Modeling of an axisymmetric shape of an equilibrium drop resting on a horizontal plane

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The problem of calculating the equilibrium axisymmetric shape of a liquid drop resting on a non-deformable horizontal plane is formulated. For the first time, an equation for the balance of forces acting on a drop in the vertical direction has been obtained, which completes the formulation of the problem under consideration. A high-precision numerical method for solving the formulated nonlinear problem has been developed. The dependence of the wetting angles of drops on variation of the input data of the problem: the chemical composition of the drop, gas pressure, and the strength of additional weak interaction (for example, van der Waals or electrochemical origin) is studied. For drops of small diameters, the possibility of the existence of two solutions is shown, which correspond to significantly different contact angles: in the first solution, the contact angles are less than 90°, and in the second, they are greater than 90°, reaching values of 160° and more. The existence of two equilibrium forms of a small-diameter drop is confirmed by full-scale experiments. Equilibrium forms of droplets of large diameters can exist only in the presence of an additional weak repulsive force between the liquid and the supporting surface, having an intensity of the order of 10–7…10–5 Pa. In this case, for drops of large diameters, there is only one solution.

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Sobre autores

A. Yankovskii

Khristianovich Institute of Theoretical and Applied Mechanics of the SB RAS

Autor responsável pela correspondência
Email: yankovsky_ap@itam.nsc.ru
Rússia, Novosibirsk

Bibliografia

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2. Fig. 1. Meridional cross-section of an equilibrium axisymmetric droplet resting on a horizontal non-deformable substrate

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3. Fig. 2. The edge point and its vicinity in a drop and substrate (a), only in a drop (b) and only in the substrate (c) with an indication of the system of forces applied to this point

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4. Fig. 3. The shape of the drop meridian and its geometric characteristics

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5. Fig. 4. Meridional cross-section of a drop with a contact angle of less than 90° and the system of forces applied to it

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6. Fig. 5. Profile of a drop with a contact angle greater than 90° (a) and the lower part of this drop after applying the section method (b) indicating the system of forces applied to it

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7. Fig. 6. Dependence of the residual in the force balance equation (2.20) on the magnitude of excess pressure at the top of a water drop: a) for drops with a standard diameter of 1 and 2 mm; b) for drops with a standard diameter of 3 and 3.894 mm.

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8. Fig. 7. Calculated meridional cross-sections of water droplets of different standard diameters: a) first type of solution; b) second type of solution

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9. Fig. 8. Calculated meridional cross-sections of ethyl alcohol droplets of different standard diameters: a) first type of solution; b) second type of solution

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10. Fig. 9. Two equilibrium shapes of water droplets of the same reference diameter, resting on a polycarbonate substrate

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11. Fig. 10. Calculated meridional cross-sections of water droplets with a standard diameter in the presence of additional interaction between the liquid and the substrate

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12. Fig. 11. Calculated meridional cross-sections of water droplets of large standard diameters

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