Motion of an Elastic Drop through an Orifice in a Thin Plate

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Abstract

Impingement of drops of water and polymer solutions on a thin plate with a solitary round orifice is studied. The drop diameter before the impingement di coincides with that of the orifice dt and is equal to 3 mm. The drops fell from heights of 5, 10, and 20 mm, their velocities before the impingement amounting to 0.31, 0.44, and 0.63 m/s. The drops flew through the orifice touching slightly its edges. High-speed photography was used to fix different stages of the collision between a drop and the obstacle. It is found that a considerable deceleration of the jet by the orifice can be observable for the impingement parameters considered, down to the complete stopping of the drop flight. The mechanisms of the observable phenomena and the effect of different factors are discussed.

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About the authors

A. O. Rudenko

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences

Author for correspondence.
Email: arudenko@ipmnet.ru
Russian Federation, Moscow

A. N. Rozhkov

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences

Email: rozhkov@ipmnet.ru
Russian Federation, Moscow

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Supplementary files

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2. Fig. 1. Schematic diagram of the experiment.

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3. Fig. 2. Video recordings of the motion of water droplets, PAA-100 and PAA-1k (a-c) through the hole in the plate when a drop falls from a height of 5 mm. The division value of the ruler on the frame is 1 mm. B = πdiGθ2/(4m0) is a quantitative parameter describing the assumed transition to drop collapse [4].

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4. Fig. 3. Video recordings of the motion of water droplets, PAA-100 and PAA-1k (a-c) through the hole when falling from a height of h0 = 10 mm. The value of ruler divisions on the frame is 1 mm.

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5. Fig. 4. Video recordings of the movement of water droplets, PAA-100 and PAA-1k (a-c) through the hole when falling from a height of h0 = 20 mm. The value of ruler divisions on the frame is 1 mm.

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6. Fig. 5. Dependence of jet displacement z on time for different liquids when droplets fall from heights h0 = 5, 10 and 20 mm. 1 - water h0 = 5 mm, 2 - water h0 = 10 mm, 3 - water h0 = 20 mm, 4 - PAA100 h0 = 5 mm, 5 - PAA100 h0 = 10 mm, 6 - PAA100 h0 = 20 mm, 7 - PAA1k h0 = 5 mm, 8 - PAA1k h0 = 10 mm, 9 - PAA1k h0 = 20 mm; The dotted line shows the theoretical ‘unobstructed’ droplet trajectories z = (2gh0)1/2t + gt2/2 for heights h0 = 5, 10 and 20 mm. The horizontal dashed line separates the region of droplet detachment from the plate z > 3 mm and the region of droplet capture by the hole in the plate z < 3 mm.

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7. Fig. 6. Flow regimes as functions of determining parameters. Numbers denote variants: 1 - G = 0, γ = 0, g = 9.81 m/s2, 2 - G = 0, γ = 0.072 N/m, g = 0, 3 - G = 100 Pa, θ = 0.1 s, γ = 0.072 N/m, g = 9.81 m/s2, 4 - G = 100 Pa, θ = 0.1 s, γ = 0, g = 0. Calculations were carried out using the MatLab application package for the case vi = 0.49 m/s, a0 = 3 mm.

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8. Fig. 7. Numerical solutions of equation (3.2) (solid curves) in comparison with experimental data for droplets of different liquids falling from the height h0 = 5 mm, vi = 0.2011 m/s (Fig. 2). 1 - water, G = 0, 2 - PAA100, G = 51 Pa, θ = 0.061s, 3 - PAA1k, G = 146 Pa, θ = 0.031s. The zeros correspond to droplet entrapment by the orifice. The rheological parameters G and q were estimated by selecting the best approximation using the least squares method.

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9. Fig. 8. Numerical solutions of equation (3.2) in comparison with experimental data for droplets of different liquids falling from the height h0 = 10 mm, vi = 0.2736 m/s (Fig. 3). 1 - water, G = 0, 2 - PAA100, G = 71 Pa, θ = 0.021 s, 3 - PAA1k, G = 151 Pa, θ = 0.021 s. Crosses correspond to droplet detachment from the orifice, zeros to droplet entrapment by the orifice. The rheological parameters G and q were estimated by selecting the best approximation using the least squares method.

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10. Fig. 9. Numerical solutions of equation (3.2) versus experimental data for droplets falling from a height of h0 = 20 mm, vi = 0.4931 m/s (Fig. 4). 1 - water, G = 0, 2 - PAA100, G = 91 Pa, θ = 0.011 s, 3 - PAA1k, G = 151 Pa, θ = 0.021 s. The crosses correspond to droplet detachment from the hole.

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