singular behaviors in drop impacts · formation of intense jets, bubble entrapments outline. ......

Singular behaviors in drop impacts

Christophe JosserandInst. D’Alembert, CNRS-UPMC,

Paris-France

Outline

Drop impacts dynamics form or stand numerous different singularities

Outline

Drop impacts dynamics form or stand numerous different singularities

Formation of intense jets, bubble entrapments

Outline

Drop impacts dynamics form or stand numerous different singularities

Formation of intense jets, bubble entrapments

pressure field produced by the impact

Outline

Drop impacts dynamics form or stand numerous different singularities

Formation of intense jets, bubble entrapments

pressure field produced by the impact

singular boundary layers

Outline

Impact on hydrophobic surface

Bartolo, Josserand and Bonn, PRL 96, 124501 (2006)

(a)

(b)

Bubble collapseDuchemin, Popinet, Josserand and Zaleski, POF 14, 3000-3008 (2002)

Pressure field: numerical simulation

Pressure field at short time?

Self-similar structure can be identified

Pressure impact theory

Pressure decreases like 1/Sqrt(t)

Parabolic profile near the center

Pressure impact decreases dramatically for large time as expected by the theory

Film thin equation in cylindrical geometry

Pressure field near the bottom

deviates the velocity field from vertical to horizontal directions

self-similar zone of deviation with intersection radius

P(r, t)ρU2

0=

R0√2R0U0t! r2

Pressure peak near the edge --> boundary layer?

Impact on thin liquid film

Splahs-spreading transition: Influence of the viscosity

We!

Re

Splahs-spreading transition: Influence of the viscosity

We!

Re

Viscous boundary layer near the edge

high pressure peak and vorticity creation

balance between ejection of liquid through the thin liquid sheet and capillary retraction

jet velocity scales like squareroot of the Reynolds number

S.T. Thoroddsen, JFM 451, 373 (2002)