Spherical shape of drops before impact, from left to right , and .
Drag coefficient versus Reynolds number. —: Shiller and Nauman correlation. Experiments: ◻: case I, ▵: case II, 엯: case III.
Pictures at every [from (a) to (l)], of the first rebound of a drop .
Example of drop bouncing . 엯: Distance of the drop’s mass center to the wall in radius, value to be read on the left axis. ◇: Velocity divided by drop’s rising velocity , value to be read on the right axis. : physical time, with origin when drop’s deformation is maximum.
Relative velocity decrease at impact versus the Stokes number . 엯: Experimental values, ▴: relation (9).
Shape of drops when leaving the wall after the first bounce, respectively, , and from left to right and every from top to bottom.
Ellipsoidal shape of drops at maximum deformation, respectively, , and .
Deformation of a drop from a sphere to an ellipsoid.
Dimensionless deformation versus Weber number at impact. ◇: Deformation deduced from the ellipsoidal shape. Deformation deduced from the trajectory of the drop: 엯: first bounce, ▵: second bounce, ◻: third bounce, —: .
Dimensionless contact time evolution versus the impact velocity . 엯: First bounce, ▵: second bounce, ◻: third bounce, —: relation (14).
Energy lost during the impact versus the kinetic energy at impact . 엯: First bounce, ▵: second bounce, ◻: third bounce,—: Eq. (15).
Comparison between the dynamical model system with experimental results for . —: Solution of (17), ●: first bounce, ∎: second bounce. (a) Position of the mass center of the drop, (b) velocity of the mass center of the drop.
Comparison between the velocity of the drop given by the dynamical model system. —: Solution of (17), ⋯ solution of (17) with the nonlinear correction (see the text), ●: and ∎: . (a) First bounce, (b) second bounce.
Evolution of the two coefficients of restitution: (filled symbol) versus the drop velocity at impact and (empty symbol) versus the terminal velocity . 엯: First bounce, ▵: second bounce, ◻: third bounce.
Restitution coefficient versus the modified Stokes number . ●: This study (first bounce), +: solid sphere [Joseph et al. (Ref. 1)], 엯: solid sphere [Gondret et al. (Ref. 2)], ▵: solid sphere [Foerster et al. (Ref. 24)], ▾: liquid drop in air [Richard and Quéré (Ref. 9)], ◻: spherical balloon [Richard and Quéré (Ref. 9)], ∎: spherical bubble [Tsao and Koch (Ref. 6)], ▴: ellipsoidal bubble [Tsao and Koch (Ref. 7)], ▯: numerical bubble [Benkenida (Ref. 19)], ◆: this study (first bounce), —: correlation given by relation (22) with , ⋯: with .
Physical properties of the water/toluene system. , , , and being, respectively, the temperature, density, dynamic viscosity, surface tension and the diameter of the drops. The subindex is used for the drop (toluene), properties without subindex refer to the continuous phase (water).
Dimensionless numbers characterizing the water/toluene system. , , , and being, respectively, the Reynolds, Stokes, Weber, Eötvös and capillarity numbers.
Main results concerning the bounce of the drops. is the terminal velocity, is the velocity at impact, is the velocity when the drop leave the wall after the first bounce, , and are the maximum deformation for the first, second and third bounces, , and are the contact time during the first, second and third bounces.
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