the splash development scenarios is exerted by surface tension of the film connecting the rim to the disks.

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Sobre autores

A. Bazilevskii

Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences

Autor responsável pela correspondência
Email: baz@ipmnet.ru
Rússia, Moscow

A. Rozhkov

Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences

Email: rozhkov@ipmnet.ru
Rússia, Moscow

Bibliografia

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2. Fig. 1. Method (a) and experimental setup (b): 1 – cylindrical guide; 2 – impact disk; 3 – drop; 4 – fixed disk; 5 – video camera; 6 – LED illuminator. The graph in (a) is a calculation using formula (1.1) for r2= 2.5 mm, u0 = 2.1 m/s, h0 = 1 mm and 2 mm.

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3. Fig. 2. Glycerol splashes: (a) – u0=1.4 m/s (H=100 mm), m0=29 mg, (b) – u0=2.1 m/s (H=225 mm), m0=17.6 mg, (c) – u0=2.1 m/s, m0=22 mg. Arrow 1 shows the film, arrow 2 – the disturbance growing on the edge jet. The time elapsed since the impact disk stopped is indicated.

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4. Fig. 3. Diameter of glycerol splashes as a function of time: 1 – u0=1.4 m/s, m0=29 mg, without film destruction; 2 – u0=2.1 m/s, m0=17.6 mg, without film destruction; 3 – u0=2.1 m/s, m0=22 mg, with film destruction. The arrow shows the moment of the beginning of film rupture. Time is counted from the moment of closing of the gap (stopping of the impact disk).

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5. Fig. 4. To the calculation of the pulsed ejection of liquid from the gap.

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6. Fig. 5. Results of calculations using formulas (2.6) and (2.9): (a) – outflow velocity v and total velocity V, (b) – kinetic energy E of the splash as functions of the gap between the disks. Inserts: gap between the disks (a) and excess pressure in the center of the disks (b) as functions of time. Parameters used: µ = 0, 0.1, 1.35 Pa s, u0 = = 2.1 m/s, h0 = 1.5 mm, r2 = 2.5 mm, r1=1 mm, M = 6 g.

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7. Fig. 6. Splash diagram.

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8. Fig. 7. Calculations of splash trajectories: 1 – experiment with glycerol (points, H=100 mm, m0=29 mg) and the corresponding calculation (line for V0=1.43 m/s, m0=29 mg, r0=2.97 mm, µ=1.35 Pa⋅s); 2 – experiment with glycerol (H=225 mm, m0=17.6 mg) and the corresponding calculation (V0=2.07 m/s, m0=17.6 mg, r0=3.3 mm, µ=1.35 Pa⋅s); 3 – calculation of a low-viscosity splash for V0=2.07 m/s, m0=17.6 mg, r0=3.3 mm, µ=0.01 Pa⋅s; 4 – analytical solution of inviscid splash (2.15) for V0=2.07 m/s, m0=17.6 mg, r0=3.3 mm; 5 – calculation of viscous splash without film for V0=2.07 m/s, m0=17.6 mg, r0=3.3 mm, µ=1.35 Pa⋅s.

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9. Fig. 8. The appearance and expansion of holes in the glycerol film (a). Distortion of the splash shape during its collapse with the destruction of the internal film (b) and without its destruction (c). The impact velocity u0=1.4 m/s. The time interval between frames is 0.5 ms (a, b) and 1 ms (c).

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